segment

Module: segment.benchmarks

Module: segment.benchmarks.bench_quickbundles

Benchmarks for QuickBundles

Run all benchmarks with:

import dipy.segment as dipysegment
dipysegment.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_quickbundles.py
MDFpy

Attributes

Metric Computes a distance between two sequential data.
QB_New alias of QuickBundles
QB_Old alias of QuickBundles
assert_array_equal(x, y[, err_msg, verbose]) Raises an AssertionError if two array_like objects are not equal.
assert_arrays_equal(arrays1, arrays2)
assert_equal Fail if the two objects are unequal as determined by the ‘==’ operator.
bench_quickbundles()
get_data([name]) provides filenames of some test datasets or other useful parametrisations
measure(code_str[, times, label]) Return elapsed time for executing code in the namespace of the caller.

Module: segment.bundles

BundleMinDistanceAsymmetricMetric([num_threads]) Asymmetric Bundle-based Minimum distance
BundleMinDistanceMetric([num_threads]) Bundle-based Minimum Distance aka BMD
BundleSumDistanceMatrixMetric([num_threads]) Bundle-based Sum Distance aka BMD
RecoBundles(streamlines[, cluster_map, ...])

Methods

StreamlineLinearRegistration([metric, x0, ...])

Methods

Streamlines(*args, **kwargs)

Attributes

chain chain(*iterables) –> chain object
apply_affine(aff, pts) Apply affine matrix aff to points pts
bundles_distances_mam Calculate distances between list of tracks A and list of tracks B
bundles_distances_mdf Calculate distances between list of tracks A and list of tracks B
nbytes(streamlines)
qbx_and_merge(streamlines, thresholds[, ...]) Run QuickBundlesX and then run again on the centroids of the last layer
select_random_set_of_streamlines(...) Select a random set of streamlines
set_number_of_points Change the number of points of streamlines
time(() -> floating point number) Return the current time in seconds since the Epoch.

Module: segment.clustering

ABCMeta Metaclass for defining Abstract Base Classes (ABCs).
AveragePointwiseEuclideanMetric Computes the average of pointwise Euclidean distances between two sequential data.
Cluster([id, indices, refdata]) Provides functionalities for interacting with a cluster.
ClusterCentroid(centroid[, id, indices, refdata]) Provides functionalities for interacting with a cluster.
ClusterMap([refdata]) Provides functionalities for interacting with clustering outputs.
ClusterMapCentroid([refdata]) Provides functionalities for interacting with clustering outputs that have centroids.
Clustering

Methods

Identity Provides identity indexing functionality.
Metric Computes a distance between two sequential data.
MinimumAverageDirectFlipMetric Computes the MDF distance (minimum average direct-flip) between two sequential data.
QuickBundles(threshold[, metric, ...]) Clusters streamlines using QuickBundles [Garyfallidis12].
QuickBundlesX(thresholds[, metric]) Clusters streamlines using QuickBundlesX.
ResampleFeature Extracts features from a sequential datum.
TreeCluster(threshold, centroid[, indices])

Attributes

TreeClusterMap(root)

Attributes

abstractmethod(funcobj) A decorator indicating abstract methods.
nbytes(streamlines)
qbx_and_merge(streamlines, thresholds[, ...]) Run QuickBundlesX and then run again on the centroids of the last layer
set_number_of_points Change the number of points of streamlines
time(() -> floating point number) Return the current time in seconds since the Epoch.

Module: segment.mask

applymask(vol, mask) Mask vol with mask.
binary_dilation(input[, structure, ...]) Multi-dimensional binary dilation with the given structuring element.
bounding_box(vol) Compute the bounding box of nonzero intensity voxels in the volume.
clean_cc_mask(mask) Cleans a segmentation of the corpus callosum so no random pixels are included.
color_fa(fa, evecs) Color fractional anisotropy of diffusion tensor
crop(vol, mins, maxs) Crops the input volume.
fractional_anisotropy(evals[, axis]) Fractional anisotropy (FA) of a diffusion tensor.
generate_binary_structure(rank, connectivity) Generate a binary structure for binary morphological operations.
median_filter(input[, size, footprint, ...]) Calculates a multidimensional median filter.
median_otsu(input_volume[, median_radius, ...]) Simple brain extraction tool method for images from DWI data.
multi_median(input, median_radius, numpass) Applies median filter multiple times on input data.
otsu(image[, nbins]) Return threshold value based on Otsu’s method.
segment_from_cfa(tensor_fit, roi, threshold) Segment the cfa inside roi using the values from threshold as bounds.
warn Issue a warning, or maybe ignore it or raise an exception.

Module: segment.metric

ArcLengthFeature Extracts features from a sequential datum.
AveragePointwiseEuclideanMetric Computes the average of pointwise Euclidean distances between two sequential data.
CenterOfMassFeature Extracts features from a sequential datum.
CosineMetric Computes the cosine distance between two vectors.
EuclideanMetric alias of SumPointwiseEuclideanMetric
Feature Extracts features from a sequential datum.
IdentityFeature Extracts features from a sequential datum.
Metric Computes a distance between two sequential data.
MidpointFeature Extracts features from a sequential datum.
MinimumAverageDirectFlipMetric Computes the MDF distance (minimum average direct-flip) between two sequential data.
ResampleFeature Extracts features from a sequential datum.
SumPointwiseEuclideanMetric Computes the sum of pointwise Euclidean distances between two sequential data.
VectorOfEndpointsFeature Extracts features from a sequential datum.
dist Computes a distance between datum1 and datum2.
distance_matrix Computes the distance matrix between two lists of sequential data.
mdf(s1, s2) Computes the MDF (Minimum average Direct-Flip) distance [Garyfallidis12] between two streamlines.

Module: segment.quickbundles

QuickBundles(tracks[, dist_thr, pts])

Attributes

bundles_distances_mdf Calculate distances between list of tracks A and list of tracks B
downsample(xyz[, n_pols]) downsample for a specific number of points along the curve/track
local_skeleton_clustering Efficient tractography clustering
warn Issue a warning, or maybe ignore it or raise an exception.

Module: segment.threshold

otsu(image[, nbins]) Return threshold value based on Otsu’s method.
upper_bound_by_percent(data[, percent]) Find the upper bound for visualization of medical images
upper_bound_by_rate(data[, rate]) Adjusts upper intensity boundary using rates

Module: segment.tissue

ConstantObservationModel Observation model assuming that the intensity of each class is constant.
IteratedConditionalModes

Methods

TissueClassifierHMRF([save_history, verbose]) This class contains the methods for tissue classification using the Markov
add_noise(signal, snr, S0[, noise_type]) Add noise of specified distribution to the signal from a single voxel.

MDFpy

class dipy.segment.benchmarks.bench_quickbundles.MDFpy

Bases: dipy.segment.metricspeed.Metric

Attributes

feature Feature object used to extract features from sequential data
is_order_invariant Is this metric invariant to the sequence’s ordering

Methods

are_compatible(shape1, shape2)
dist(features1, features2)
__init__()

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

are_compatible(shape1, shape2)
dist(features1, features2)

Metric

class dipy.segment.benchmarks.bench_quickbundles.Metric

Bases: object

Computes a distance between two sