# tracking¶

Tracking objects

 Streamlines alias of ArraySequence bench Run benchmarks for module using nose. test Run tests for module using nose.

## Module: tracking._utils¶

 warn Issue a warning, or maybe ignore it or raise an exception.

## Module: tracking.benchmarks.bench_streamline¶

Benchmarks for functions related to streamline

Run all benchmarks with:

import dipy.tracking as dipytracking
dipytracking.bench()


If you have doctests enabled by default in nose (with a noserc file or environment variable), and you have a numpy version <= 1.6.1, this will also run the doctests, let’s hope they pass.

Run this benchmark with:

nosetests -s –match ‘(?:^|[b_.//-])[Bb]ench’ bench_streamline.py
 Streamlines alias of ArraySequence assert_array_almost_equal(x, y[, decimal, ...]) Raises an AssertionError if two objects are not equal up to desired precision. assert_array_equal(x, y[, err_msg, verbose]) Raises an AssertionError if two array_like objects are not equal. bench_compress_streamlines() bench_length() bench_set_number_of_points() compress_streamlines Compress streamlines by linearization as in [Presseau15]. compress_streamlines_python(streamline[, ...]) Python version of the FiberCompression found on https://github.com/scilus/FiberCompression. generate_streamlines(nb_streamlines, ...) get_data([name]) provides filenames of some test datasets or other useful parametrisations length Euclidean length of streamlines length_python(xyz[, along]) measure(code_str[, times, label]) Return elapsed time for executing code in the namespace of the caller. set_number_of_points Change the number of points of streamlines set_number_of_points_python(xyz[, n_pols]) setup()

## Module: tracking.eudx¶

EuDX(a, ind, seeds, odf_vertices[, a_low, ...]) Euler Delta Crossings
eudx_both_directions
get_sphere([name]) provide triangulated spheres

## Module: tracking.learning¶

Learning algorithms for tractography

 detect_corresponding_tracks(indices, ...) Detect corresponding tracks from list tracks1 to list tracks2 detect_corresponding_tracks_plus(indices, ...) Detect corresponding tracks from 1 to 2 where tracks1 & tracks2 are

## Module: tracking.life¶

This is an implementation of the Linear Fascicle Evaluation (LiFE) algorithm described in:

Pestilli, F., Yeatman, J, Rokem, A. Kay, K. and Wandell B.A. (2014). Validation and statistical inference in living connectomes. Nature Methods 11: 1058-1063. doi:10.1038/nmeth.3098

 FiberFit(fiber_model, life_matrix, ...) A fit of the LiFE model to diffusion data FiberModel(gtab) A class for representing and solving predictive models based on tractography solutions. LifeSignalMaker(gtab[, evals, sphere]) A class for generating signals from streamlines in an efficient and speedy manner. ReconstFit(model, data) Abstract class which holds the fit result of ReconstModel ReconstModel(gtab) Abstract class for signal reconstruction models range((stop) -> range object) range(start, stop[, step]) -> range object grad_tensor(grad, evals) Calculate the 3 by 3 tensor for a given spatial gradient, given a canonical gradient(f) Return the gradient of an N-dimensional array. setup_test() Set numpy print options to “legacy” for new versions of numpy streamline_gradients(streamline) Calculate the gradients of the streamline along the spatial dimension streamline_signal(streamline, gtab[, evals]) The signal from a single streamline estimate along each of its nodes. streamline_tensors(streamline[, evals]) The tensors generated by this fiber. transform_streamlines(streamlines, mat) Apply affine transformation to streamlines unique_rows(in_array[, dtype]) This (quickly) finds the unique rows in an array voxel2streamline(streamline[, transformed, ...]) Maps voxels to streamlines and streamlines to voxels, for setting up

## Module: tracking.local¶

 ActTissueClassifier Anatomically-Constrained Tractography (ACT) stopping criteria from [R480]. BinaryTissueClassifier cdef: CmcTissueClassifier Continuous map criterion (CMC) stopping criteria from [R481]. ConstrainedTissueClassifier Abstract class that takes as input included and excluded tissue maps. DirectionGetter Methods LocalTracking(direction_getter, ...[, ...]) ParticleFilteringTracking(direction_getter, ...) ThresholdTissueClassifier # Declarations from tissue_classifier.pxd bellow TissueClassifier Methods

## Module: tracking.local.localtracking¶

 Bunch(**kwds) ConstrainedTissueClassifier Abstract class that takes as input included and excluded tissue maps. LocalTracking(direction_getter, ...[, ...]) ParticleFilteringTracking(direction_getter, ...) local_tracker Tracks one direction from a seed. pft_tracker Tracks one direction from a seed using the particle filtering algorithm.

## Module: tracking.metrics¶

Metrics for tracks, where tracks are arrays of points

xrange alias of range
arbitrarypoint(xyz, distance) Select an arbitrary point along distance on the track (curve)
bytes(xyz) Size of track in bytes.
center_of_mass(xyz) Center of mass of streamline
downsample(xyz[, n_pols]) downsample for a specific number of points along the curve/track
endpoint(xyz)
frenet_serret(xyz) Frenet-Serret Space Curve Invariants
generate_combinations(items, n) Combine sets of size n from items
inside_sphere(xyz, center, radius) If any point of the track is inside a sphere of a specified center and radius return True otherwise False.
inside_sphere_points(xyz, center, radius) If a track intersects with a sphere of a specified center and radius return the points that are inside the sphere otherwise False.
intersect_sphere(xyz, center, radius) If any segment of the track is intersecting with a sphere of
length(xyz[, along]) Euclidean length of track line
longest_track_bundle(bundle[, sort]) Return longest track or length sorted track indices in bundle
magn(xyz[, n]) magnitude of vector
mean_curvature(xyz) Calculates the mean curvature of a curve
mean_orientation(xyz) Calculates the mean orientation of a curve
midpoint(xyz) Midpoint of track
midpoint2point(xyz, p) Calculate distance from midpoint of a curve to arbitrary point p
principal_components(xyz) We use PCA to calculate the 3 principal directions for a track
setup_test() Set numpy print options to “legacy” for new versions of numpy
splev(x, tck[, der, ext]) Evaluate a B-spline or its derivatives.
spline(xyz[, s, k, nest]) Generate B-splines as documented in
splprep(x[, w, u, ub, ue, k, task, s, t, ...]) Find the B-spline representation of an N-dimensional curve.
startpoint(xyz) First point of the track
winding(xyz) Total turning angle projected.

## Module: tracking.streamline¶

 ArraySequence([iterable, buffer_size]) Sequence of ndarrays having variable first dimension sizes. LooseVersion([vstring]) Version numbering for anarchists and software realists. Streamlines(*args, **kwargs) Attributes apply_affine(aff, pts) Apply affine matrix aff to points pts cdist(XA, XB[, metric, p, V, VI, w]) Computes distance between each pair of the two collections of inputs. center_streamlines(streamlines) Move streamlines to the origin compress_streamlines Compress streamlines by linearization as in [Presseau15]. deepcopy(x[, memo, _nil]) Deep copy operation on arbitrary Python objects. deform_streamlines(streamlines, ...) Apply deformation field to streamlines dist_to_corner(affine) Calculate the maximal distance from the center to a corner of a voxel, length Euclidean length of streamlines mul mul(a, b) – Same as a * b. nbytes(streamlines) orient_by_rois(streamlines, roi1, roi2[, ...]) Orient a set of streamlines according to a pair of ROIs reduce((function, sequence[, initial]) -> value) Apply a function of two arguments cumulatively to the items of a sequence, from left to right, so as to reduce the sequence to a single value. relist_streamlines(points, offsets) Given a representation of a set of streamlines as a large array and an offsets array return the streamlines as a list of shorter arrays. select_by_rois(streamlines, rois, include[, ...]) Select streamlines based on logical relations with several regions of interest (ROIs). select_random_set_of_streamlines(...) Select a random set of streamlines set_number_of_points Change the number of points of streamlines setup_test() Set numpy print options to “legacy” for new versions of numpy streamline_near_roi(streamline, roi_coords, tol) Is a streamline near an ROI. transform_streamlines(streamlines, mat) Apply affine transformation to streamlines unlist_streamlines(streamlines) Return the streamlines not as a list but as an array and an offset values_from_volume(data, streamlines[, affine]) Extract values of a scalar/vector along each streamline from a volume. warn Issue a warning, or maybe ignore it or raise an exception.

## Module: tracking.utils¶

Various tools related to creating and working with streamlines

This module provides tools for targeting streamlines using ROIs, for making connectivity matrices from whole brain fiber tracking and some other tools that allow streamlines to interact with image data.

### Important Note:¶

Dipy uses affine matrices to represent the relationship between streamline points, which are defined as points in a continuous 3d space, and image voxels, which are typically arranged in a discrete 3d grid. Dipy uses a convention similar to nifti files to interpret these affine matrices. This convention is that the point at the center of voxel [i, j, k] is represented by the point [x, y, z] where [x, y, z, 1] = affine * [i, j, k, 1]. Also when the phrase “voxel coordinates” is used, it is understood to be the same as affine = eye(4).

As an example, lets take a 2d image where the affine is:

[[1., 0., 0.],
[0., 2., 0.],
[0., 0., 1.]]


The pixels of an image with this affine would look something like:

A------------
|   |   |   |
| C |   |   |
|   |   |   |
----B--------
|   |   |   |
|   |   |   |
|   |   |   |
-------------
|   |   |   |
|   |   |   |
|   |   |   |
------------D


And the letters A-D represent the following points in “real world coordinates”:

A = [-.5, -1.]
B = [ .5,  1.]
C = [ 0.,  0.]
D = [ 2.5,  5.]

 defaultdict defaultdict(default_factory[, ...]) –> dict with default factory map map(func, *iterables) –> map object xrange alias of range affine_for_trackvis(voxel_size[, ...]) Returns an affine which maps points for voxel indices to trackvis space. affine_from_fsl_mat_file(mat_affine, ...) Converts an affine matrix from flirt (FSLdot) and a given voxel size for input and output images and returns an adjusted affine matrix for trackvis. apply_affine(aff, pts) Apply affine matrix aff to points pts asarray(a[, dtype, order]) Convert the input to an array. cdist(XA, XB[, metric, p, V, VI, w]) Computes distance between each pair of the two collections of inputs. connectivity_matrix(streamlines, label_volume) Counts the streamlines that start and end at each label pair. density_map(streamlines, vol_dims[, ...]) Counts the number of unique streamlines that pass through each voxel. dist_to_corner(affine) Calculate the maximal distance from the center to a corner of a voxel, dot(a, b[, out]) Dot product of two arrays. empty(shape[, dtype, order]) Return a new array of given shape and type, without initializing entries. eye(N[, M, k, dtype]) Return a 2-D array with ones on the diagonal and zeros elsewhere. flexi_tvis_affine(sl_vox_order, grid_affine, ...) Computes the mapping from voxel indices to streamline points, get_flexi_tvis_affine(tvis_hdr, nii_aff) Computes the mapping from voxel indices to streamline points, length(streamlines[, affine]) Calculate the lengths of many streamlines in a bundle. minimum_at(a, indices[, b]) Performs unbuffered in place operation on operand ‘a’ for elements specified by ‘indices’. move_streamlines(streamlines, output_space) Applies a linear transformation, given by affine, to streamlines. ndbincount(x[, weights, shape]) Like bincount, but for nd-indicies. near_roi(streamlines, region_of_interest[, ...]) Provide filtering criteria for a set of streamlines based on whether orientation_from_string(string_ornt) Returns an array representation of an ornt string ornt_mapping(ornt1, ornt2) Calculates the mapping needing to get from orn1 to orn2 path_length(streamlines, aoi, affine[, ...]) Computes the shortest path, along any streamline, between aoi and each voxel. random_seeds_from_mask(mask[, seeds_count, ...]) Creates randomly placed seeds for fiber tracking from a binary mask. ravel_multi_index(multi_index, dims[, mode, ...]) Converts a tuple of index arrays into an array of flat indices, applying boundary modes to the multi-index. reduce_labels(label_volume) Reduces an array of labels to the integers from 0 to n with smallest possible n. reduce_rois(rois, include) Reduce multiple ROIs to one inclusion and one exclusion ROI reorder_voxels_affine(input_ornt, ...) Calculates a linear transformation equivalent to changing voxel order. seeds_from_mask(mask[, density, voxel_size, ...]) Creates seeds for fiber tracking from a binary mask. setup_test() Set numpy print options to “legacy” for new versions of numpy streamline_near_roi(streamline, roi_coords, tol) Is a streamline near an ROI. subsegment(streamlines, max_segment_length) Splits the segments of the streamlines into small segments. target(streamlines, target_mask, affine[, ...]) Filters streamlines based on whether or not they pass through an ROI. target_line_based(streamlines, target_mask) Filters streamlines based on whether or not they pass through a ROI, using a line-based algorithm. unique_rows(in_array[, dtype]) This (quickly) finds the unique rows in an array warn Issue a warning, or maybe ignore it or raise an exception. wraps(wrapped[, assigned, updated]) Decorator factory to apply update_wrapper() to a wrapper function

### Streamlines¶

dipy.tracking.Streamlines

alias of ArraySequence

### bench¶

dipy.tracking.bench(self, label='fast', verbose=1, extra_argv=None)

Run benchmarks for module using nose.

Parameters: label : {‘fast’, ‘full’, ‘’, attribute identifier}, optional Identifies the benchmarks to run. This can be a string to pass to the nosetests executable with the ‘-A’ option, or one of several special values. Special values are: * ‘fast’ - the default - which corresponds to the nosetests -A option of ‘not slow’. ‘full’ - fast (as above) and slow benchmarks as in the ‘no -A’ option to nosetests - this is the same as ‘’. None or ‘’ - run all tests. attribute_identifier - string passed directly to nosetests as ‘-A’. verbose : int, optional Verbosity value for benchmark outputs, in the range 1-10. Default is 1. extra_argv : list, optional List with any extra arguments to pass to nosetests. success : bool Returns True if running the benchmarks works, False if an error occurred.

Notes

Benchmarks are like tests, but have names starting with “bench” instead of “test”, and can be found under the “benchmarks” sub-directory of the module.

Each NumPy module exposes bench in its namespace to run all benchmarks for it.

Examples

>>> success = np.lib.bench()
Running benchmarks for numpy.lib
...
using 562341 items:
unique:
0.11
unique1d:
0.11
ratio: 1.0
nUnique: 56230 == 56230
...
OK

>>> success
True


### test¶

dipy.tracking.test(self, label='fast', verbose=1, extra_argv=None, doctests=False, coverage=False, raise_warnings=None)

Run tests for module using nose.

Parameters: label : {‘fast’, ‘full’, ‘’, attribute identifier}, optional Identifies the tests to run. This can be a string to pass to the nosetests executable with the ‘-A’ option, or one of several special values. Special values are: * ‘fast’ - the default - which corresponds to the nosetests -A option of ‘not slow’. ‘full’ - fast (as above) and slow tests as in the ‘no -A’ option to nosetests - this is the same as ‘’. None or ‘’ - run all tests. attribute_identifier - string passed directly to nosetests as ‘-A’. verbose : int, optional Verbosity value for test outputs, in the range 1-10. Default is 1. extra_argv : list, optional List with any extra arguments to pass to nosetests. doctests : bool, optional If True, run doctests in module. Default is False. coverage : bool, optional If True, report coverage of NumPy code. Default is False. (This requires the coverage module: raise_warnings : None, str or sequence of warnings, optional This specifies which warnings to configure as ‘raise’ instead of being shown once during the test execution. Valid strings are: “develop” : equals (Warning,) “release” : equals (), don’t raise on any warnings. The default is to use the class initialization value. result : object Returns the result of running the tests as a nose.result.TextTestResult object.

Notes

Each NumPy module exposes test in its namespace to run all tests for it. For example, to run all tests for numpy.lib:

>>> np.lib.test()


Examples

>>> result = np.lib.test()
Running unit tests for numpy.lib
...
Ran 976 tests in 3.933s


OK

>>> result.errors
[]
>>> result.knownfail
[]


### warn¶

dipy.tracking._utils.warn()

Issue a warning, or maybe ignore it or raise an exception.

### Streamlines¶

dipy.tracking.benchmarks.bench_streamline.Streamlines

alias of ArraySequence

### assert_array_almost_equal¶

dipy.tracking.benchmarks.bench_streamline.assert_array_almost_equal(x, y, decimal=6, err_msg='', verbose=True)

Raises an AssertionError if two objects are not equal up to desired precision.

Note

It is recommended to use one of assert_allclose, assert_array_almost_equal_nulp or assert_array_max_ulp instead of this function for more consistent floating point comparisons.

The test verifies identical shapes and that the elements of actual and desired satisfy.

abs(desired-actual) < 1.5 * 10**(-decimal)

That is a looser test than originally documented, but agrees with what the actual implementation did up to rounding vagaries. An exception is raised at shape mismatch or conflicting values. In contrast to the standard usage in numpy, NaNs are compared like numbers, no assertion is raised if both objects have NaNs in the same positions.

Parameters: x : array_like The actual object to check. y : array_like The desired, expected object. decimal : int, optional Desired precision, default is 6. err_msg : str, optional The error message to be printed in case of failure. verbose : bool, optional If True, the conflicting values are appended to the error message. AssertionError If actual and desired are not equal up to specified precision.

assert_allclose
Compare two array_like objects for equality with desired relative and/or absolute precision.

assert_array_almost_equal_nulp, assert_array_max_ulp, assert_equal

Examples

the first assert does not raise an exception

>>> np.testing.assert_array_almost_equal([1.0,2.333,np.nan],
[1.0,2.333,np.nan])

>>> np.testing.assert_array_almost_equal([1.0,2.33333,np.nan],
...                                      [1.0,2.33339,np.nan], decimal=5)
...
<type 'exceptions.AssertionError'>:
AssertionError:
Arrays are not almost equal

(mismatch 50.0%)
x: array([ 1.     ,  2.33333,      NaN])
y: array([ 1.     ,  2.33339,      NaN])

>>> np.testing.assert_array_almost_equal([1.0,2.33333,np.nan],
...                                      [1.0,2.33333, 5], decimal=5)
<type 'exceptions.ValueError'>:
ValueError:
Arrays are not almost equal
x: array([ 1.     ,  2.33333,      NaN])
y: array([ 1.     ,  2.33333,  5.     ])


### assert_array_equal¶

dipy.tracking.benchmarks.bench_streamline.assert_array_equal(x, y, err_msg='', verbose=True)

Raises an AssertionError if two array_like objects are not equal.

Given two array_like objects, check that the shape is equal and all elements of these objects are equal. An exception is raised at shape mismatch or conflicting values. In contrast to the standard usage in numpy, NaNs are compared like numbers, no assertion is raised if both objects have NaNs in the same positions.

The usual caution for verifying equality with floating point numbers is advised.

Parameters: x : array_like The actual object to check. y : array_like The desired, expected object. err_msg : str, optional The error message to be printed in case of failure. verbose : bool, optional If True, the conflicting values are appended to the error message. AssertionError If actual and desired objects are not equal.

assert_allclose
Compare two array_like objects for equality with desired relative and/or absolute precision.

assert_array_almost_equal_nulp, assert_array_max_ulp, assert_equal

Examples

The first assert does not raise an exception:

>>> np.testing.assert_array_equal([1.0,2.33333,np.nan],
...                               [np.exp(0),2.33333, np.nan])


Assert fails with numerical inprecision with floats:

>>> np.testing.assert_array_equal([1.0,np.pi,np.nan],
...                               [1, np.sqrt(np.pi)**2, np.nan])
...
<type 'exceptions.ValueError'>:
AssertionError:
Arrays are not equal

(mismatch 50.0%)
x: array([ 1.        ,  3.14159265,         NaN])
y: array([ 1.        ,  3.14159265,         NaN])


Use assert_allclose or one of the nulp (number of floating point values) functions for these cases instead:

>>> np.testing.assert_allclose([1.0,np.pi,np.nan],
...                            [1, np.sqrt(np.pi)**2, np.nan],
...                            rtol=1e-10, atol=0)


### bench_compress_streamlines¶

dipy.tracking.benchmarks.bench_streamline.bench_compress_streamlines()

### bench_length¶

dipy.tracking.benchmarks.bench_streamline.bench_length()

### bench_set_number_of_points¶

dipy.tracking.benchmarks.bench_streamline.bench_set_number_of_points()

### compress_streamlines¶

dipy.tracking.benchmarks.bench_streamline.compress_streamlines()

Compress streamlines by linearization as in [Presseau15].

The compression consists in merging consecutive segments that are nearly collinear. The merging is achieved by removing the point the two segments have in common.

The linearization process [Presseau15] ensures that every point being removed are within a certain margin (in mm) of the resulting streamline. Recommendations for setting this margin can be found in [Presseau15] (in which they called it tolerance error).

The compression also ensures that two consecutive points won’t be too far from each other (precisely less or equal than max_segment_lengthmm). This is a tradeoff to speed up the linearization process [Rheault15]. A low value will result in a faster linearization but low compression, whereas a high value will result in a slower linearization but high compression.

Parameters: streamlines : one or a list of array-like of shape (N,3) Array representing x,y,z of N points in a streamline. tol_error : float (optional) Tolerance error in mm (default: 0.01). A rule of thumb is to set it to 0.01mm for deterministic streamlines and 0.1mm for probabilitic streamlines. max_segment_length : float (optional) Maximum length in mm of any given segment produced by the compression. The default is 10mm. (In [Presseau15], they used a value of np.inf). compressed_streamlines : one or a list of array-like Results of the linearization process.

Notes

Be aware that compressed streamlines have variable step sizes. One needs to be careful when computing streamlines-based metrics [Houde15].

References

 [Presseau15] Presseau C. et al., A new compression format for fiber tracking datasets, NeuroImage, no 109, 73-83, 2015.
 [Rheault15] Rheault F. et al., Real Time Interaction with Millions of Streamlines, ISMRM, 2015.
 [Houde15] Houde J.-C. et al. How to Avoid Biased Streamlines-Based Metrics for Streamlines with Variable Step Sizes, ISMRM, 2015.

Examples

>>> from dipy.tracking.streamline import compress_streamlines
>>> import numpy as np
>>> # One streamline: a wiggling line
>>> rng = np.random.RandomState(42)
>>> streamline = np.linspace(0, 10, 100*3).reshape((100, 3))
>>> streamline += 0.2 * rng.rand(100, 3)
>>> c_streamline = compress_streamlines(streamline, tol_error=0.2)
>>> len(streamline)
100
>>> len(c_streamline)
10
>>> # Multiple streamlines
>>> streamlines = [streamline, streamline[::2]]
>>> c_streamlines = compress_streamlines(streamlines, tol_error=0.2)
>>> [len(s) for s in streamlines]
[100, 50]
>>> [len(s) for s in c_streamlines]
[10, 7]


### compress_streamlines_python¶

dipy.tracking.benchmarks.bench_streamline.compress_streamlines_python(streamline, tol_error=0.01, max_segment_length=10)

Python version of the FiberCompression found on https://github.com/scilus/FiberCompression.

### generate_streamlines¶

dipy.tracking.benchmarks.bench_streamline.generate_streamlines(nb_streamlines, min_nb_points, max_nb_points, rng)

### get_data¶

dipy.tracking.benchmarks.bench_streamline.get_data(name='small_64D')

provides filenames of some test datasets or other useful parametrisations

Parameters: name : str the filename/s of which dataset to return, one of: ‘small_64D’ small region of interest nifti,bvecs,bvals 64 directions ‘small_101D’ small region of interest nifti,bvecs,bvals 101 directions ‘aniso_vox’ volume with anisotropic voxel size as Nifti ‘fornix’ 300 tracks in Trackvis format (from Pittsburgh Brain Competition) ‘gqi_vectors’ the scanner wave vectors needed for a GQI acquisitions of 101 directions tested on Siemens 3T Trio ‘small_25’ small ROI (10x8x2) DTI data (b value 2000, 25 directions) ‘test_piesno’ slice of N=8, K=14 diffusion data ‘reg_c’ small 2D image used for validating registration ‘reg_o’ small 2D image used for validation registration ‘cb_2’ two vectorized cingulum bundles fnames : tuple filenames for dataset

Examples

>>> import numpy as np
>>> from dipy.data import get_data
>>> fimg,fbvals,fbvecs=get_data('small_101D')
>>> import nibabel as nib
>>> data=img.get_data()
>>> data.shape == (6, 10, 10, 102)
True
>>> bvals.shape == (102,)
True
>>> bvecs.shape == (102, 3)
True


### length¶

dipy.tracking.benchmarks.bench_streamline.length()

Euclidean length of streamlines

Length is in mm only if streamlines are expressed in world coordinates.

Parameters: streamlines : ndarray or a list or dipy.tracking.Streamlines If ndarray, must have shape (N,3) where N is the number of points of the streamline. If list, each item must be ndarray shape (Ni,3) where Ni is the number of points of streamline i. If dipy.tracking.Streamlines, its common_shape must be 3. lengths : scalar or ndarray shape (N,) If there is only one streamline, a scalar representing the length of the streamline. If there are several streamlines, ndarray containing the length of every streamline.

Examples

>>> from dipy.tracking.streamline import length
>>> import numpy as np
>>> streamline = np.array([[1, 1, 1], [2, 3, 4], [0, 0, 0]])
>>> expected_length = np.sqrt([1+2**2+3**2, 2**2+3**2+4**2]).sum()
>>> length(streamline) == expected_length
True
>>> streamlines = [streamline, np.vstack([streamline, streamline[::-1]])]
>>> expected_lengths = [expected_length, 2*expected_length]
>>> lengths = [length(streamlines[0]), length(streamlines[1])]
>>> np.allclose(lengths, expected_lengths)
True
>>> length([])
0.0
>>> length(np.array([[1, 2, 3]]))
0.0


### length_python¶

dipy.tracking.benchmarks.bench_streamline.length_python(xyz, along=False)

### measure¶

dipy.tracking.benchmarks.bench_streamline.measure(code_str, times=1, label=None)

Return elapsed time for executing code in the namespace of the caller.

The supplied code string is compiled with the Python builtin compile. The precision of the timing is 10 milli-seconds. If the code will execute fast on this timescale, it can be executed many times to get reasonable timing accuracy.

Parameters: code_str : str The code to be timed. times : int, optional The number of times the code is executed. Default is 1. The code is only compiled once. label : str, optional A label to identify code_str with. This is passed into compile as the second argument (for run-time error messages). elapsed : float Total elapsed time in seconds for executing code_str times times.

Examples

>>> etime = np.testing.measure('for i in range(1000): np.sqrt(i**2)',
...                            times=times)
>>> print("Time for a single execution : ", etime / times, "s")
Time for a single execution :  0.005 s


### set_number_of_points¶

dipy.tracking.benchmarks.bench_streamline.set_number_of_points()
Change the number of points of streamlines
(either by downsampling or upsampling)

Change the number of points of streamlines in order to obtain nb_points-1 segments of equal length. Points of streamlines will be modified along the curve.

Parameters: streamlines : ndarray or a list or dipy.tracking.Streamlines If ndarray, must have shape (N,3) where N is the number of points of the streamline. If list, each item must be ndarray shape (Ni,3) where Ni is the number of points of streamline i. If dipy.tracking.Streamlines, its common_shape must be 3. nb_points : int integer representing number of points wanted along the curve. new_streamlines : ndarray or a list or dipy.tracking.Streamlines Results of the downsampling or upsampling process.

Examples

>>> from dipy.tracking.streamline import set_number_of_points
>>> import numpy as np


One streamline, a semi-circle:

>>> theta = np.pi*np.linspace(0, 1, 100)
>>> x = np.cos(theta)
>>> y = np.sin(theta)
>>> z = 0 * x
>>> streamline = np.vstack((x, y, z)).T
>>> modified_streamline = set_number_of_points(streamline, 3)
>>> len(modified_streamline)
3


Multiple streamlines:

>>> streamlines = [streamline, streamline[::2]]
>>> new_streamlines = set_number_of_points(streamlines, 10)
>>> [len(s) for s in streamlines]
[100, 50]
>>> [len(s) for s in new_streamlines]
[10, 10]


### set_number_of_points_python¶

dipy.tracking.benchmarks.bench_streamline.set_number_of_points_python(xyz, n_pols=3)

### setup¶

dipy.tracking.benchmarks.bench_streamline.setup()

### EuDX¶

class dipy.tracking.eudx.EuDX(a, ind, seeds, odf_vertices, a_low=0.0239, step_sz=0.5, ang_thr=60.0, length_thr=0.0, total_weight=0.5, max_points=1000, affine=None)

Bases: object

Euler Delta Crossings

Generates tracks with termination criteria defined by a delta function [R488] and it has similarities with FACT algorithm [R489] and Basser’s method but uses trilinear interpolation.

Can be used with any reconstruction method as DTI, DSI, QBI, GQI which can calculate an orientation distribution function and find the local peaks of that function. For example a single tensor model can give you only one peak a dual tensor model 2 peaks and quantitative anisotropy method as used in GQI can give you 3,4,5 or even more peaks.

The parameters of the delta function are checking thresholds for the direction propagation magnitude and the angle of propagation.

A specific number of seeds is defined randomly and then the tracks are generated for that seed if the delta function returns true.

Trilinear interpolation is being used for defining the weights of the propagation.

Notes

The coordinate system of the tractography is that of native space of image coordinates not native space world coordinates therefore voxel size is always considered as having size (1,1,1). Therefore, the origin is at the center of the center of the first voxel of the volume and all i,j,k coordinates start from the center of the voxel they represent.

References

 [R488] (1, 2) Garyfallidis, Towards an accurate brain tractography, PhD thesis, University of Cambridge, 2012.
 [R489] (1, 2) Mori et al. Three-dimensional tracking of axonal projections in the brain by magnetic resonance imaging. Ann. Neurol. 1999.
__init__(a, ind, seeds, odf_vertices, a_low=0.0239, step_sz=0.5, ang_thr=60.0, length_thr=0.0, total_weight=0.5, max_points=1000, affine=None)

Euler integration with multiple stopping criteria and supporting multiple multiple fibres in crossings [R490].

Parameters: a : array, Shape (I, J, K, Np), magnitude of the peak of a scalar anisotropic function e.g. QA (quantitative anisotropy) where Np is the number of peaks or a different function of shape (I, J, K) e.g FA or GFA. ind : array, shape(x, y, z, Np) indices of orientations of the scalar anisotropic peaks found on the resampling sphere seeds : int or ndarray If an int is specified then that number of random seeds is generated in the volume. If an (N, 3) array of points is given, each of the N points is used as a seed. Seed points should be given in the point space of the track (see affine). The latter is useful when you need to track from specific regions e.g. the white/gray matter interface or a specific ROI e.g. in the corpus callosum. odf_vertices : ndarray, shape (N, 3) sphere points which define a discrete representation of orientations for the peaks, the same for all voxels. Usually the same sphere is used as an input for a reconstruction algorithm e.g. DSI. a_low : float, optional low threshold for QA(typical 0.023) or FA(typical 0.2) or any other anisotropic function step_sz : float, optional euler propagation step size ang_thr : float, optional if turning angle is bigger than this threshold then tracking stops. total_weight : float, optional total weighting threshold max_points : int, optional maximum number of points in a track. Used to stop tracks from looping forever. affine : array (4, 4) optional An affine mapping from the voxel indices of the input data to the point space of the streamlines. That is if [x, y, z, 1] == point_space * [i, j, k, 1], then the streamline with point [x, y, z] passes though the center of voxel [i, j, k]. If no point_space is given, the point space will be in voxel coordinates. generator : obj By iterating this generator you can obtain all the streamlines.

Notes

This works as an iterator class because otherwise it could fill your entire memory if you generate many tracks. Something very common as you can easily generate millions of tracks if you have many seeds.

References

 [R490] (1, 2) E. Garyfallidis (2012), “Towards an accurate brain tractography”, PhD thesis, University of Cambridge, UK.

Examples

>>> import nibabel as nib
>>> from dipy.reconst.dti import TensorModel, quantize_evecs
>>> from dipy.data import get_data, get_sphere
>>> fimg,fbvals,fbvecs = get_data('small_101D')
>>> affine = img.affine
>>> data = img.get_data()
>>> model = TensorModel(gtab)
>>> ten = model.fit(data)
>>> sphere = get_sphere('symmetric724')
>>> ind = quantize_evecs(ten.evecs, sphere.vertices)
>>> eu = EuDX(a=ten.fa, ind=ind, seeds=100, odf_vertices=sphere.vertices, a_low=.2)
>>> tracks = [e for e in eu]


### eudx_both_directions¶

dipy.tracking.eudx.eudx_both_directions()
Parameters: seed : array, float64 shape (3,) Point where the tracking starts. ref : cnp.npy_intp int Index of peak to follow first. qa : array, float64 shape (X, Y, Z, Np) Anisotropy matrix, where Np is the number of maximum allowed peaks. ind : array, float64 shape(x, y, z, Np) Index of the track orientation. odf_vertices : double array shape (N, 3) Sampling directions on the sphere. qa_thr : float Threshold for QA, we want everything higher than this threshold. ang_thr : float Angle threshold, we only select fiber orientation within this range. step_sz : double total_weight : double max_points : cnp.npy_intp track : array, shape (N,3)

### get_sphere¶

dipy.tracking.eudx.get_sphere(name='symmetric362')

provide triangulated spheres

Parameters: name : str which sphere - one of: * ‘symmetric362’ * ‘symmetric642’ * ‘symmetric724’ * ‘repulsion724’ * ‘repulsion100’ * ‘repulsion200’ sphere : a dipy.core.sphere.Sphere class instance

Examples

>>> import numpy as np
>>> from dipy.data import get_sphere
>>> sphere = get_sphere('symmetric362')
>>> verts, faces = sphere.vertices, sphere.faces
>>> verts.shape == (362, 3)
True
>>> faces.shape == (720, 3)
True
>>> verts, faces = get_sphere('not a sphere name')
Traceback (most recent call last):
...
DataError: No sphere called "not a sphere name"


### detect_corresponding_tracks¶

dipy.tracking.learning.detect_corresponding_tracks(indices, tracks1, tracks2)

Detect corresponding tracks from list tracks1 to list tracks2 where tracks1 & tracks2 are lists of tracks

Parameters: indices : sequence of indices of tracks1 that are to be detected in tracks2 tracks1 : sequence of tracks as arrays, shape (N1,3) .. (Nm,3) tracks2 : sequence of tracks as arrays, shape (M1,3) .. (Mm,3) track2track : array (N,2) where N is len(indices) of int it shows the correspondance in the following way: the first column is the current index in tracks1 the second column is the corresponding index in tracks2

Notes

To find the corresponding tracks we use mam_distances with ‘avg’ option. Then we calculate the argmin of all the calculated distances and return it for every index. (See 3rd column of arr in the example given below.)

Examples

>>> import numpy as np
>>> import dipy.tracking.learning as tl
>>> A = np.array([[0, 0, 0], [1, 1, 1], [2, 2, 2]])
>>> B = np.array([[1, 0, 0], [2, 0, 0], [3, 0, 0]])
>>> C = np.array([[0, 0, -1], [0, 0, -2], [0, 0, -3]])
>>> bundle1 = [A, B, C]
>>> bundle2 = [B, A]
>>> indices = [0, 1]
>>> arr = tl.detect_corresponding_tracks(indices, bundle1, bundle2)


### detect_corresponding_tracks_plus¶

dipy.tracking.learning.detect_corresponding_tracks_plus(indices, tracks1, indices2, tracks2)

Detect corresponding tracks from 1 to 2 where tracks1 & tracks2 are sequences of tracks

Parameters: indices : sequence of indices of tracks1 that are to be detected in tracks2 tracks1 : sequence of tracks as arrays, shape (N1,3) .. (Nm,3) indices2 : sequence of indices of tracks2 in the initial brain tracks2 : sequence of tracks as arrays, shape (M1,3) .. (Mm,3) track2track : array (N,2) where N is len(indices) of int showing the correspondance in th following way the first colum is the current index of tracks1 the second column is the corresponding index in tracks2

distances.mam_distances

Notes

To find the corresponding tracks we use mam_distances with ‘avg’ option. Then we calculate the argmin of all the calculated distances and return it for every index. (See 3rd column of arr in the example given below.)

Examples

>>> import numpy as np
>>> import dipy.tracking.learning as tl
>>> A = np.array([[0, 0, 0], [1, 1, 1], [2, 2, 2]])
>>> B = np.array([[1, 0, 0], [2, 0, 0], [3, 0, 0]])
>>> C = np.array([[0, 0, -1], [0, 0, -2], [0, 0, -3]])
>>> bundle1 = [A, B, C]
>>> bundle2 = [B, A]
>>> indices = [0, 1]
>>> indices2 = indices
>>> arr = tl.detect_corresponding_tracks_plus(indices, bundle1, indices2, bundle2)


### FiberFit¶

class dipy.tracking.life.FiberFit(fiber_model, life_matrix, vox_coords, to_fit, beta, weighted_signal, b0_signal, relative_signal, mean_sig, vox_data, streamline, affine, evals)

A fit of the LiFE model to diffusion data

Methods

 predict([gtab, S0]) Predict the signal
__init__(fiber_model, life_matrix, vox_coords, to_fit, beta, weighted_signal, b0_signal, relative_signal, mean_sig, vox_data, streamline, affine, evals)
Parameters: fiber_model : A FiberModel class instance params : the parameters derived from a fit of the model to the data.
predict(gtab=None, S0=None)

Predict the signal

Parameters: gtab : GradientTable Default: use self.gtab S0 : float or array The non-diffusion-weighted signal in the voxels for which a prediction is made. Default: use self.b0_signal prediction : ndarray of shape (voxels, bvecs) An array with a prediction of the signal in each voxel/direction

### FiberModel¶

class dipy.tracking.life.FiberModel(gtab)

A class for representing and solving predictive models based on tractography solutions.

Notes

This is an implementation of the LiFE model described in [1]_

[1] Pestilli, F., Yeatman, J, Rokem, A. Kay, K. and Wandell
B.A. (2014). Validation and statistical inference in living connectomes. Nature Methods.

Methods

 fit(data, streamline[, affine, evals, sphere]) Fit the LiFE FiberModel for data and a set of streamlines associated setup(streamline, affine[, evals, sphere]) Set up the necessary components for the LiFE model: the matrix of
__init__(gtab)
Parameters: gtab : a GradientTable class instance
fit(data, streamline, affine=None, evals=[0.001, 0, 0], sphere=None)

Fit the LiFE FiberModel for data and a set of streamlines associated with this data

Parameters: data : 4D array Diffusion-weighted data streamline : list A bunch of streamlines affine: 4 by 4 array (optional) The affine to go from the streamline coordinates to the data coordinates. Defaults to use np.eye(4) evals : list (optional) The eigenvalues of the tensor response function used in constructing the model signal. Default: [0.001, 0, 0] sphere: dipy.core.Sphere instance, or False Whether to approximate (and cache) the signal on a discrete sphere. This may confer a significant speed-up in setting up the problem, but is not as accurate. If False, we use the exact gradients along the streamlines to calculate the matrix, instead of an approximation. FiberFit class instance
setup(streamline, affine, evals=[0.001, 0, 0], sphere=None)

Set up the necessary components for the LiFE model: the matrix of fiber-contributions to the DWI signal, and the coordinates of voxels for which the equations will be solved

Parameters: streamline : list Streamlines, each is an array of shape (n, 3) affine : 4 by 4 array Mapping from the streamline coordinates to the data evals : list (3 items, optional) The eigenvalues of the canonical tensor used as a response function. Default:[0.001, 0, 0]. sphere: dipy.core.Sphere instance. Whether to approximate (and cache) the signal on a discrete sphere. This may confer a significant speed-up in setting up the problem, but is not as accurate. If False, we use the exact gradients along the streamlines to calculate the matrix, instead of an approximation. Defaults to use the 724-vertex symmetric sphere from dipy.data

### LifeSignalMaker¶

class dipy.tracking.life.LifeSignalMaker(gtab, evals=[0.001, 0, 0], sphere=None)

Bases: object

A class for generating signals from streamlines in an efficient and speedy manner.

Methods

 calc_signal(xyz) streamline_signal(streamline) Approximate the signal for a given streamline
__init__(gtab, evals=[0.001, 0, 0], sphere=None)

Initialize a signal maker

Parameters: gtab : GradientTable class instance The gradient table on which the signal is calculated. evals : list of 3 items The eigenvalues of the canonical tensor to use in calculating the signal. n_points : dipy.core.Sphere class instance The discrete sphere to use as an approximation for the continuous sphere on which the signal is represented. If integer - we will use an instance of one of the symmetric spheres cached in dps.get_sphere. If a ‘dipy.core.Sphere’ class instance is provided, we will use this object. Default: the dipy.data symmetric sphere with 724 vertices
calc_signal(xyz)
streamline_signal(streamline)

Approximate the signal for a given streamline

### ReconstFit¶

class dipy.tracking.life.ReconstFit(model, data)

Bases: object

Abstract class which holds the fit result of ReconstModel

For example that could be holding FA or GFA etc.

__init__(model, data)

### ReconstModel¶

class dipy.tracking.life.ReconstModel(gtab)

Bases: object

Abstract class for signal reconstruction models

Methods

 fit(data[, mask])
__init__(gtab)

Initialization of the abstract class for signal reconstruction models

Parameters: gtab : GradientTable class instance
fit(data, mask=None, **kwargs)

### range¶

class dipy.tracking.life.range(stop) → range object

Bases: object

range(start, stop[, step]) -> range object

Return an object that produces a sequence of integers from start (inclusive) to stop (exclusive) by step. range(i, j) produces i, i+1, i+2, ..., j-1. start defaults to 0, and stop is omitted! range(4) produces 0, 1, 2, 3. These are exactly the valid indices for a list of 4 elements. When step is given, it specifies the increment (or decrement).

Methods

 count(...) index((value, [start, ...) Raise ValueError if the value is not present.
__init__()

Initialize self. See help(type(self)) for accurate signature.

count(value) → integer -- return number of occurrences of value
index(value[, start[, stop]]) → integer -- return index of value.

Raise ValueError if the value is not present.

start
step
stop

dipy.tracking.life.grad_tensor(grad, evals)

Calculate the 3 by 3 tensor for a given spatial gradient, given a canonical tensor shape (also as a 3 by 3), pointing at [1,0,0]

Parameters: grad : 1d array of shape (3,) The spatial gradient (e.g between two nodes of a streamline). evals: 1d array of shape (3,) The eigenvalues of a canonical tensor to be used as a response function.

dipy.tracking.life.gradient(f)

Return the gradient of an N-dimensional array.

The gradient is computed using central differences in the interior and first differences at the boundaries. The returned gradient hence has the same shape as the input array.

Parameters: f : array_like An N-dimensional array containing samples of a scalar function. gradient : ndarray N arrays of the same shape as f giving the derivative of f with respect to each dimension.

Examples

>>> x = np.array([1, 2, 4, 7, 11, 16], dtype=np.float)
array([ 1. ,  1.5,  2.5,  3.5,  4.5,  5. ])

>>> gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=np.float))
[array([[ 2.,  2., -1.],
[ 2.,  2., -1.]]), array([[ 1. ,  2.5,  4. ],
[ 1. ,  1. ,  1. ]])]


### setup_test¶

dipy.tracking.life.setup_test()

Set numpy print options to “legacy” for new versions of numpy

If imported into a file, nosetest will run this before any doctests.

References

dipy.tracking.life.streamline_gradients(streamline)

Calculate the gradients of the streamline along the spatial dimension

Parameters: streamline : array-like of shape (n, 3) The 3d coordinates of a single streamline Array of shape (3, n): Spatial gradients along the length of the streamline.

### streamline_signal¶

dipy.tracking.life.streamline_signal(streamline, gtab, evals=[0.001, 0, 0])

The signal from a single streamline estimate along each of its nodes.

Parameters: streamline : a single streamline gtab : GradientTable class instance evals : list of length 3 (optional. Default: [0.001, 0, 0]) The eigenvalues of the canonical tensor used as an estimate of the signal generated by each node of the streamline.

### streamline_tensors¶

dipy.tracking.life.streamline_tensors(streamline, evals=[0.001, 0, 0])

The tensors generated by this fiber.

Parameters: streamline : array-like of shape (n, 3) The 3d coordinates of a single streamline evals : iterable with three entries The estimated eigenvalues of a single fiber tensor. (default: [0.001, 0, 0]). An n_nodes by 3 by 3 array with the tensor for each node in the fiber.

### transform_streamlines¶

dipy.tracking.life.transform_streamlines(streamlines, mat)

Apply affine transformation to streamlines

Parameters: streamlines : list List of 2D ndarrays of shape[-1]==3 mat : array, (4, 4) transformation matrix new_streamlines : list List of the transformed 2D ndarrays of shape[-1]==3

### unique_rows¶

dipy.tracking.life.unique_rows(in_array, dtype='f4')

This (quickly) finds the unique rows in an array

Parameters: in_array: ndarray The array for which the unique rows should be found dtype: str, optional This determines the intermediate representation used for the values. Should at least preserve the values of the input array. u_return: ndarray Array with the unique rows of the original array.

### voxel2streamline¶

dipy.tracking.life.voxel2streamline(streamline, transformed=False, affine=None, unique_idx=None)

Maps voxels to streamlines and streamlines to voxels, for setting up the LiFE equations matrix

Parameters: streamline : list A collection of streamlines, each n by 3, with n being the number of nodes in the fiber. affine : 4 by 4 array (optional) Defines the spatial transformation from streamline to data. Default: np.eye(4) transformed : bool (optional) Whether the streamlines have been already transformed (in which case they don’t need to be transformed in here). unique_idx : array (optional). The unique indices in the streamlines v2f, v2fn : tuple of dicts The first dict in the tuple answers the question: Given a voxel (from the unique indices in this model), which fibers pass through it? The second answers the question: Given a streamline, for each voxel that this streamline passes through, which nodes of that streamline are in that voxel?

### ActTissueClassifier¶

class dipy.tracking.local.ActTissueClassifier

Bases: dipy.tracking.local.tissue_classifier.ConstrainedTissueClassifier

Anatomically-Constrained Tractography (ACT) stopping criteria from [R491]. This implements the use of partial volume fraction (PVE) maps to determine when the tracking stops. The proposed ([R491]) method that cuts streamlines going through subcortical gray matter regions is not implemented here. The backtracking technique for streamlines reaching INVALIDPOINT is not implemented either. cdef:

double interp_out_double[1] double[:] interp_out_view = interp_out_view double[:, :, :] include_map, exclude_map
 [R491] (1, 2) Smith, R. E., Tournier, J.-D., Calamante, F., & Connelly, A.

“Anatomically-constrained tractography: Improved diffusion MRI streamlines tractography through effective use of anatomical information.” NeuroImage, 63(3), 1924-1938, 2012.

Methods

 check_point from_pve ConstrainedTissueClassifier from partial volume fraction (PVE) maps. get_exclude get_include
__init__()

Initialize self. See help(type(self)) for accurate signature.

### BinaryTissueClassifier¶

class dipy.tracking.local.BinaryTissueClassifier

Bases: dipy.tracking.local.tissue_classifier.TissueClassifier

cdef:

Methods

 check_point
__init__()

Initialize self. See help(type(self)) for accurate signature.

### CmcTissueClassifier¶

class dipy.tracking.local.CmcTissueClassifier

Bases: dipy.tracking.local.tissue_classifier.ConstrainedTissueClassifier

Continuous map criterion (CMC) stopping criteria from [R492]. This implements the use of partial volume fraction (PVE) maps to determine when the tracking stops.

cdef:
double interp_out_double[1] double[:] interp_out_view = interp_out_view double[:, :, :] include_map, exclude_map double step_size double average_voxel_size double correction_factor

References

 [R492] (1, 2) Girard, G., Whittingstall, K., Deriche, R., & Descoteaux, M.

“Towards quantitative connectivity analysis: reducing tractography biases.” NeuroImage, 98, 266-278, 2014.

Methods

 check_point from_pve ConstrainedTissueClassifier from partial volume fraction (PVE) maps. get_exclude get_include
__init__()

Initialize self. See help(type(self)) for accurate signature.

### ConstrainedTissueClassifier¶

class dipy.tracking.local.ConstrainedTissueClassifier

Bases: dipy.tracking.local.tissue_classifier.TissueClassifier

Abstract class that takes as input included and excluded tissue maps. The ‘include_map’ defines when the streamline reached a ‘valid’ stopping region (e.g. gray matter partial volume estimation (PVE) map) and the ‘exclude_map’ defines when the streamline reached an ‘invalid’ stopping region (e.g. corticospinal fluid PVE map). The background of the anatomical image should be added to the ‘include_map’ to keep streamlines exiting the brain (e.g. through the brain stem).

cdef:
double interp_out_double[1] double[:] interp_out_view = interp_out_view double[:, :, :] include_map, exclude_map

Methods

 check_point from_pve ConstrainedTissueClassifier from partial volume fraction (PVE) maps. get_exclude get_include
__init__()

Initialize self. See help(type(self)) for accurate signature.

from_pve()

ConstrainedTissueClassifier from partial volume fraction (PVE) maps.

Parameters: wm_map : array The partial volume fraction of white matter at each voxel. gm_map : array The partial volume fraction of gray matter at each voxel. csf_map : array The partial volume fraction of corticospinal fluid at each voxel.
get_exclude()
get_include()

### DirectionGetter¶

class dipy.tracking.local.DirectionGetter

Bases: object

Methods

__init__()

Initialize self. See help(type(self)) for accurate signature.

get_direction()
initial_direction()

### LocalTracking¶

class dipy.tracking.local.LocalTracking(direction_getter, tissue_classifier, seeds, affine, step_size, max_cross=None, maxlen=500, fixedstep=True, return_all=True)

Bases: object

__init__(direction_getter, tissue_classifier, seeds, affine, step_size, max_cross=None, maxlen=500, fixedstep=True, return_all=True)

Creates streamlines by using local fiber-tracking.

Parameters: direction_getter : instance of DirectionGetter Used to get directions for fiber tracking. tissue_classifier : instance of TissueClassifier Identifies endpoints and invalid points to inform tracking. seeds : array (N, 3) Points to seed the tracking. Seed points should be given in point space of the track (see affine). affine : array (4, 4) Coordinate space for the streamline point with respect to voxel indices of input data. This affine can contain scaling, rotational, and translational components but should not contain any shearing. An identity matrix can be used to generate streamlines in “voxel coordinates” as long as isotropic voxels were used to acquire the data. step_size : float Step size used for tracking. max_cross : int or None The maximum number of direction to track from each seed in crossing voxels. By default all initial directions are tracked. maxlen : int Maximum number of steps to track from seed. Used to prevent infinite loops. fixedstep : bool If true, a fixed stepsize is used, otherwise a variable step size is used. return_all : bool If true, return all generated streamlines, otherwise only streamlines reaching end points or exiting the image.

### ParticleFilteringTracking¶

class dipy.tracking.local.ParticleFilteringTracking(direction_getter, tissue_classifier, seeds, affine, step_size, max_cross=None, maxlen=500, pft_back_tracking_dist=2, pft_front_tracking_dist=1, pft_max_trial=20, particle_count=15, return_all=True)
__init__(direction_getter, tissue_classifier, seeds, affine, step_size, max_cross=None, maxlen=500, pft_back_tracking_dist=2, pft_front_tracking_dist=1, pft_max_trial=20, particle_count=15, return_all=True)

A streamline generator using the particle filtering tractography method [R493].

Parameters: direction_getter : instance of ProbabilisticDirectionGetter Used to get directions for fiber tracking. tissue_classifier : instance of ConstrainedTissueClassifier Identifies endpoints and invalid points to inform tracking. seeds : array (N, 3) Points to seed the tracking. Seed points should be given in point space of the track (see affine). affine : array (4, 4) Coordinate space for the streamline point with respect to voxel indices of input data. This affine can contain scaling, rotational, and translational components but should not contain any shearing. An identity matrix can be used to generate streamlines in “voxel coordinates” as long as isotropic voxels were used to acquire the data. step_size : float Step size used for tracking. max_cross : int or None The maximum number of direction to track from each seed in crossing voxels. By default all initial directions are tracked. maxlen : int Maximum number of steps to track from seed. Used to prevent infinite loops. pft_back_tracking_dist : float Distance in mm to back track before starting the particle filtering tractography. The total particle filtering tractography distance is equal to back_tracking_dist + front_tracking_dist. By default this is set to 2 mm. pft_front_tracking_dist : float Distance in mm to run the particle filtering tractography after the the back track distance. The total particle filtering tractography distance is equal to back_tracking_dist + front_tracking_dist. By default this is set to 1 mm. pft_max_trial : int Maximum number of trial for the particle filtering tractography (Prevents infinite loops). particle_count : int Number of particles to use in the particle filter. return_all : bool If true, return all generated streamlines, otherwise only streamlines reaching end points or exiting the image.

References

 [R493] (1, 2) Girard, G., Whittingstall, K., Deriche, R., & Descoteaux, M. Towards quantitative connectivity analysis: reducing tractography biases. NeuroImage, 98, 266-278, 2014.

### ThresholdTissueClassifier¶

class dipy.tracking.local.ThresholdTissueClassifier

Bases: dipy.tracking.local.tissue_classifier.TissueClassifier

# Declarations from tissue_classifier.pxd bellow cdef:

double threshold, interp_out_double[1] double[:] interp_out_view = interp_out_view double[:, :, :] metric_map

Methods

 check_point
__init__()

Initialize self. See help(type(self)) for accurate signature.

### TissueClassifier¶

class dipy.tracking.local.TissueClassifier

Bases: object

Methods

__init__()

Initialize self. See help(type(self)) for accurate signature.

check_point()

### Bunch¶

class dipy.tracking.local.localtracking.Bunch(**kwds)

Bases: object

__init__(**kwds)

A ‘bunch’ of values (a replacement of Enum)

This is a temporary replacement of Enum, which is not available on all versions of Python 2

### ConstrainedTissueClassifier¶

class dipy.tracking.local.localtracking.ConstrainedTissueClassifier

Bases: dipy.tracking.local.tissue_classifier.TissueClassifier

Abstract class that takes as input included and excluded tissue maps. The ‘include_map’ defines when the streamline reached a ‘valid’ stopping region (e.g. gray matter partial volume estimation (PVE) map) and the ‘exclude_map’ defines when the streamline reached an ‘invalid’ stopping region (e.g. corticospinal fluid PVE map). The background of the anatomical image should be added to the ‘include_map’ to keep streamlines exiting the brain (e.g. through the brain stem).

cdef:
double interp_out_double[1] double[:] interp_out_view = interp_out_view double[:, :, :] include_map, exclude_map

Methods

 check_point from_pve ConstrainedTissueClassifier from partial volume fraction (PVE) maps. get_exclude get_include
__init__()

Initialize self. See help(type(self)) for accurate signature.

from_pve()

ConstrainedTissueClassifier from partial volume fraction (PVE) maps.

Parameters: wm_map : array The partial volume fraction of white matter at each voxel. gm_map : array The partial volume fraction of gray matter at each voxel. csf_map : array The partial volume fraction of corticospinal fluid at each voxel.
get_exclude()
get_include()

### LocalTracking¶

class dipy.tracking.local.localtracking.LocalTracking(direction_getter, tissue_classifier, seeds, affine, step_size, max_cross=None, maxlen=500, fixedstep=True, return_all=True)

Bases: object

__init__(direction_getter, tissue_classifier, seeds, affine, step_size, max_cross=None, maxlen=500, fixedstep=True, return_all=True)

Creates streamlines by using local fiber-tracking.

Parameters: direction_getter : instance of DirectionGetter Used to get directions for fiber tracking. tissue_classifier : instance of TissueClassifier Identifies endpoints and invalid points to inform tracking. seeds : array (N, 3) Points to seed the tracking. Seed points should be given in point space of the track (see affine). affine : array (4, 4) Coordinate space for the streamline point with respect to voxel indices of input data. This affine can contain scaling, rotational, and translational components but should not contain any shearing. An identity matrix can be used to generate streamlines in “voxel coordinates” as long as isotropic voxels were used to acquire the data. step_size : float Step size used for tracking. max_cross : int or None The maximum number of direction to track from each seed in crossing voxels. By default all initial directions are tracked. maxlen : int Maximum number of steps to track from seed. Used to prevent infinite loops. fixedstep : bool If true, a fixed stepsize is used, otherwise a variable step size is used. return_all : bool If true, return all generated streamlines, otherwise only streamlines reaching end points or exiting the image.

### ParticleFilteringTracking¶

class dipy.tracking.local.localtracking.ParticleFilteringTracking(direction_getter, tissue_classifier, seeds, affine, step_size, max_cross=None, maxlen=500, pft_back_tracking_dist=2, pft_front_tracking_dist=1, pft_max_trial=20, particle_count=15, return_all=True)
__init__(direction_getter, tissue_classifier, seeds, affine, step_size, max_cross=None, maxlen=500, pft_back_tracking_dist=2, pft_front_tracking_dist=1, pft_max_trial=20, particle_count=15, return_all=True)

A streamline generator using the particle filtering tractography method [R494].

Parameters: direction_getter : instance of ProbabilisticDirectionGetter Used to get directions for fiber tracking. tissue_classifier : instance of ConstrainedTissueClassifier Identifies endpoints and invalid points to inform tracking. seeds : array (N, 3) Points to seed the tracking. Seed points should be given in point space of the track (see affine). affine : array (4, 4) Coordinate space for the streamline point with respect to voxel indices of input data. This affine can contain scaling, rotational, and translational components but should not contain any shearing. An identity matrix can be used to generate streamlines in “voxel coordinates” as long as isotropic voxels were used to acquire the data. step_size : float Step size used for tracking. max_cross : int or None The maximum number of direction to track from each seed in crossing voxels. By default all initial directions are tracked. maxlen : int Maximum number of steps to track from seed. Used to prevent infinite loops. pft_back_tracking_dist : float Distance in mm to back track before starting the particle filtering tractography. The total particle filtering tractography distance is equal to back_tracking_dist + front_tracking_dist. By default this is set to 2 mm. pft_front_tracking_dist : float Distance in mm to run the particle filtering tractography after the the back track distance. The total particle filtering tractography distance is equal to back_tracking_dist + front_tracking_dist. By default this is set to 1 mm. pft_max_trial : int Maximum number of trial for the particle filtering tractography (Prevents infinite loops). particle_count : int Number of particles to use in the particle filter. return_all : bool If true, return all generated streamlines, otherwise only streamlines reaching end points or exiting the image.

References

 [R494] (1, 2) Girard, G., Whittingstall, K., Deriche, R., & Descoteaux, M. Towards quantitative connectivity analysis: reducing tractography biases. NeuroImage, 98, 266-278, 2014.

### local_tracker¶

dipy.tracking.local.localtracking.local_tracker()

Tracks one direction from a seed.

This function is the main workhorse of the LocalTracking class defined in dipy.tracking.local.localtracking.

Parameters: dg : DirectionGetter Used to choosing tracking directions. tc : TissueClassifier Used to check tissue type along path. seed_pos : array, float, 1d, (3,) First point of the (partial) streamline. first_step : array, float, 1d, (3,) Initial seeding direction. Used as prev_dir for selecting the step direction from the seed point. voxel_size : array, float, 1d, (3,) Size of voxels in the data set. streamline : array, float, 2d, (N, 3) Output of tracking will be put into this array. The length of this array, N, will set the maximum allowable length of the streamline. step_size : float Size of tracking steps in mm if fixed_step. fixedstep : bool If true, a fixed step_size is used, otherwise a variable step size is used. end : int Length of the tracked streamline tissue_class : TissueClass Ending state of the streamlines as determined by the TissueClassifier.

### pft_tracker¶

dipy.tracking.local.localtracking.pft_tracker()

Tracks one direction from a seed using the particle filtering algorithm.

This function is the main workhorse of the ParticleFilteringTracking class defined in dipy.tracking.local.localtracking.

Parameters: dg : DirectionGetter Used to choosing tracking directions. tc : TissueClassifier Used to check tissue type along path. seed_pos : array, float, 1d, (3,) First point of the (partial) streamline. first_step : array, float, 1d, (3,) Initial seeding direction. Used as prev_dir for selecting the step direction from the seed point. voxel_size : array, float, 1d, (3,) Size of voxels in the data set. streamline : array, float, 2d, (N, 3) Output of tracking will be put into this array. The length of this array, N, will set the maximum allowable length of the streamline. directions : array, float, 2d, (N, 3) Output of tracking directions will be put into this array. The length of this array, N, will set the maximum allowable length of the streamline. step_size : float Size of tracking steps in mm if fixed_step. pft_max_nbr_back_steps : int Number of tracking steps to back track before starting the particle filtering tractography. pft_max_nbr_front_steps : int Number of additional tracking steps to track. pft_max_trials : int Maximum number of trials for the particle filtering tractography (Prevents infinite loops). particle_count : int Number of particles to use in the particle filter. particle_paths : array, float, 4d, (2, particle_count, pft_max_steps, 3) Temporary array for paths followed by all particles. particle_dirs : array, float, 4d, (2, particle_count, pft_max_steps, 3) Temporary array for directions followed by particles. particle_weights : array, float, 1d (particle_count) Temporary array for the weights of particles. particle_steps : array, float, (2, particle_count) Temporary array for the number of steps of particles. particle_tissue_classes : array, float, (2, particle_count) Temporary array for the tissue classes of particles. end : int Length of the tracked streamline tissue_class : TissueClass Ending state of the streamlines as determined by the TissueClassifier.

### xrange¶

dipy.tracking.metrics.xrange

alias of range

### arbitrarypoint¶

dipy.tracking.metrics.arbitrarypoint(xyz, distance)

Select an arbitrary point along distance on the track (curve)

Parameters: xyz : array-like shape (N,3) array representing x,y,z of N points in a track distance : float float representing distance travelled from the xyz[0] point of the curve along the curve. ap : array shape (3,) Arbitrary point of line, such that, if the arbitrary point is not a point in xyz, then we take the interpolation between the two nearest xyz points. If xyz is empty, return a ValueError

Examples

>>> import numpy as np
>>> from dipy.tracking.metrics import arbitrarypoint, length
>>> theta=np.pi*np.linspace(0,1,100)
>>> x=np.cos(theta)
>>> y=np.sin(theta)
>>> z=0*x
>>> xyz=np.vstack((x,y,z)).T
>>> ap=arbitrarypoint(xyz,length(xyz)/3)


### bytes¶

dipy.tracking.metrics.bytes(xyz)

Size of track in bytes.

Parameters: xyz : array-like shape (N,3) Array representing x,y,z of N points in a track. b : int Number of bytes.

### center_of_mass¶

dipy.tracking.metrics.center_of_mass(xyz)

Center of mass of streamline

Parameters: xyz : array-like shape (N,3) array representing x,y,z of N points in a track com : array shape (3,) center of mass of streamline

Examples

>>> from dipy.tracking.metrics import center_of_mass
>>> center_of_mass([])
Traceback (most recent call last):
...
ValueError: xyz array cannot be empty
>>> center_of_mass([[1,1,1]])
array([ 1.,  1.,  1.])
>>> xyz = np.array([[0,0,0],[1,1,1],[2,2,2]])
>>> center_of_mass(xyz)
array([ 1.,  1.,  1.])


### downsample¶

dipy.tracking.metrics.downsample(xyz, n_pols=3)

downsample for a specific number of points along the curve/track

Uses the length of the curve. It works in a similar fashion to midpoint and arbitrarypoint but it also reduces the number of segments of a track.

Parameters: xyz : array-like shape (N,3) array representing x,y,z of N points in a track n_pol : int integer representing number of points (poles) we need along the curve. xyz2 : array shape (M,3) array representing x,y,z of M points that where extrapolated. M should be equal to n_pols

Examples

>>> import numpy as np
>>> # a semi-circle
>>> theta=np.pi*np.linspace(0,1,100)
>>> x=np.cos(theta)
>>> y=np.sin(theta)
>>> z=0*x
>>> xyz=np.vstack((x,y,z)).T
>>> xyz2=downsample(xyz,3)
>>> # a cosine
>>> x=np.pi*np.linspace(0,1,100)
>>> y=np.cos(theta)
>>> z=0*y
>>> xyz=np.vstack((x,y,z)).T
>>> _= downsample(xyz,3)
>>> len(xyz2)
3
>>> xyz3=downsample(xyz,10)
>>> len(xyz3)
10


### endpoint¶

dipy.tracking.metrics.endpoint(xyz)
Parameters: xyz : array, shape(N,3) Track. ep : array, shape(3,) First track point.

Examples

>>> from dipy.tracking.metrics import endpoint
>>> import numpy as np
>>> theta=np.pi*np.linspace(0,1,100)
>>> x=np.cos(theta)
>>> y=np.sin(theta)
>>> z=0*x
>>> xyz=np.vstack((x,y,z)).T
>>> ep=endpoint(xyz)
>>> ep.any()==xyz[-1].any()
True


### frenet_serret¶

dipy.tracking.metrics.frenet_serret(xyz)

Frenet-Serret Space Curve Invariants

Calculates the 3 vector and 2 scalar invariants of a space curve defined by vectors r = (x,y,z). If z is omitted (i.e. the array xyz has shape (N,2)), then the curve is only 2D (planar), but the equations are still valid.

In the following equations the prime ($$'$$) indicates differentiation with respect to the parameter $$s$$ of a parametrised curve $$\mathbf{r}(s)$$.

• $$\mathbf{T}=\mathbf{r'}/|\mathbf{r'}|\qquad$$ (Tangent vector)}
• $$\mathbf{N}=\mathbf{T'}/|\mathbf{T'}|\qquad$$ (Normal vector)
• $$\mathbf{B}=\mathbf{T}\times\mathbf{N}\qquad$$ (Binormal vector)
• $$\kappa=|\mathbf{T'}|\qquad$$ (Curvature)
• $$\mathrm{\tau}=-\mathbf{B'}\cdot\mathbf{N}$$ (Torsion)
Parameters: xyz : array-like shape (N,3) array representing x,y,z of N points in a track T : array shape (N,3) array representing the tangent of the curve xyz N : array shape (N,3) array representing the normal of the curve xyz B : array shape (N,3) array representing the binormal of the curve xyz k : array shape (N,1) array representing the curvature of the curve xyz t : array shape (N,1) array representing the torsion of the curve xyz

Examples

Create a helix and calculate its tangent, normal, binormal, curvature and torsion

>>> from dipy.tracking import metrics as tm
>>> import numpy as np
>>> theta = 2*np.pi*np.linspace(0,2,100)
>>> x=np.cos(theta)
>>> y=np.sin(theta)
>>> z=theta/(2*np.pi)
>>> xyz=np.vstack((x,y,z)).T
>>> T,N,B,k,t=tm.frenet_serret(xyz)


### generate_combinations¶

dipy.tracking.metrics.generate_combinations(items, n)

Combine sets of size n from items

Parameters: items : sequence n : int ic : iterator

Examples

>>> from dipy.tracking.metrics import generate_combinations
>>> ic=generate_combinations(range(3),2)
>>> for i in ic: print(i)
[0, 1]
[0, 2]
[1, 2]


### inside_sphere¶

dipy.tracking.metrics.inside_sphere(xyz, center, radius)

If any point of the track is inside a sphere of a specified center and radius return True otherwise False. Mathematicaly this can be simply described by $$|x-c|\le r$$ where $$x$$ a point $$c$$ the center of the sphere and $$r$$ the radius of the sphere.

Parameters: xyz : array, shape (N,3) representing x,y,z of the N points of the track center : array, shape (3,) center of the sphere radius : float radius of the sphere tf : {True,False} Whether point is inside sphere.

Examples

>>> from dipy.tracking.metrics import inside_sphere
>>> line=np.array(([0,0,0],[1,1,1],[2,2,2]))
>>> sph_cent=np.array([1,1,1])
True


### inside_sphere_points¶

dipy.tracking.metrics.inside_sphere_points(xyz, center, radius)

If a track intersects with a sphere of a specified center and radius return the points that are inside the sphere otherwise False. Mathematicaly this can be simply described by $$|x-c| \le r$$ where $$x$$ a point $$c$$ the center of the sphere and $$r$$ the radius of the sphere.

Parameters: xyz : array, shape (N,3) representing x,y,z of the N points of the track center : array, shape (3,) center of the sphere radius : float radius of the sphere xyzn : array, shape(M,3) array representing x,y,z of the M points inside the sphere

Examples

>>> from dipy.tracking.metrics import inside_sphere_points
>>> line=np.array(([0,0,0],[1,1,1],[2,2,2]))
>>> sph_cent=np.array([1,1,1])
array([[1, 1, 1]])


### intersect_sphere¶

dipy.tracking.metrics.intersect_sphere(xyz, center, radius)

If any segment of the track is intersecting with a sphere of specific center and radius return True otherwise False

Parameters: xyz : array, shape (N,3) representing x,y,z of the N points of the track center : array, shape (3,) center of the sphere radius : float radius of the sphere tf : {True, False} True if track xyz intersects sphere >>> from dipy.tracking.metrics import intersect_sphere  >>> line=np.array(([0,0,0],[1,1,1],[2,2,2]))  >>> sph_cent=np.array([1,1,1])  >>> sph_radius = 1  >>> intersect_sphere(line,sph_cent,sph_radius)  True

Notes

The ray to sphere intersection method used here is similar with http://local.wasp.uwa.edu.au/~pbourke/geometry/sphereline/ http://local.wasp.uwa.edu.au/~pbourke/geometry/sphereline/source.cpp we just applied it for every segment neglecting the intersections where the intersecting points are not inside the segment

### length¶

dipy.tracking.metrics.length(xyz, along=False)

Euclidean length of track line

This will give length in mm if tracks are expressed in world coordinates.

Parameters: xyz : array-like shape (N,3) array representing x,y,z of N points in a track along : bool, optional If True, return array giving cumulative length along track, otherwise (default) return scalar giving total length. L : scalar or array shape (N-1,) scalar in case of along == False, giving total length, array if along == True, giving cumulative lengths.

Examples

>>> from dipy.tracking.metrics import length
>>> xyz = np.array([[1,1,1],[2,3,4],[0,0,0]])
>>> expected_lens = np.sqrt([1+2**2+3**2, 2**2+3**2+4**2])
>>> length(xyz) == expected_lens.sum()
True
>>> len_along = length(xyz, along=True)
>>> np.allclose(len_along, expected_lens.cumsum())
True
>>> length([])
0
>>> length([[1, 2, 3]])
0
>>> length([], along=True)
array([0])


### longest_track_bundle¶

dipy.tracking.metrics.longest_track_bundle(bundle, sort=False)

Return longest track or length sorted track indices in bundle

If sort == True, return the indices of the sorted tracks in the bundle, otherwise return the longest track.

Parameters: bundle : sequence of tracks as arrays, shape (N1,3) ... (Nm,3) sort : bool, optional If False (default) return longest track. If True, return length sorted indices for tracks in bundle longest_or_indices : array longest track - shape (N,3) - (if sort is False), or indices of length sorted tracks (if sort is True)

Examples

>>> from dipy.tracking.metrics import longest_track_bundle
>>> import numpy as np
>>> bundle = [np.array([[0,0,0],[2,2,2]]),np.array([[0,0,0],[4,4,4]])]
>>> longest_track_bundle(bundle)
array([[0, 0, 0],
[4, 4, 4]])
>>> longest_track_bundle(bundle, True)
array([0, 1]...)


### magn¶

dipy.tracking.metrics.magn(xyz, n=1)

magnitude of vector

### mean_curvature¶

dipy.tracking.metrics.mean_curvature(xyz)

Calculates the mean curvature of a curve

Parameters: xyz : array-like shape (N,3) array representing x,y,z of N points in a curve m : float Mean curvature.

Examples

Create a straight line and a semi-circle and print their mean curvatures

>>> from dipy.tracking import metrics as tm
>>> import numpy as np
>>> x=np.linspace(0,1,100)
>>> y=0*x
>>> z=0*x
>>> xyz=np.vstack((x,y,z)).T
>>> m=tm.mean_curvature(xyz) #mean curvature straight line
>>> theta=np.pi*np.linspace(0,1,100)
>>> x=np.cos(theta)
>>> y=np.sin(theta)
>>> z=0*x
>>> xyz=np.vstack((x,y,z)).T
>>> _= tm.mean_curvature(xyz) #mean curvature for semi-circle


### mean_orientation¶

dipy.tracking.metrics.mean_orientation(xyz)

Calculates the mean orientation of a curve

Parameters: xyz : array-like shape (N,3) array representing x,y,z of N points in a curve m : float Mean orientation.

### midpoint¶

dipy.tracking.metrics.midpoint(xyz)

Midpoint of track

Parameters: xyz : array-like shape (N,3) array representing x,y,z of N points in a track mp : array shape (3,) Middle point of line, such that, if L is the line length then np is the point such that the length xyz[0] to mp and from mp to xyz[-1] is L/2. If the middle point is not a point in xyz, then we take the interpolation between the two nearest xyz points. If xyz is empty, return a ValueError

Examples

>>> from dipy.tracking.metrics import midpoint
>>> midpoint([])
Traceback (most recent call last):
...
ValueError: xyz array cannot be empty
>>> midpoint([[1, 2, 3]])
array([1, 2, 3])
>>> xyz = np.array([[1,1,1],[2,3,4]])
>>> midpoint(xyz)
array([ 1.5,  2. ,  2.5])
>>> xyz = np.array([[0,0,0],[1,1,1],[2,2,2]])
>>> midpoint(xyz)
array([ 1.,  1.,  1.])
>>> xyz = np.array([[0,0,0],[1,0,0],[3,0,0]])
>>> midpoint(xyz)
array([ 1.5,  0. ,  0. ])
>>> xyz = np.array([[0,9,7],[1,9,7],[3,9,7]])
>>> midpoint(xyz)
array([ 1.5,  9. ,  7. ])


### midpoint2point¶

dipy.tracking.metrics.midpoint2point(xyz, p)

Calculate distance from midpoint of a curve to arbitrary point p

Parameters: xyz : array-like shape (N,3) array representing x,y,z of N points in a track p : array shape (3,) array representing an arbitrary point with x,y,z coordinates in space. d : float a float number representing Euclidean distance

Examples

>>> import numpy as np
>>> from dipy.tracking.metrics import midpoint2point, midpoint
>>> theta=np.pi*np.linspace(0,1,100)
>>> x=np.cos(theta)
>>> y=np.sin(theta)
>>> z=0*x
>>> xyz=np.vstack((x,y,z)).T
>>> dist=midpoint2point(xyz,np.array([0,0,0]))


### principal_components¶

dipy.tracking.metrics.principal_components(xyz)

We use PCA to calculate the 3 principal directions for a track

Parameters: xyz : array-like shape (N,3) array representing x,y,z of N points in a track va : array_like eigenvalues ve : array_like eigenvectors

Examples

>>> import numpy as np
>>> from dipy.tracking.metrics import principal_components
>>> theta=np.pi*np.linspace(0,1,100)
>>> x=np.cos(theta)
>>> y=np.sin(theta)
>>> z=0*x
>>> xyz=np.vstack((x,y,z)).T
>>> va, ve = principal_components(xyz)
>>> np.allclose(va, [0.51010101, 0.09883545, 0])
True


### setup_test¶

dipy.tracking.metrics.setup_test()

Set numpy print options to “legacy” for new versions of numpy

If imported into a file, nosetest will run this before any doctests.

References

### splev¶

dipy.tracking.metrics.splev(x, tck, der=0, ext=0)

Evaluate a B-spline or its derivatives.

Given the knots and coefficients of a B-spline representation, evaluate the value of the smoothing polynomial and its derivatives. This is a wrapper around the FORTRAN routines splev and splder of FITPACK.

Parameters: x : array_like An array of points at which to return the value of the smoothed spline or its derivatives. If tck was returned from splprep, then the parameter values, u should be given. tck : 3-tuple or a BSpline object If a tuple, then it should be a sequence of length 3 returned by splrep or splprep containing the knots, coefficients, and degree of the spline. (Also see Notes.) der : int, optional The order of derivative of the spline to compute (must be less than or equal to k). ext : int, optional Controls the value returned for elements of x not in the interval defined by the knot sequence. if ext=0, return the extrapolated value. if ext=1, return 0 if ext=2, raise a ValueError if ext=3, return the boundary value. The default value is 0. y : ndarray or list of ndarrays An array of values representing the spline function evaluated at the points in x. If tck was returned from splprep, then this is a list of arrays representing the curve in N-dimensional space.

splprep, splrep, sproot, spalde, splint, bisplrep, bisplev, BSpline

Notes

Manipulating the tck-tuples directly is not recommended. In new code, prefer using BSpline objects.

References

 [R495] C. de Boor, “On calculating with b-splines”, J. Approximation Theory, 6, p.50-62, 1972.
 [R496] M. G. Cox, “The numerical evaluation of b-splines”, J. Inst. Maths Applics, 10, p.134-149, 1972.
 [R497] P. Dierckx, “Curve and surface fitting with splines”, Monographs on Numerical Analysis, Oxford University Press, 1993.

### spline¶

dipy.tracking.metrics.spline(xyz, s=3, k=2, nest=-1)

Generate B-splines as documented in http://www.scipy.org/Cookbook/Interpolation

The scipy.interpolate packages wraps the netlib FITPACK routines (Dierckx) for calculating smoothing splines for various kinds of data and geometries. Although the data is evenly spaced in this example, it need not be so to use this routine.

Parameters: xyz : array, shape (N,3) array representing x,y,z of N points in 3d space s : float, optional A smoothing condition. The amount of smoothness is determined by satisfying the conditions: sum((w * (y - g))**2,axis=0) <= s where g(x) is the smoothed interpolation of (x,y). The user can use s to control the tradeoff between closeness and smoothness of fit. Larger satisfying the conditions: sum((w * (y - g))**2,axis=0) <= s where g(x) is the smoothed interpolation of (x,y). The user can use s to control the tradeoff between closeness and smoothness of fit. Larger s means more smoothing while smaller values of s indicate less smoothing. Recommended values of s depend on the weights, w. If the weights represent the inverse of the standard-deviation of y, then a: good s value should be found in the range (m-sqrt(2*m),m+sqrt(2*m)) where m is the number of datapoints in x, y, and w. k : int, optional Degree of the spline. Cubic splines are recommended. Even values of k should be avoided especially with a small s-value. for the same set of data. If task=-1 find the weighted least square spline for a given set of knots, t. nest : None or int, optional An over-estimate of the total number of knots of the spline to help in determining the storage space. None results in value m+2*k. -1 results in m+k+1. Always large enough is nest=m+k+1. Default is -1. xyzn : array, shape (M,3) array representing x,y,z of the M points inside the sphere

scipy.interpolate.splprep, scipy.interpolate.splev

Examples

>>> import numpy as np
>>> t=np.linspace(0,1.75*2*np.pi,100)# make ascending spiral in 3-space
>>> x = np.sin(t)
>>> y = np.cos(t)
>>> z = t
>>> x+= np.random.normal(scale=0.1, size=x.shape) # add noise
>>> y+= np.random.normal(scale=0.1, size=y.shape)
>>> z+= np.random.normal(scale=0.1, size=z.shape)
>>> xyz=np.vstack((x,y,z)).T
>>> xyzn=spline(xyz,3,2,-1)
>>> len(xyzn) > len(xyz)
True


### splprep¶

dipy.tracking.metrics.splprep(x, w=None, u=None, ub=None, ue=None, k=3, task=0, s=None, t=None, full_output=0, nest=None, per=0, quiet=1)

Find the B-spline representation of an N-dimensional curve.

Given a list of N rank-1 arrays, x, which represent a curve in N-dimensional space parametrized by u, find a smooth approximating spline curve g(u). Uses the FORTRAN routine parcur from FITPACK.

Parameters: x : array_like A list of sample vector arrays representing the curve. w : array_like, optional Strictly positive rank-1 array of weights the same length as x[0]. The weights are used in computing the weighted least-squares spline fit. If the errors in the x values have standard-deviation given by the vector d, then w should be 1/d. Default is ones(len(x[0])). u : array_like, optional An array of parameter values. If not given, these values are calculated automatically as M = len(x[0]), where v[0] = 0 v[i] = v[i-1] + distance(x[i], x[i-1]) u[i] = v[i] / v[M-1] ub, ue : int, optional The end-points of the parameters interval. Defaults to u[0] and u[-1]. k : int, optional Degree of the spline. Cubic splines are recommended. Even values of k should be avoided especially with a small s-value. 1 <= k <= 5, default is 3. task : int, optional If task==0 (default), find t and c for a given smoothing factor, s. If task==1, find t and c for another value of the smoothing factor, s. There must have been a previous call with task=0 or task=1 for the same set of data. If task=-1 find the weighted least square spline for a given set of knots, t. s : float, optional A smoothing condition. The amount of smoothness is determined by satisfying the conditions: sum((w * (y - g))**2,axis=0) <= s, where g(x) is the smoothed interpolation of (x,y). The user can use s to control the trade-off between closeness and smoothness of fit. Larger s means more smoothing while smaller values of s indicate less smoothing. Recommended values of s depend on the weights, w. If the weights represent the inverse of the standard-deviation of y, then a good s value should be found in the range (m-sqrt(2*m),m+sqrt(2*m)), where m is the number of data points in x, y, and w. t : int, optional The knots needed for task=-1. full_output : int, optional If non-zero, then return optional outputs. nest : int, optional An over-estimate of the total number of knots of the spline to help in determining the storage space. By default nest=m/2. Always large enough is nest=m+k+1. per : int, optional If non-zero, data points are considered periodic with period x[m-1] - x[0] and a smooth periodic spline approximation is returned. Values of y[m-1] and w[m-1] are not used. quiet : int, optional Non-zero to suppress messages. This parameter is deprecated; use standard Python warning filters instead. tck : tuple (t,c,k) a tuple containing the vector of knots, the B-spline coefficients, and the degree of the spline. u : array An array of the values of the parameter. fp : float The weighted sum of squared residuals of the spline approximation. ier : int An integer flag about splrep success. Success is indicated if ier<=0. If ier in [1,2,3] an error occurred but was not raised. Otherwise an error is raised. msg : str A message corresponding to the integer flag, ier.

splrep, splev, sproot, spalde, splint, bisplrep, bisplev, UnivariateSpline, BivariateSpline, BSpline, make_interp_spline

Notes

See splev for evaluation of the spline and its derivatives. The number of dimensions N must be smaller than 11.

References

 [R498] P. Dierckx, “Algorithms for smoothing data with periodic and parametric splines, Computer Graphics and Image Processing”, 20 (1982) 171-184.
 [R499] P. Dierckx, “Algorithms for smoothing data with periodic and parametric splines”, report tw55, Dept. Computer Science, K.U.Leuven, 1981.
 [R500] P. Dierckx, “Curve and surface fitting with splines”, Monographs on Numerical Analysis, Oxford University Press, 1993.

Examples

Generate a discretization of a limacon curve in the polar coordinates:

>>> phi = np.linspace(0, 2.*np.pi, 40)
>>> r = 0.5 + np.cos(phi)         # polar coords
>>> x, y = r * np.cos(phi), r * np.sin(phi)    # convert to cartesian


And interpolate:

>>> from scipy.interpolate import splprep, splev
>>> tck, u = splprep([x, y], s=0)
>>> new_points = splev(u, tck)


Notice that (i) we force interpolation by using s=0, (ii) the parameterization, u, is generated automatically. Now plot the result:

>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots()
>>> ax.plot(x, y, 'ro')
>>> ax.plot(new_points[0], new_points[1], 'r-')
>>> plt.show()


### startpoint¶

dipy.tracking.metrics.startpoint(xyz)

First point of the track

Parameters: xyz : array, shape(N,3) Track. sp : array, shape(3,) First track point.

Examples

>>> from dipy.tracking.metrics import startpoint
>>> import numpy as np
>>> theta=np.pi*np.linspace(0,1,100)
>>> x=np.cos(theta)
>>> y=np.sin(theta)
>>> z=0*x
>>> xyz=np.vstack((x,y,z)).T
>>> sp=startpoint(xyz)
>>> sp.any()==xyz[0].any()
True


### winding¶

dipy.tracking.metrics.winding(xyz)

Total turning angle projected.

Project space curve to best fitting plane. Calculate the cumulative signed angle between each line segment and the previous one.

Parameters: xyz : array-like shape (N,3) Array representing x,y,z of N points in a track. a : scalar Total turning angle in degrees.

### ArraySequence¶

class dipy.tracking.streamline.ArraySequence(iterable=None, buffer_size=4)

Bases: object

Sequence of ndarrays having variable first dimension sizes.

This is a container that can store multiple ndarrays where each ndarray might have a different first dimension size but a common size for the remaining dimensions.

More generally, an instance of ArraySequence of length $$N$$ is composed of $$N$$ ndarrays of shape $$(d_1, d_2, ... d_D)$$ where $$d_1$$ can vary in length between arrays but $$(d_2, ..., d_D)$$ have to be the same for every ndarray.

Attributes

 common_shape Matching shape of the elements in this array sequence. data Elements in this array sequence. is_array_sequence total_nb_rows Total number of rows in this array sequence.

Methods

 append(element[, cache_build]) Appends element to this array sequence. copy() Creates a copy of this ArraySequence object. extend(elements) Appends all elements to this array sequence. finalize_append() Finalize process of appending several elements to self load(filename) Loads a ArraySequence object from a .npz file. save(filename) Saves this ArraySequence object to a .npz file. shrink_data()
__init__(iterable=None, buffer_size=4)

Initialize array sequence instance

Parameters: iterable : None or iterable or ArraySequence, optional If None, create an empty ArraySequence object. If iterable, create a ArraySequence object initialized from array-like objects yielded by the iterable. If ArraySequence, create a view (no memory is allocated). For an actual copy use copy() instead. buffer_size : float, optional Size (in Mb) for memory allocation when iterable is a generator.
append(element, cache_build=False)

Appends element to this array sequence.

Append can be a lot faster if it knows that it is appending several elements instead of a single element. In that case it can cache the parameters it uses between append operations, in a “build cache”. To tell append to do this, use cache_build=True. If you use cache_build=True, you need to finalize the append operations with finalize_append().

Parameters: element : ndarray Element to append. The shape must match already inserted elements shape except for the first dimension. cache_build : {False, True} Whether to save the build cache from this append routine. If True, append can assume it is the only player updating self, and the caller must finalize self after all append operations, with self.finalize_append(). None

Notes

If you need to add multiple elements you should consider ArraySequence.extend.

common_shape

Matching shape of the elements in this array sequence.

copy()

Creates a copy of this ArraySequence object.

Returns: seq_copy : ArraySequence instance Copy of self.

Notes

We do not simply deepcopy this object because we have a chance to use less memory. For example, if the array sequence being copied is the result of a slicing operation on an array sequence.

data

Elements in this array sequence.

extend(elements)

Appends all elements to this array sequence.

Parameters: elements : iterable of ndarrays or ArraySequence object If iterable of ndarrays, each ndarray will be concatenated along the first dimension then appended to the data of this ArraySequence. If ArraySequence object, its data are simply appended to the data of this ArraySequence. None

Notes

The shape of the elements to be added must match the one of the data of this ArraySequence except for the first dimension.

finalize_append()

Finalize process of appending several elements to self

append() can be a lot faster if it knows that it is appending several elements instead of a single element. To tell the append method this is the case, use cache_build=True. This method finalizes the series of append operations after a call to append() with cache_build=True.

is_array_sequence
classmethod load(filename)

Loads a ArraySequence object from a .npz file.

save(filename)

Saves this ArraySequence object to a .npz file.

shrink_data()
total_nb_rows

Total number of rows in this array sequence.

### LooseVersion¶

class dipy.tracking.streamline.LooseVersion(vstring=None)

Bases: distutils.version.Version

Version numbering for anarchists and software realists. Implements the standard interface for version number classes as described above. A version number consists of a series of numbers, separated by either periods or strings of letters. When comparing version numbers, the numeric components will be compared numerically, and the alphabetic components lexically. The following are all valid version numbers, in no particular order:

1.5.1 1.5.2b2 161 3.10a 8.02 3.4j 1996.07.12 3.2.pl0 3.1.1.6 2g6 11g 0.960923 2.2beta29 1.13++ 5.5.kw 2.0b1pl0

In fact, there is no such thing as an invalid version number under this scheme; the rules for comparison are simple and predictable, but may not always give the results you want (for some definition of “want”).

Methods

 parse(vstring)
__init__(vstring=None)
component_re = re.compile('(\\d+ | [a-z]+ | \\.)', re.VERBOSE)
parse(vstring)

### Streamlines¶

class dipy.tracking.streamline.Streamlines(*args, **kwargs)

Bases: nibabel.streamlines.array_sequence.ArraySequence

Attributes

 common_shape Matching shape of the elements in this array sequence. data Elements in this array sequence. is_array_sequence total_nb_rows Total number of rows in this array sequence.

Methods

 append(element[, cache_build]) Appends element to this array sequence. copy() Creates a copy of this ArraySequence object. extend(elements) Appends all elements to this array sequence. finalize_append() Finalize process of appending several elements to self append() can be a lot faster if it knows that it is appending several elements instead of a single element. load(filename) Loads a ArraySequence object from a .npz file. save(filename) Saves this ArraySequence object to a .npz file. shrink_data()
__init__(*args, **kwargs)
append(element, cache_build=False)

Appends element to this array sequence. Append can be a lot faster if it knows that it is appending several elements instead of a single element. In that case it can cache the parameters it uses between append operations, in a “build cache”. To tell append to do this, use cache_build=True. If you use cache_build=True, you need to finalize the append operations with finalize_append(). Parameters ———- element : ndarray

Element to append. The shape must match already inserted elements shape except for the first dimension.
cache_build : {False, True}
Whether to save the build cache from this append routine. If True, append can assume it is the only player updating self, and the caller must finalize self after all append operations, with self.finalize_append().

None Notes —– If you need to add multiple elements you should consider ArraySequence.extend.

extend(elements)

Appends all elements to this array sequence. Parameters ———- elements : iterable of ndarrays or ArraySequence object

If iterable of ndarrays, each ndarray will be concatenated along the first dimension then appended to the data of this ArraySequence. If ArraySequence object, its data are simply appended to the data of this ArraySequence.

None Notes —– The shape of the elements to be added must match the one of the data of this ArraySequence except for the first dimension.

finalize_append()

Finalize process of appending several elements to self append() can be a lot faster if it knows that it is appending several elements instead of a single element. To tell the append method this is the case, use cache_build=True. This method finalizes the series of append operations after a call to append() with cache_build=True.

### apply_affine¶

dipy.tracking.streamline.apply_affine(aff, pts)

Apply affine matrix aff to points pts

Returns result of application of aff to the right of pts. The coordinate dimension of pts should be the last.

For the 3D case, aff will be shape (4,4) and pts will have final axis length 3 - maybe it will just be N by 3. The return value is the transformed points, in this case:

res = np.dot(aff[:3,:3], pts.T) + aff[:3,3:4]
transformed_pts = res.T


This routine is more general than 3D, in that aff can have any shape (N,N), and pts can have any shape, as long as the last dimension is for the coordinates, and is therefore length N-1.

Parameters: aff : (N, N) array-like Homogenous affine, for 3D points, will be 4 by 4. Contrary to first appearance, the affine will be applied on the left of pts. pts : (..., N-1) array-like Points, where the last dimension contains the coordinates of each point. For 3D, the last dimension will be length 3. transformed_pts : (..., N-1) array transformed points

Examples

>>> aff = np.array([[0,2,0,10],[3,0,0,11],[0,0,4,12],[0,0,0,1]])
>>> pts = np.array([[1,2,3],[2,3,4],[4,5,6],[6,7,8]])
>>> apply_affine(aff, pts)
array([[14, 14, 24],
[16, 17, 28],
[20, 23, 36],
[24, 29, 44]]...)


Just to show that in the simple 3D case, it is equivalent to:

>>> (np.dot(aff[:3,:3], pts.T) + aff[:3,3:4]).T
array([[14, 14, 24],
[16, 17, 28],
[20, 23, 36],
[24, 29, 44]]...)


But pts can be a more complicated shape:

>>> pts = pts.reshape((2,2,3))
>>> apply_affine(aff, pts)
array([[[14, 14, 24],
[16, 17, 28]],

[[20, 23, 36],
[24, 29, 44]]]...)


### cdist¶

dipy.tracking.streamline.cdist(XA, XB, metric='euclidean', p=None, V=None, VI=None, w=None)

Computes distance between each pair of the two collections of inputs.

See Notes for common calling conventions.

Parameters: XA : ndarray An $$m_A$$ by $$n$$ array of $$m_A$$ original observations in an $$n$$-dimensional space. Inputs are converted to float type. XB : ndarray An $$m_B$$ by $$n$$ array of $$m_B$$ original observations in an $$n$$-dimensional space. Inputs are converted to float type. metric : str or callable, optional The distance metric to use. If a string, the distance function can be ‘braycurtis’, ‘canberra’, ‘chebyshev’, ‘cityblock’, ‘correlation’, ‘cosine’, ‘dice’, ‘euclidean’, ‘hamming’, ‘jaccard’, ‘kulsinski’, ‘mahalanobis’, ‘matching’, ‘minkowski’, ‘rogerstanimoto’, ‘russellrao’, ‘seuclidean’, ‘sokalmichener’, ‘sokalsneath’, ‘sqeuclidean’, ‘wminkowski’, ‘yule’. p : double, optional The p-norm to apply Only for Minkowski, weighted and unweighted. Default: 2. w : ndarray, optional The weight vector. Only for weighted Minkowski. Mandatory V : ndarray, optional The variance vector Only for standardized Euclidean. Default: var(vstack([XA, XB]), axis=0, ddof=1) VI : ndarray, optional The inverse of the covariance matrix Only for Mahalanobis. Default: inv(cov(vstack([XA, XB]).T)).T Y : ndarray A $$m_A$$ by $$m_B$$ distance matrix is returned. For each $$i$$ and $$j$$, the metric dist(u=XA[i], v=XB[j]) is computed and stored in the $$ij$$ th entry. ValueError An exception is thrown if XA and XB do not have the same number of columns.

Notes

The following are common calling conventions:

1. Y = cdist(XA, XB, 'euclidean')

Computes the distance between $$m$$ points using Euclidean distance (2-norm) as the distance metric between the points. The points are arranged as $$m$$ $$n$$-dimensional row vectors in the matrix X.

2. Y = cdist(XA, XB, 'minkowski', p)

Computes the distances using the Minkowski distance $$||u-v||_p$$ ($$p$$-norm) where $$p \geq 1$$.

3. Y = cdist(XA, XB, 'cityblock')

Computes the city block or Manhattan distance between the points.

4. Y = cdist(XA, XB, 'seuclidean', V=None)

Computes the standardized Euclidean distance. The standardized Euclidean distance between two n-vectors u and v is

$\sqrt{\sum {(u_i-v_i)^2 / V[x_i]}}.$

V is the variance vector; V[i] is the variance computed over all the i’th components of the points. If not passed, it is automatically computed.

5. Y = cdist(XA, XB, 'sqeuclidean')

Computes the squared Euclidean distance $$||u-v||_2^2$$ between the vectors.

6. Y = cdist(XA, XB, 'cosine')

Computes the cosine distance between vectors u and v,

$1 - \frac{u \cdot v} {{||u||}_2 {||v||}_2}$

where $$||*||_2$$ is the 2-norm of its argument *, and $$u \cdot v$$ is the dot product of $$u$$ and $$v$$.

7. Y = cdist(XA, XB, 'correlation')

Computes the correlation distance between vectors u and v. This is

$1 - \frac{(u - \bar{u}) \cdot (v - \bar{v})} {{||(u - \bar{u})||}_2 {||(v - \bar{v})||}_2}$

where $$\bar{v}$$ is the mean of the elements of vector v, and $$x \cdot y$$ is the dot product of $$x$$ and $$y$$.

8. Y = cdist(XA, XB, 'hamming')

Computes the normalized Hamming distance, or the proportion of those vector elements between two n-vectors u and v which disagree. To save memory, the matrix X can be of type boolean.

9. Y = cdist(XA, XB, 'jaccard')

Computes the Jaccard distance between the points. Given two vectors, u and v, the Jaccard distance is the proportion of those elements u[i] and v[i] that disagree where at least one of them is non-zero.

10. Y = cdist(XA, XB, 'chebyshev')

Computes the Chebyshev distance between the points. The Chebyshev distance between two n-vectors u and v is the maximum norm-1 distance between their respective elements. More precisely, the distance is given by

$d(u,v) = \max_i {|u_i-v_i|}.$
1. Y = cdist(XA, XB, 'canberra')

Computes the Canberra distance between the points. The Canberra distance between two points u and v is

$d(u,v) = \sum_i \frac{|u_i-v_i|} {|u_i|+|v_i|}.$
1. Y = cdist(XA, XB, 'braycurtis')

Computes the Bray-Curtis distance between the points. The Bray-Curtis distance between two points u and v is

$d(u,v) = \frac{\sum_i (|u_i-v_i|)} {\sum_i (|u_i+v_i|)}$
1. Y = cdist(XA, XB, 'mahalanobis', VI=None)
Computes the Mahalanobis distance between the points. The Mahalanobis distance between two points u and v is $$\sqrt{(u-v)(1/V)(u-v)^T}$$ where $$(1/V)$$ (the VI variable) is the inverse covariance. If VI is not None, VI will be used as the inverse covariance matrix.
1. Y = cdist(XA, XB, 'yule')
Computes the Yule distance between the boolean vectors. (see yule function documentation)
1. Y = cdist(XA, XB, 'matching')
Synonym for ‘hamming’.
1. Y = cdist(XA, XB, 'dice')
Computes the Dice distance between the boolean vectors. (see dice function documentation)
1. Y = cdist(XA, XB, 'kulsinski')
Computes the Kulsinski distance between the boolean vectors. (see kulsinski function documentation)
1. Y = cdist(XA, XB, 'rogerstanimoto')
Computes the Rogers-Tanimoto distance between the boolean vectors. (see rogerstanimoto function documentation)
1. Y = cdist(XA, XB, 'russellrao')
Computes the Russell-Rao distance between the boolean vectors. (see russellrao function documentation)
1. Y = cdist(XA, XB, 'sokalmichener')
Computes the Sokal-Michener distance between the boolean vectors. (see sokalmichener function documentation)
1. Y = cdist(XA, XB, 'sokalsneath')
Computes the Sokal-Sneath distance between the vectors. (see sokalsneath function documentation)
1. Y = cdist(XA, XB, 'wminkowski')
Computes the weighted Minkowski distance between the vectors. (see wminkowski function documentation)
1. Y = cdist(XA, XB, f)

Computes the distance between all pairs of vectors in X using the user supplied 2-arity function f. For example, Euclidean distance between the vectors could be computed as follows:

dm = cdist(XA, XB, lambda u, v: np.sqrt(((u-v)**2).sum()))


Note that you should avoid passing a reference to one of the distance functions defined in this library. For example,:

dm = cdist(XA, XB, sokalsneath)


would calculate the pair-wise distances between the vectors in X using the Python function sokalsneath. This would result in sokalsneath being called $${n \choose 2}$$ times, which is inefficient. Instead, the optimized C version is more efficient, and we call it using the following syntax:

dm = cdist(XA, XB, 'sokalsneath')


Examples

Find the Euclidean distances between four 2-D coordinates:

>>> from scipy.spatial import distance
>>> coords = [(35.0456, -85.2672),
...           (35.1174, -89.9711),
...           (35.9728, -83.9422),
...           (36.1667, -86.7833)]
>>> distance.cdist(coords, coords, 'euclidean')
array([[ 0.    ,  4.7044,  1.6172,  1.8856],
[ 4.7044,  0.    ,  6.0893,  3.3561],
[ 1.6172,  6.0893,  0.    ,  2.8477],
[ 1.8856,  3.3561,  2.8477,  0.    ]])


Find the Manhattan distance from a 3-D point to the corners of the unit cube:

>>> a = np.array([[0, 0, 0],
...               [0, 0, 1],
...               [0, 1, 0],
...               [0, 1, 1],
...               [1, 0, 0],
...               [1, 0, 1],
...               [1, 1, 0],
...               [1, 1, 1]])
>>> b = np.array([[ 0.1,  0.2,  0.4]])
>>> distance.cdist(a, b, 'cityblock')
array([[ 0.7],
[ 0.9],
[ 1.3],
[ 1.5],
[ 1.5],
[ 1.7],
[ 2.1],
[ 2.3]])


### center_streamlines¶

dipy.tracking.streamline.center_streamlines(streamlines)

Move streamlines to the origin

Parameters: streamlines : list List of 2D ndarrays of shape[-1]==3 new_streamlines : list List of 2D ndarrays of shape[-1]==3 inv_shift : ndarray Translation in x,y,z to go back in the initial position

### compress_streamlines¶

dipy.tracking.streamline.compress_streamlines()

Compress streamlines by linearization as in [Presseau15].

The compression consists in merging consecutive segments that are nearly collinear. The merging is achieved by removing the point the two segments have in common.

The linearization process [Presseau15] ensures that every point being removed are within a certain margin (in mm) of the resulting streamline. Recommendations for setting this margin can be found in [Presseau15] (in which they called it tolerance error).

The compression also ensures that two consecutive points won’t be too far from each other (precisely less or equal than max_segment_lengthmm). This is a tradeoff to speed up the linearization process [Rheault15]. A low value will result in a faster linearization but low compression, whereas a high value will result in a slower linearization but high compression.

Parameters: streamlines : one or a list of array-like of shape (N,3) Array representing x,y,z of N points in a streamline. tol_error : float (optional) Tolerance error in mm (default: 0.01). A rule of thumb is to set it to 0.01mm for deterministic streamlines and 0.1mm for probabilitic streamlines. max_segment_length : float (optional) Maximum length in mm of any given segment produced by the compression. The default is 10mm. (In [Presseau15], they used a value of np.inf). compressed_streamlines : one or a list of array-like Results of the linearization process.

Notes

Be aware that compressed streamlines have variable step sizes. One needs to be careful when computing streamlines-based metrics [Houde15].

References

 [Presseau15] Presseau C. et al., A new compression format for fiber tracking datasets, NeuroImage, no 109, 73-83, 2015.
 [Rheault15] Rheault F. et al., Real Time Interaction with Millions of Streamlines, ISMRM, 2015.
 [Houde15] Houde J.-C. et al. How to Avoid Biased Streamlines-Based Metrics for Streamlines with Variable Step Sizes, ISMRM, 2015.

Examples

>>> from dipy.tracking.streamline import compress_streamlines
>>> import numpy as np
>>> # One streamline: a wiggling line
>>> rng = np.random.RandomState(42)
>>> streamline = np.linspace(0, 10, 100*3).reshape((100, 3))
>>> streamline += 0.2 * rng.rand(100, 3)
>>> c_streamline = compress_streamlines(streamline, tol_error=0.2)
>>> len(streamline)
100
>>> len(c_streamline)
10
>>> # Multiple streamlines
>>> streamlines = [streamline, streamline[::2]]
>>> c_streamlines = compress_streamlines(streamlines, tol_error=0.2)
>>> [len(s) for s in streamlines]
[100, 50]
>>> [len(s) for s in c_streamlines]
[10, 7]


### deepcopy¶

dipy.tracking.streamline.deepcopy(x, memo=None, _nil=[])

Deep copy operation on arbitrary Python objects.

### deform_streamlines¶

dipy.tracking.streamline.deform_streamlines(streamlines, deform_field, stream_to_current_grid, current_grid_to_world, stream_to_ref_grid, ref_grid_to_world)

Apply deformation field to streamlines

Parameters: streamlines : list List of 2D ndarrays of shape[-1]==3 deform_field : 4D numpy array x,y,z displacements stored in volume, shape[-1]==3 stream_to_current_grid : array, (4, 4) transform matrix voxmm space to original grid space current_grid_to_world : array (4, 4) transform matrix original grid space to world coordinates stream_to_ref_grid : array (4, 4) transform matrix voxmm space to new grid space ref_grid_to_world : array(4, 4) transform matrix new grid space to world coordinates new_streamlines : list List of the transformed 2D ndarrays of shape[-1]==3

### dist_to_corner¶

dipy.tracking.streamline.dist_to_corner(affine)

Calculate the maximal distance from the center to a corner of a voxel, given an affine

Parameters: affine : 4 by 4 array. The spatial transformation from the measurement to the scanner space. dist: float The maximal distance to the corner of a voxel, given voxel size encoded in the affine.

### length¶

dipy.tracking.streamline.length()

Euclidean length of streamlines

Length is in mm only if streamlines are expressed in world coordinates.

Parameters: streamlines : ndarray or a list or dipy.tracking.Streamlines If ndarray, must have shape (N,3) where N is the number of points of the streamline. If list, each item must be ndarray shape (Ni,3) where Ni is the number of points of streamline i. If dipy.tracking.Streamlines, its common_shape must be 3. lengths : scalar or ndarray shape (N,) If there is only one streamline, a scalar representing the length of the streamline. If there are several streamlines, ndarray containing the length of every streamline.

Examples

>>> from dipy.tracking.streamline import length
>>> import numpy as np
>>> streamline = np.array([[1, 1, 1], [2, 3, 4], [0, 0, 0]])
>>> expected_length = np.sqrt([1+2**2+3**2, 2**2+3**2+4**2]).sum()
>>> length(streamline) == expected_length
True
>>> streamlines = [streamline, np.vstack([streamline, streamline[::-1]])]
>>> expected_lengths = [expected_length, 2*expected_length]
>>> lengths = [length(streamlines[0]), length(streamlines[1])]
>>> np.allclose(lengths, expected_lengths)
True
>>> length([])
0.0
>>> length(np.array([[1, 2, 3]]))
0.0


### mul¶

dipy.tracking.streamline.mul()

mul(a, b) – Same as a * b.

### nbytes¶

dipy.tracking.streamline.nbytes(streamlines)

### orient_by_rois¶

dipy.tracking.streamline.orient_by_rois(streamlines, roi1, roi2, in_place=False, as_generator=False, affine=None)

Orient a set of streamlines according to a pair of ROIs

Parameters: streamlines : list or generator List or generator of 2d arrays of 3d coordinates. Each array contains the xyz coordinates of a single streamline. roi1, roi2 : ndarray Binary masks designating the location of the regions of interest, or coordinate arrays (n-by-3 array with ROI coordinate in each row). in_place : bool Whether to make the change in-place in the original list (and return a reference to the list), or to make a copy of the list and return this copy, with the relevant streamlines reoriented. Default: False. as_generator : bool Whether to return a generator as output. Default: False affine : ndarray Affine transformation from voxels to streamlines. Default: identity. streamlines : list or generator The same 3D arrays as a list or generator, but reoriented with respect to the ROIs

Examples

>>> streamlines = [np.array([[0, 0., 0],
...                          [1, 0., 0.],
...                          [2, 0., 0.]]),
...                np.array([[2, 0., 0.],
...                          [1, 0., 0],
...                          [0, 0,  0.]])]
>>> roi1 = np.zeros((4, 4, 4), dtype=bool)
>>> roi2 = np.zeros_like(roi1)
>>> roi1[0, 0, 0] = True
>>> roi2[1, 0, 0] = True
>>> orient_by_rois(streamlines, roi1, roi2)
[array([[ 0.,  0.,  0.],
[ 1.,  0.,  0.],
[ 2.,  0.,  0.]]), array([[ 0.,  0.,  0.],
[ 1.,  0.,  0.],
[ 2.,  0.,  0.]])]


### reduce¶

dipy.tracking.streamline.reduce(function, sequence[, initial]) → value

Apply a function of two arguments cumulatively to the items of a sequence, from left to right, so as to reduce the sequence to a single value. For example, reduce(lambda x, y: x+y, [1, 2, 3, 4, 5]) calculates ((((1+2)+3)+4)+5). If initial is present, it is placed before the items of the sequence in the calculation, and serves as a default when the sequence is empty.

### relist_streamlines¶

dipy.tracking.streamline.relist_streamlines(points, offsets)

Given a representation of a set of streamlines as a large array and an offsets array return the streamlines as a list of shorter arrays.

Parameters: points : array offsets : array streamlines: sequence

### select_by_rois¶

dipy.tracking.streamline.select_by_rois(streamlines, rois, include, mode=None, affine=None, tol=None)

Select streamlines based on logical relations with several regions of interest (ROIs). For example, select streamlines that pass near ROI1, but only if they do not pass near ROI2.

Parameters: streamlines : list A list of candidate streamlines for selection rois : list or ndarray A list of 3D arrays, each with shape (x, y, z) corresponding to the shape of the brain volume, or a 4D array with shape (n_rois, x, y, z). Non-zeros in each volume are considered to be within the region include : array or list A list or 1D array of boolean values marking inclusion or exclusion criteria. If a streamline is near any of the inclusion ROIs, it should evaluate to True, unless it is also near any of the exclusion ROIs. mode : string, optional One of {“any”, “all”, “either_end”, “both_end”}, where a streamline is associated with an ROI if: “any” : any point is within tol from ROI. Default. “all” : all points are within tol from ROI. “either_end” : either of the end-points is within tol from ROI “both_end” : both end points are within tol from ROI. affine : ndarray Affine transformation from voxels to streamlines. Default: identity. tol : float Distance (in the units of the streamlines, usually mm). If any coordinate in the streamline is within this distance from the center of any voxel in the ROI, the filtering criterion is set to True for this streamline, otherwise False. Defaults to the distance between the center of each voxel and the corner of the voxel. generator Generates the streamlines to be included based on these criteria.

Notes

The only operation currently possible is “(A or B or ...) and not (X or Y or ...)”, where A, B are inclusion regions and X, Y are exclusion regions.

Examples

>>> streamlines = [np.array([[0, 0., 0.9],
...                          [1.9, 0., 0.]]),
...                np.array([[0., 0., 0],
...                          [0, 1., 1.],
...                          [0, 2., 2.]]),
...                np.array([[2, 2, 2],
...                          [3, 3, 3]])]
>>> mask1 = np.zeros((4, 4, 4), dtype=bool)
>>> mask1[0, 0, 0] = True
>>> mask2[1, 0, 0] = True
...                            [True, True],
...                            tol=1)
>>> list(selection) # The result is a generator
[array([[ 0. ,  0. ,  0.9],
[ 1.9,  0. ,  0. ]]), array([[ 0.,  0.,  0.],
[ 0.,  1.,  1.],
[ 0.,  2.,  2.]])]
...                            [True, False],
...                            tol=0.87)
>>> list(selection)
[array([[ 0.,  0.,  0.],
[ 0.,  1.,  1.],
[ 0.,  2.,  2.]])]
...                            [True, True],
...                            mode="both_end",
...                            tol=1.0)
>>> list(selection)
[array([[ 0. ,  0. ,  0.9],
[ 1.9,  0. ,  0. ]])]
>>> mask2[0, 2, 2] = True
...                            [True, True],
...                            mode="both_end",
...                            tol=1.0)
>>> list(selection)
[array([[ 0. ,  0. ,  0.9],
[ 1.9,  0. ,  0. ]]), array([[ 0.,  0.,  0.],
[ 0.,  1.,  1.],
[ 0.,  2.,  2.]])]


### select_random_set_of_streamlines¶

dipy.tracking.streamline.select_random_set_of_streamlines(streamlines, select)

Select a random set of streamlines

Parameters: streamlines : list List of 2D ndarrays of shape[-1]==3 select : int Number of streamlines to select. If there are less streamlines than select then select=len(streamlines). selected_streamlines : list

Notes

The same streamline will not be selected twice.

### set_number_of_points¶

dipy.tracking.streamline.set_number_of_points()
Change the number of points of streamlines
(either by downsampling or upsampling)

Change the number of points of streamlines in order to obtain nb_points-1 segments of equal length. Points of streamlines will be modified along the curve.

Parameters: streamlines : ndarray or a list or dipy.tracking.Streamlines If ndarray, must have shape (N,3) where N is the number of points of the streamline. If list, each item must be ndarray shape (Ni,3) where Ni is the number of points of streamline i. If dipy.tracking.Streamlines, its common_shape must be 3. nb_points : int integer representing number of points wanted along the curve. new_streamlines : ndarray or a list or dipy.tracking.Streamlines Results of the downsampling or upsampling process.

Examples

>>> from dipy.tracking.streamline import set_number_of_points
>>> import numpy as np


One streamline, a semi-circle:

>>> theta = np.pi*np.linspace(0, 1, 100)
>>> x = np.cos(theta)
>>> y = np.sin(theta)
>>> z = 0 * x
>>> streamline = np.vstack((x, y, z)).T
>>> modified_streamline = set_number_of_points(streamline, 3)
>>> len(modified_streamline)
3


Multiple streamlines:

>>> streamlines = [streamline, streamline[::2]]
>>> new_streamlines = set_number_of_points(streamlines, 10)
>>> [len(s) for s in streamlines]
[100, 50]
>>> [len(s) for s in new_streamlines]
[10, 10]


### setup_test¶

dipy.tracking.streamline.setup_test()

Set numpy print options to “legacy” for new versions of numpy

If imported into a file, nosetest will run this before any doctests.

References

### streamline_near_roi¶

dipy.tracking.streamline.streamline_near_roi(streamline, roi_coords, tol, mode='any')

Is a streamline near an ROI.

Implements the inner loops of the near_roi() function.

Parameters: streamline : array, shape (N, 3) A single streamline roi_coords : array, shape (M, 3) ROI coordinates transformed to the streamline coordinate frame. tol : float Distance (in the units of the streamlines, usually mm). If any coordinate in the streamline is within this distance from the center of any voxel in the ROI, this function returns True. mode : string One of {“any”, “all”, “either_end”, “both_end”}, where return True if: “any” : any point is within tol from ROI. “all” : all points are within tol from ROI. “either_end” : either of the end-points is within tol from ROI “both_end” : both end points are within tol from ROI. out : boolean

### transform_streamlines¶

dipy.tracking.streamline.transform_streamlines(streamlines, mat)

Apply affine transformation to streamlines

Parameters: streamlines : list List of 2D ndarrays of shape[-1]==3 mat : array, (4, 4) transformation matrix new_streamlines : list List of the transformed 2D ndarrays of shape[-1]==3

### unlist_streamlines¶

dipy.tracking.streamline.unlist_streamlines(streamlines)

Return the streamlines not as a list but as an array and an offset

Parameters: streamlines: sequence points : array offsets : array

### values_from_volume¶

dipy.tracking.streamline.values_from_volume(data, streamlines, affine=None)

Extract values of a scalar/vector along each streamline from a volume.

Parameters: data : 3D or 4D array Scalar (for 3D) and vector (for 4D) values to be extracted. For 4D data, interpolation will be done on the 3 spatial dimensions in each volume. streamlines : ndarray or list If array, of shape (n_streamlines, n_nodes, 3) If list, len(n_streamlines) with (n_nodes, 3) array in each element of the list. affine : ndarray, shape (4, 4) Affine transformation from voxels (image coordinates) to streamlines. Default: identity. For example, if no affine is provided and the first coordinate of the first streamline is [1, 0, 0], data[1, 0, 0] would be returned as the value for that streamline coordinate

Notes

Values are extracted from the image based on the 3D coordinates of the nodes that comprise the points in the streamline, without any interpolation into segments between the nodes. Using this function with streamlines that have been resampled into a very small number of nodes will result in very few values.

### warn¶

dipy.tracking.streamline.warn()

Issue a warning, or maybe ignore it or raise an exception.

### defaultdict¶

class dipy.tracking.utils.defaultdict

Bases: dict

defaultdict(default_factory[, ...]) –> dict with default factory

The default factory is called without arguments to produce a new value when a key is not present, in __getitem__ only. A defaultdict compares equal to a dict with the same items. All remaining arguments are treated the same as if they were passed to the dict constructor, including keyword arguments.

Methods

 clear(() -> None.  Remove all items from D.) copy(() -> a shallow copy of D.) fromkeys Returns a new dict with keys from iterable and values equal to value. get((k[,d]) -> D[k] if k in D, ...) items(...) keys(...) pop((k[,d]) -> v, ...) If key is not found, d is returned if given, otherwise KeyError is raised popitem(() -> (k, v), ...) 2-tuple; but raise KeyError if D is empty. setdefault((k[,d]) -> D.get(k,d), ...) update(([E, ...) If E is present and has a .keys() method, then does: for k in E: D[k] = E[k] values(...)
__init__()

Initialize self. See help(type(self)) for accurate signature.

copy() → a shallow copy of D.
default_factory

Factory for default value called by __missing__().

### map¶

class dipy.tracking.utils.map

Bases: object

map(func, *iterables) –> map object

Make an iterator that computes the function using arguments from each of the iterables. Stops when the shortest iterable is exhausted.

__init__()

Initialize self. See help(type(self)) for accurate signature.

### xrange¶

dipy.tracking.utils.xrange

alias of range

### affine_for_trackvis¶

dipy.tracking.utils.affine_for_trackvis(voxel_size, voxel_order=None, dim=None, ref_img_voxel_order=None)

Returns an affine which maps points for voxel indices to trackvis space.

Parameters: voxel_size : array (3,) The sizes of the voxels in the reference image. affine : array (4, 4) Mapping from the voxel indices of the reference image to trackvis space.

### affine_from_fsl_mat_file¶

dipy.tracking.utils.affine_from_fsl_mat_file(mat_affine, input_voxsz, output_voxsz)

Converts an affine matrix from flirt (FSLdot) and a given voxel size for input and output images and returns an adjusted affine matrix for trackvis.

Parameters: mat_affine : array of shape (4, 4) An FSL flirt affine. input_voxsz : array of shape (3,) The input image voxel dimensions. output_voxsz : array of shape (3,) affine : array of shape (4, 4) A trackvis-compatible affine.

### apply_affine¶

dipy.tracking.utils.apply_affine(aff, pts)

Apply affine matrix aff to points pts

Returns result of application of aff to the right of pts. The coordinate dimension of pts should be the last.

For the 3D case, aff will be shape (4,4) and pts will have final axis length 3 - maybe it will just be N by 3. The return value is the transformed points, in this case:

res = np.dot(aff[:3,:3], pts.T) + aff[:3,3:4]
transformed_pts = res.T


This routine is more general than 3D, in that aff can have any shape (N,N), and pts can have any shape, as long as the last dimension is for the coordinates, and is therefore length N-1.

Parameters: aff : (N, N) array-like Homogenous affine, for 3D points, will be 4 by 4. Contrary to first appearance, the affine will be applied on the left of pts. pts : (..., N-1) array-like Points, where the last dimension contains the coordinates of each point. For 3D, the last dimension will be length 3. transformed_pts : (..., N-1) array transformed points

Examples

>>> aff = np.array([[0,2,0,10],[3,0,0,11],[0,0,4,12],[0,0,0,1]])
>>> pts = np.array([[1,2,3],[2,3,4],[4,5,6],[6,7,8]])
>>> apply_affine(aff, pts)
array([[14, 14, 24],
[16, 17, 28],
[20, 23, 36],
[24, 29, 44]]...)


Just to show that in the simple 3D case, it is equivalent to:

>>> (np.dot(aff[:3,:3], pts.T) + aff[:3,3:4]).T
array([[14, 14, 24],
[16, 17, 28],
[20, 23, 36],
[24, 29, 44]]...)


But pts can be a more complicated shape:

>>> pts = pts.reshape((2,2,3))
>>> apply_affine(aff, pts)
array([[[14, 14, 24],
[16, 17, 28]],

[[20, 23, 36],
[24, 29, 44]]]...)


### asarray¶

dipy.tracking.utils.asarray(a, dtype=None, order=None)

Convert the input to an array.

Parameters: a : array_like Input data, in any form that can be converted to an array. This includes lists, lists of tuples, tuples, tuples of tuples, tuples of lists and ndarrays. dtype : data-type, optional By default, the data-type is inferred from the input data. order : {‘C’, ‘F’}, optional Whether to use row-major (C-style) or column-major (Fortran-style) memory representation. Defaults to ‘C’. out : ndarray Array interpretation of a. No copy is performed if the input is already an ndarray with matching dtype and order. If a is a subclass of ndarray, a base class ndarray is returned.

asanyarray
Similar function which passes through subclasses.
ascontiguousarray
Convert input to a contiguous array.
asfarray
Convert input to a floating point ndarray.
asfortranarray
Convert input to an ndarray with column-major memory order.
asarray_chkfinite
Similar function which checks input for NaNs and Infs.
fromiter
Create an array from an iterator.
fromfunction
Construct an array by executing a function on grid positions.

Examples

Convert a list into an array:

>>> a = [1, 2]
>>> np.asarray(a)
array([1, 2])


Existing arrays are not copied:

>>> a = np.array([1, 2])
>>> np.asarray(a) is a
True


If dtype is set, array is copied only if dtype does not match:

>>> a = np.array([1, 2], dtype=np.float32)
>>> np.asarray(a, dtype=np.float32) is a
True
>>> np.asarray(a, dtype=np.float64) is a
False


Contrary to asanyarray, ndarray subclasses are not passed through:

>>> issubclass(np.matrix, np.ndarray)
True
>>> a = np.matrix([[1, 2]])
>>> np.asarray(a) is a
False
>>> np.asanyarray(a) is a
True


### cdist¶

dipy.tracking.utils.cdist(XA, XB, metric='euclidean', p=None, V=None, VI=None, w=None)

Computes distance between each pair of the two collections of inputs.

See Notes for common calling conventions.

Parameters: XA : ndarray An $$m_A$$ by $$n$$ array of $$m_A$$ original observations in an $$n$$-dimensional space. Inputs are converted to float type. XB : ndarray An $$m_B$$ by $$n$$ array of $$m_B$$ original observations in an $$n$$-dimensional space. Inputs are converted to float type. metric : str or callable, optional The distance metric to use. If a string, the distance function can be ‘braycurtis’, ‘canberra’, ‘chebyshev’, ‘cityblock’, ‘correlation’, ‘cosine’, ‘dice’, ‘euclidean’, ‘hamming’, ‘jaccard’, ‘kulsinski’, ‘mahalanobis’, ‘matching’, ‘minkowski’, ‘rogerstanimoto’, ‘russellrao’, ‘seuclidean’, ‘sokalmichener’, ‘sokalsneath’, ‘sqeuclidean’, ‘wminkowski’, ‘yule’. p : double, optional The p-norm to apply Only for Minkowski, weighted and unweighted. Default: 2. w : ndarray, optional The weight vector. Only for weighted Minkowski. Mandatory V : ndarray, optional The variance vector Only for standardized Euclidean. Default: var(vstack([XA, XB]), axis=0, ddof=1) VI : ndarray, optional The inverse of the covariance matrix Only for Mahalanobis. Default: inv(cov(vstack([XA, XB]).T)).T Y : ndarray A $$m_A$$ by $$m_B$$ distance matrix is returned. For each $$i$$ and $$j$$, the metric dist(u=XA[i], v=XB[j]) is computed and stored in the $$ij$$ th entry. ValueError An exception is thrown if XA and XB do not have the same number of columns.

Notes

The following are common calling conventions:

1. Y = cdist(XA, XB, 'euclidean')

Computes the distance between $$m$$ points using Euclidean distance (2-norm) as the distance metric between the points. The points are arranged as $$m$$ $$n$$-dimensional row vectors in the matrix X.

2. Y = cdist(XA, XB, 'minkowski', p)

Computes the distances using the Minkowski distance $$||u-v||_p$$ ($$p$$-norm) where $$p \geq 1$$.

3. Y = cdist(XA, XB, 'cityblock')

Computes the city block or Manhattan distance between the points.

4. Y = cdist(XA, XB, 'seuclidean', V=None)

Computes the standardized Euclidean distance. The standardized Euclidean distance between two n-vectors u and v is

$\sqrt{\sum {(u_i-v_i)^2 / V[x_i]}}.$

V is the variance vector; V[i] is the variance computed over all the i’th components of the points. If not passed, it is automatically computed.

5. Y = cdist(XA, XB, 'sqeuclidean')

Computes the squared Euclidean distance $$||u-v||_2^2$$ between the vectors.

6. Y = cdist(XA, XB, 'cosine')

Computes the cosine distance between vectors u and v,

$1 - \frac{u \cdot v} {{||u||}_2 {||v||}_2}$

where $$||*||_2$$ is the 2-norm of its argument *, and $$u \cdot v$$ is the dot product of $$u$$ and $$v$$.

7. Y = cdist(XA, XB, 'correlation')

Computes the correlation distance between vectors u and v. This is

$1 - \frac{(u - \bar{u}) \cdot (v - \bar{v})} {{||(u - \bar{u})||}_2 {||(v - \bar{v})||}_2}$

where $$\bar{v}$$ is the mean of the elements of vector v, and $$x \cdot y$$ is the dot product of $$x$$ and $$y$$.

8. Y = cdist(XA, XB, 'hamming')

Computes the normalized Hamming distance, or the proportion of those vector elements between two n-vectors u and v which disagree. To save memory, the matrix X can be of type boolean.

9. Y = cdist(XA, XB, 'jaccard')

Computes the Jaccard distance between the points. Given two vectors, u and v, the Jaccard distance is the proportion of those elements u[i] and v[i] that disagree where at least one of them is non-zero.

10. Y = cdist(XA, XB, 'chebyshev')

Computes the Chebyshev distance between the points. The Chebyshev distance between two n-vectors u and v is the maximum norm-1 distance between their respective elements. More precisely, the distance is given by

$d(u,v) = \max_i {|u_i-v_i|}.$
1. Y = cdist(XA, XB, 'canberra')

Computes the Canberra distance between the points. The Canberra distance between two points u and v is

$d(u,v) = \sum_i \frac{|u_i-v_i|} {|u_i|+|v_i|}.$
1. Y = cdist(XA, XB, 'braycurtis')

Computes the Bray-Curtis distance between the points. The Bray-Curtis distance between two points u and v is

$d(u,v) = \frac{\sum_i (|u_i-v_i|)} {\sum_i (|u_i+v_i|)}$
1. Y = cdist(XA, XB, 'mahalanobis', VI=None)
Computes the Mahalanobis distance between the points. The Mahalanobis distance between two points u and v is $$\sqrt{(u-v)(1/V)(u-v)^T}$$ where $$(1/V)$$ (the VI variable) is the inverse covariance. If VI is not None, VI will be used as the inverse covariance matrix.
1. Y = cdist(XA, XB, 'yule')
Computes the Yule distance between the boolean vectors. (see yule function documentation)
1. Y = cdist(XA, XB, 'matching')
Synonym for ‘hamming’.
1. Y = cdist(XA, XB, 'dice')
Computes the Dice distance between the boolean vectors. (see dice function documentation)
1. Y = cdist(XA, XB, 'kulsinski')
Computes the Kulsinski distance between the boolean vectors. (see kulsinski function documentation)
1. Y = cdist(XA, XB, 'rogerstanimoto')
Computes the Rogers-Tanimoto distance between the boolean vectors. (see rogerstanimoto function documentation)
1. Y = cdist(XA, XB, 'russellrao')
Computes the Russell-Rao distance between the boolean vectors. (see russellrao function documentation)
1. Y = cdist(XA, XB, 'sokalmichener')
Computes the Sokal-Michener distance between the boolean vectors. (see sokalmichener function documentation)
1. Y = cdist(XA, XB, 'sokalsneath')
Computes the Sokal-Sneath distance between the vectors. (see sokalsneath function documentation)
1. Y = cdist(XA, XB, 'wminkowski')
Computes the weighted Minkowski distance between the vectors. (see wminkowski function documentation)
1. Y = cdist(XA, XB, f)

Computes the distance between all pairs of vectors in X using the user supplied 2-arity function f. For example, Euclidean distance between the vectors could be computed as follows:

dm = cdist(XA, XB, lambda u, v: np.sqrt(((u-v)**2).sum()))


Note that you should avoid passing a reference to one of the distance functions defined in this library. For example,:

dm = cdist(XA, XB, sokalsneath)


would calculate the pair-wise distances between the vectors in X using the Python function sokalsneath. This would result in sokalsneath being called $${n \choose 2}$$ times, which is inefficient. Instead, the optimized C version is more efficient, and we call it using the following syntax:

dm = cdist(XA, XB, 'sokalsneath')


Examples

Find the Euclidean distances between four 2-D coordinates:

>>> from scipy.spatial import distance
>>> coords = [(35.0456, -85.2672),
...           (35.1174, -89.9711),
...           (35.9728, -83.9422),
...           (36.1667, -86.7833)]
>>> distance.cdist(coords, coords, 'euclidean')
array([[ 0.    ,  4.7044,  1.6172,  1.8856],
[ 4.7044,  0.    ,  6.0893,  3.3561],
[ 1.6172,  6.0893,  0.    ,  2.8477],
[ 1.8856,  3.3561,  2.8477,  0.    ]])


Find the Manhattan distance from a 3-D point to the corners of the unit cube:

>>> a = np.array([[0, 0, 0],
...               [0, 0, 1],
...               [0, 1, 0],
...               [0, 1, 1],
...               [1, 0, 0],
...               [1, 0, 1],
...               [1, 1, 0],
...               [1, 1, 1]])
>>> b = np.array([[ 0.1,  0.2,  0.4]])
>>> distance.cdist(a, b, 'cityblock')
array([[ 0.7],
[ 0.9],
[ 1.3],
[ 1.5],
[ 1.5],
[ 1.7],
[ 2.1],
[ 2.3]])


### connectivity_matrix¶

dipy.tracking.utils.connectivity_matrix(streamlines, label_volume, voxel_size=None, affine=None, symmetric=True, return_mapping=False, mapping_as_streamlines=False)

Counts the streamlines that start and end at each label pair.

Parameters: streamlines : sequence A sequence of streamlines. label_volume : ndarray An image volume with an integer data type, where the intensities in the volume map to anatomical structures. voxel_size : This argument is deprecated. affine : array_like (4, 4) The mapping from voxel coordinates to streamline coordinates. symmetric : bool, False by default Symmetric means we don’t distinguish between start and end points. If symmetric is True, matrix[i, j] == matrix[j, i]. return_mapping : bool, False by default If True, a mapping is returned which maps matrix indices to streamlines. mapping_as_streamlines : bool, False by default If True voxel indices map to lists of streamline objects. Otherwise voxel indices map to lists of integers. matrix : ndarray The number of connection between each pair of regions in label_volume. mapping : defaultdict(list) mapping[i, j] returns all the streamlines that connect region i to region j. If symmetric is True mapping will only have one key for each start end pair such that if i < j mapping will have key (i, j) but not key (j, i).

### density_map¶

dipy.tracking.utils.density_map(streamlines, vol_dims, voxel_size=None, affine=None)

Counts the number of unique streamlines that pass through each voxel.

Parameters: streamlines : iterable A sequence of streamlines. vol_dims : 3 ints The shape of the volume to be returned containing the streamlines counts voxel_size : This argument is deprecated. affine : array_like (4, 4) The mapping from voxel coordinates to streamline points. image_volume : ndarray, shape=vol_dims The number of streamline points in each voxel of volume. IndexError When the points of the streamlines lie outside of the return volume.

Notes

A streamline can pass through a voxel even if one of the points of the streamline does not lie in the voxel. For example a step from [0,0,0] to [0,0,2] passes through [0,0,1]. Consider subsegmenting the streamlines when the edges of the voxels are smaller than the steps of the streamlines.

### dist_to_corner¶

dipy.tracking.utils.dist_to_corner(affine)

Calculate the maximal distance from the center to a corner of a voxel, given an affine

Parameters: affine : 4 by 4 array. The spatial transformation from the measurement to the scanner space. dist: float The maximal distance to the corner of a voxel, given voxel size encoded in the affine.

### dot¶

dipy.tracking.utils.dot(a, b, out=None)

Dot product of two arrays.

For 2-D arrays it is equivalent to matrix multiplication, and for 1-D arrays to inner product of vectors (without complex conjugation). For N dimensions it is a sum product over the last axis of a and the second-to-last of b:

dot(a, b)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m])

Parameters: a : array_like First argument. b : array_like Second argument. out : ndarray, optional Output argument. This must have the exact kind that would be returned if it was not used. In particular, it must have the right type, must be C-contiguous, and its dtype must be the dtype that would be returned for dot(a,b). This is a performance feature. Therefore, if these conditions are not met, an exception is raised, instead of attempting to be flexible. output : ndarray Returns the dot product of a and b. If a and b are both scalars or both 1-D arrays then a scalar is returned; otherwise an array is returned. If out is given, then it is returned. ValueError If the last dimension of a is not the same size as the second-to-last dimension of b.

vdot
Complex-conjugating dot product.
tensordot
Sum products over arbitrary axes.
einsum
Einstein summation convention.
matmul
‘@’ operator as method with out parameter.

Examples

>>> np.dot(3, 4)
12


Neither argument is complex-conjugated:

>>> np.dot([2j, 3j], [2j, 3j])
(-13+0j)


For 2-D arrays it is the matrix product:

>>> a = [[1, 0], [0, 1]]
>>> b = [[4, 1], [2, 2]]
>>> np.dot(a, b)
array([[4, 1],
[2, 2]])

>>> a = np.arange(3*4*5*6).reshape((3,4,5,6))
>>> b = np.arange(3*4*5*6)[::-1].reshape((5,4,6,3))
>>> np.dot(a, b)[2,3,2,1,2,2]
499128
>>> sum(a[2,3,2,:] * b[1,2,:,2])
499128


### empty¶

dipy.tracking.utils.empty(shape, dtype=float, order='C')

Return a new array of given shape and type, without initializing entries.

Parameters: shape : int or tuple of int Shape of the empty array dtype : data-type, optional Desired output data-type. order : {‘C’, ‘F’}, optional Whether to store multi-dimensional data in row-major (C-style) or column-major (Fortran-style) order in memory. out : ndarray Array of uninitialized (arbitrary) data of the given shape, dtype, and order. Object arrays will be initialized to None.

empty_like, zeros, ones

Notes

empty, unlike zeros, does not set the array values to zero, and may therefore be marginally faster. On the other hand, it requires the user to manually set all the values in the array, and should be used with caution.

Examples

>>> np.empty([2, 2])
array([[ -9.74499359e+001,   6.69583040e-309],
[  2.13182611e-314,   3.06959433e-309]])         #random

>>> np.empty([2, 2], dtype=int)
array([[-1073741821, -1067949133],
[  496041986,    19249760]])                     #random


### eye¶

dipy.tracking.utils.eye(N, M=None, k=0, dtype=<class 'float'>)

Return a 2-D array with ones on the diagonal and zeros elsewhere.

Parameters: N : int Number of rows in the output. M : int, optional Number of columns in the output. If None, defaults to N. k : int, optional Index of the diagonal: 0 (the default) refers to the main diagonal, a positive value refers to an upper diagonal, and a negative value to a lower diagonal. dtype : data-type, optional Data-type of the returned array. I : ndarray of shape (N,M) An array where all elements are equal to zero, except for the k-th diagonal, whose values are equal to one.

identity
(almost) equivalent function
diag
diagonal 2-D array from a 1-D array specified by the user.

Examples

>>> np.eye(2, dtype=int)
array([[1, 0],
[0, 1]])
>>> np.eye(3, k=1)
array([[ 0.,  1.,  0.],
[ 0.,  0.,  1.],
[ 0.,  0.,  0.]])


### flexi_tvis_affine¶

dipy.tracking.utils.flexi_tvis_affine(sl_vox_order, grid_affine, dim, voxel_size)
Computes the mapping from voxel indices to streamline points,
reconciling streamlines and grids with different voxel orders
Parameters: sl_vox_order : string of length 3 a string that describes the voxel order of the streamlines (ex: LPS) grid_affine : array (4, 4), An affine matrix describing the current space of the grid in relation to RAS+ scanner space dim : tuple of length 3 dimension of the grid voxel_size : array (3,0) voxel size of the grid flexi_tvis_aff : this affine maps between a grid and a trackvis space

### get_flexi_tvis_affine¶

dipy.tracking.utils.get_flexi_tvis_affine(tvis_hdr, nii_aff)
Computes the mapping from voxel indices to streamline points,
reconciling streamlines and grids with different voxel orders
Parameters: tvis_hdr : header from a trackvis file nii_aff : array (4, 4), An affine matrix describing the current space of the grid in relation to RAS+ scanner space nii_data : nd array 3D array, each with shape (x, y, z) corresponding to the shape of the brain volume. flexi_tvis_aff : array (4,4) this affine maps between a grid and a trackvis space

### length¶

dipy.tracking.utils.length(streamlines, affine=None)

Calculate the lengths of many streamlines in a bundle.

Parameters: streamlines : list Each item in the list is an array with 3D coordinates of a streamline. affine : 4 x 4 array An affine transformation to move the fibers by, before computing their lengths. Iterator object which then computes the length of each streamline in the bundle, upon iteration.

### minimum_at¶

dipy.tracking.utils.minimum_at(a, indices, b=None)

Performs unbuffered in place operation on operand ‘a’ for elements specified by ‘indices’. For addition ufunc, this method is equivalent to a[indices] += b, except that results are accumulated for elements that are indexed more than once. For example, a[[0,0]] += 1 will only increment the first element once because of buffering, whereas add.at(a, [0,0], 1) will increment the first element twice.

New in version 1.8.0.

Parameters: a : array_like The array to perform in place operation on. indices : array_like or tuple Array like index object or slice object for indexing into first operand. If first operand has multiple dimensions, indices can be a tuple of array like index objects or slice objects. b : array_like Second operand for ufuncs requiring two operands. Operand must be broadcastable over first operand after indexing or slicing.

Examples

Set items 0 and 1 to their negative values:

>>> a = np.array([1, 2, 3, 4])
>>> np.negative.at(a, [0, 1])
>>> print(a)
array([-1, -2, 3, 4])


Increment items 0 and 1, and increment item 2 twice:

>>> a = np.array([1, 2, 3, 4])
>>> np.add.at(a, [0, 1, 2, 2], 1)
>>> print(a)
array([2, 3, 5, 4])


Add items 0 and 1 in first array to second array, and store results in first array:

>>> a = np.array([1, 2, 3, 4])
>>> b = np.array([1, 2])
>>> print(a)
array([2, 4, 3, 4])


### move_streamlines¶

dipy.tracking.utils.move_streamlines(streamlines, output_space, input_space=None)

Applies a linear transformation, given by affine, to streamlines.

Parameters: streamlines : sequence A set of streamlines to be transformed. output_space : array (4, 4) An affine matrix describing the target space to which the streamlines will be transformed. input_space : array (4, 4), optional An affine matrix describing the current space of the streamlines, if no input_space is specified, it’s assumed the streamlines are in the reference space. The reference space is the same as the space associated with the affine matrix np.eye(4). streamlines : generator A sequence of transformed streamlines.

### ndbincount¶

dipy.tracking.utils.ndbincount(x, weights=None, shape=None)

Like bincount, but for nd-indicies.

Parameters: x : array_like (N, M) M indices to a an Nd-array weights : array_like (M,), optional Weights associated with indices shape : optional the shape of the output

### near_roi¶

dipy.tracking.utils.near_roi(streamlines, region_of_interest, affine=None, tol=None, mode='any')

Provide filtering criteria for a set of streamlines based on whether they fall within a tolerance distance from an ROI

Parameters: streamlines : list or generator A sequence of streamlines. Each streamline should be a (N, 3) array, where N is the length of the streamline. region_of_interest : ndarray A mask used as a target. Non-zero values are considered to be within the target region. affine : ndarray Affine transformation from voxels to streamlines. Default: identity. tol : float Distance (in the units of the streamlines, usually mm). If any coordinate in the streamline is within this distance from the center of any voxel in the ROI, the filtering criterion is set to True for this streamline, otherwise False. Defaults to the distance between the center of each voxel and the corner of the voxel. mode : string, optional One of {“any”, “all”, “either_end”, “both_end”}, where return True if: “any” : any point is within tol from ROI. Default. “all” : all points are within tol from ROI. “either_end” : either of the end-points is within tol from ROI “both_end” : both end points are within tol from ROI. 1D array of boolean dtype, shape (len(streamlines), ) This contains True for indices corresponding to each streamline that passes within a tolerance distance from the target ROI, False otherwise.

### orientation_from_string¶

dipy.tracking.utils.orientation_from_string(string_ornt)

Returns an array representation of an ornt string

### ornt_mapping¶

dipy.tracking.utils.ornt_mapping(ornt1, ornt2)

Calculates the mapping needing to get from orn1 to orn2

### path_length¶

dipy.tracking.utils.path_length(streamlines, aoi, affine, fill_value=-1)

Computes the shortest path, along any streamline, between aoi and each voxel.

Parameters: streamlines : seq of (N, 3) arrays A sequence of streamlines, path length is given in mm along the curve of the streamline. aoi : array, 3d A mask (binary array) of voxels from which to start computing distance. affine : array (4, 4) The mapping from voxel indices to streamline points. fill_value : float The value of voxel in the path length map that are not connected to the aoi. plm : array Same shape as aoi. The minimum distance between every point and aoi along the path of a streamline.

dipy.tracking.utils.random_seeds_from_mask(mask, seeds_count=1, seed_count_per_voxel=True, affine=None)

Creates randomly placed seeds for fiber tracking from a binary mask.

Seeds points are placed randomly distributed in voxels of mask which are True. If seed_count_per_voxel is True, this function is similar to seeds_from_mask(), with the difference that instead of evenly distributing the seeds, it randomly places the seeds within the voxels specified by the mask. The initial random conditions can be set using numpy.random.seed(...), prior to calling this function.

Parameters: mask : binary 3d array_like A binary array specifying where to place the seeds for fiber tracking. seeds_count : int The number of seeds to generate. If seed_count_per_voxel is True, specifies the number of seeds to place in each voxel. Otherwise, specifies the total number of seeds to place in the mask. seed_count_per_voxel: bool If True, seeds_count is per voxel, else seeds_count is the total number of seeds. affine : array, (4, 4) The mapping between voxel indices and the point space for seeds. A seed point at the center the voxel [i, j, k] will be represented as [x, y, z] where [x, y, z, 1] == np.dot(affine, [i, j, k , 1]). ValueError When mask is not a three-dimensional array

Examples

>>> mask = np.zeros((3,3,3), 'bool')
>>> np.random.seed(1)
array([[-0.082978  ,  0.22032449, -0.49988563]])
array([[-0.19766743, -0.35324411, -0.40766141],
[-0.31373979, -0.15443927, -0.10323253],
[ 0.03881673, -0.08080549,  0.1852195 ],
[-0.29554775,  0.37811744, -0.47261241],
[ 0.17046751, -0.0826952 ,  0.05868983],
[-0.35961306, -0.30189851,  0.30074457]])
array([[ 0.46826158, -0.18657582,  0.19232262],
[ 0.37638915,  0.39460666, -0.41495579],
[-0.46094522,  0.66983042,  2.3781425 ],
[-0.40165317,  0.92110763,  2.45788953]])


### ravel_multi_index¶

dipy.tracking.utils.ravel_multi_index(multi_index, dims, mode='raise', order='C')

Converts a tuple of index arrays into an array of flat indices, applying boundary modes to the multi-index.

Parameters: multi_index : tuple of array_like A tuple of integer arrays, one array for each dimension. dims : tuple of ints The shape of array into which the indices from multi_index apply. mode : {‘raise’, ‘wrap’, ‘clip’}, optional Specifies how out-of-bounds indices are handled. Can specify either one mode or a tuple of modes, one mode per index. ‘raise’ – raise an error (default) ‘wrap’ – wrap around ‘clip’ – clip to the range In ‘clip’ mode, a negative index which would normally wrap will clip to 0 instead. order : {‘C’, ‘F’}, optional Determines whether the multi-index should be viewed as indexing in row-major (C-style) or column-major (Fortran-style) order. raveled_indices : ndarray An array of indices into the flattened version of an array of dimensions dims.

unravel_index

Notes

New in version 1.6.0.

Examples

>>> arr = np.array([[3,6,6],[4,5,1]])
>>> np.ravel_multi_index(arr, (7,6))
array([22, 41, 37])
>>> np.ravel_multi_index(arr, (7,6), order='F')
array([31, 41, 13])
>>> np.ravel_multi_index(arr, (4,6), mode='clip')
array([22, 23, 19])
>>> np.ravel_multi_index(arr, (4,4), mode=('clip','wrap'))
array([12, 13, 13])

>>> np.ravel_multi_index((3,1,4,1), (6,7,8,9))
1621


### reduce_labels¶

dipy.tracking.utils.reduce_labels(label_volume)

Reduces an array of labels to the integers from 0 to n with smallest possible n.

Examples

>>> labels = np.array([[1, 3, 9],
...                    [1, 3, 8],
...                    [1, 3, 7]])
>>> new_labels, lookup = reduce_labels(labels)
>>> lookup
array([1, 3, 7, 8, 9])
>>> new_labels
array([[0, 1, 4],
[0, 1, 3],
[0, 1, 2]]...)
>>> (lookup[new_labels] == labels).all()
True


### reduce_rois¶

dipy.tracking.utils.reduce_rois(rois, include)

Reduce multiple ROIs to one inclusion and one exclusion ROI

Parameters: rois : list or ndarray A list of 3D arrays, each with shape (x, y, z) corresponding to the shape of the brain volume, or a 4D array with shape (n_rois, x, y, z). Non-zeros in each volume are considered to be within the region. include : array or list A list or 1D array of boolean marking inclusion or exclusion criteria. include_roi : boolean 3D array An array marking the inclusion mask. exclude_roi : boolean 3D array An array marking the exclusion mask

### reorder_voxels_affine¶

dipy.tracking.utils.reorder_voxels_affine(input_ornt, output_ornt, shape, voxel_size)

Calculates a linear transformation equivalent to changing voxel order.

Calculates a linear tranformation A such that [a, b, c, 1] = A[x, y, z, 1]. where [x, y, z] is a point in the coordinate system defined by input_ornt and [a, b, c] is the same point in the coordinate system defined by output_ornt.

Parameters: input_ornt : array (n, 2) A description of the orientation of a point in n-space. See nibabel.orientation or dipy.io.bvectxt for more information. output_ornt : array (n, 2) A description of the orientation of a point in n-space. shape : tuple of int Shape of the image in the input orientation. map = ornt_mapping(input_ornt, output_ornt) voxel_size : int Voxel size of the image in the input orientation. A : array (n+1, n+1) Affine matrix of the transformation between input_ornt and output_ornt.

dipy.tracking.utils.seeds_from_mask(mask, density=[1, 1, 1], voxel_size=None, affine=None)

Creates seeds for fiber tracking from a binary mask.

Seeds points are placed evenly distributed in all voxels of mask which are True.

Parameters: mask : binary 3d array_like A binary array specifying where to place the seeds for fiber tracking. density : int or array_like (3,) Specifies the number of seeds to place along each dimension. A density of 2 is the same as [2, 2, 2] and will result in a total of 8 seeds per voxel. voxel_size : This argument is deprecated. affine : array, (4, 4) The mapping between voxel indices and the point space for seeds. A seed point at the center the voxel [i, j, k] will be represented as [x, y, z] where [x, y, z, 1] == np.dot(affine, [i, j, k , 1]). ValueError When mask is not a three-dimensional array

Examples

>>> mask = np.zeros((3,3,3), 'bool')
array([[ 0.5,  0.5,  0.5]])
array([[ 0.5       ,  0.25      ,  0.16666667],
[ 0.5       ,  0.75      ,  0.16666667],
[ 0.5       ,  0.25      ,  0.5       ],
[ 0.5       ,  0.75      ,  0.5       ],
[ 0.5       ,  0.25      ,  0.83333333],
[ 0.5       ,  0.75      ,  0.83333333]])
array([[ 0.55 ,  0.55 ,  0.625],
[ 0.55 ,  0.55 ,  1.875],
[ 0.55 ,  1.65 ,  5.625],
[ 0.55 ,  1.65 ,  6.875]])


### setup_test¶

dipy.tracking.utils.setup_test()

Set numpy print options to “legacy” for new versions of numpy

If imported into a file, nosetest will run this before any doctests.

References

### streamline_near_roi¶

dipy.tracking.utils.streamline_near_roi(streamline, roi_coords, tol, mode='any')

Is a streamline near an ROI.

Implements the inner loops of the near_roi() function.

Parameters: streamline : array, shape (N, 3) A single streamline roi_coords : array, shape (M, 3) ROI coordinates transformed to the streamline coordinate frame. tol : float Distance (in the units of the streamlines, usually mm). If any coordinate in the streamline is within this distance from the center of any voxel in the ROI, this function returns True. mode : string One of {“any”, “all”, “either_end”, “both_end”}, where return True if: “any” : any point is within tol from ROI. “all” : all points are within tol from ROI. “either_end” : either of the end-points is within tol from ROI “both_end” : both end points are within tol from ROI. out : boolean

### subsegment¶

dipy.tracking.utils.subsegment(streamlines, max_segment_length)

Splits the segments of the streamlines into small segments.

Replaces each segment of each of the streamlines with the smallest possible number of equally sized smaller segments such that no segment is longer than max_segment_length. Among other things, this can useful for getting streamline counts on a grid that is smaller than the length of the streamline segments.

Parameters: streamlines : sequence of ndarrays The streamlines to be subsegmented. max_segment_length : float The longest allowable segment length. output_streamlines : generator A set of streamlines.

Notes

Segments of 0 length are removed. If unchanged

Examples

>>> streamlines = [np.array([[0,0,0],[2,0,0],[5,0,0]])]
>>> list(subsegment(streamlines, 3.))
[array([[ 0.,  0.,  0.],
[ 2.,  0.,  0.],
[ 5.,  0.,  0.]])]
>>> list(subsegment(streamlines, 1))
[array([[ 0.,  0.,  0.],
[ 1.,  0.,  0.],
[ 2.,  0.,  0.],
[ 3.,  0.,  0.],
[ 4.,  0.,  0.],
[ 5.,  0.,  0.]])]
>>> list(subsegment(streamlines, 1.6))
[array([[ 0. ,  0. ,  0. ],
[ 1. ,  0. ,  0. ],
[ 2. ,  0. ,  0. ],
[ 3.5,  0. ,  0. ],
[ 5. ,  0. ,  0. ]])]


### target¶

dipy.tracking.utils.target(streamlines, target_mask, affine, include=True)

Filters streamlines based on whether or not they pass through an ROI.

Parameters: streamlines : iterable A sequence of streamlines. Each streamline should be a (N, 3) array, where N is the length of the streamline. target_mask : array-like A mask used as a target. Non-zero values are considered to be within the target region. affine : array (4, 4) The affine transform from voxel indices to streamline points. include : bool, default True If True, streamlines passing through target_mask are kept. If False, the streamlines not passing through target_mask are kept. streamlines : generator A sequence of streamlines that pass through target_mask. ValueError When the points of the streamlines lie outside of the target_mask.

### target_line_based¶

dipy.tracking.utils.target_line_based(streamlines, target_mask, affine=None, include=True)

Filters streamlines based on whether or not they pass through a ROI, using a line-based algorithm. Mostly used as a replacement of target for compressed streamlines.

This function never returns single-point streamlines, whatever the value of include.

Parameters: streamlines : iterable A sequence of streamlines. Each streamline should be a (N, 3) array, where N is the length of the streamline. target_mask : array-like A mask used as a target. Non-zero values are considered to be within the target region. affine : array (4, 4) The affine transform from voxel indices to streamline points. include : bool, default True If True, streamlines passing through target_mask are kept. If False, the streamlines not passing through target_mask are kept. streamlines : generator A sequence of streamlines that pass through target_mask.

References

[Bresenham5] Bresenham, Jack Elton. “Algorithm for computer control of a
digital plotter”, IBM Systems Journal, vol 4, no. 1, 1965.
[Houde15] Houde et al. How to avoid biased streamlines-based metrics for
streamlines with variable step sizes, ISMRM 2015.

### unique_rows¶

dipy.tracking.utils.unique_rows(in_array, dtype='f4')

This (quickly) finds the unique rows in an array

Parameters: in_array: ndarray The array for which the unique rows should be found dtype: str, optional This determines the intermediate representation used for the values. Should at least preserve the values of the input array. u_return: ndarray Array with the unique rows of the original array.

### warn¶

dipy.tracking.utils.warn()

Issue a warning, or maybe ignore it or raise an exception.

### wraps¶

dipy.tracking.utils.wraps`(wrapped, assigned=('__module__', '__name__', '__qualname__', '__doc__', '__annotations__'), updated=('__dict__', ))

Decorator factory to apply update_wrapper() to a wrapper function

Returns a decorator that invokes update_wrapper() with the decorated function as the wrapper argument and the arguments to wraps() as the remaining arguments. Default arguments are as for update_wrapper(). This is a convenience function to simplify applying partial() to update_wrapper().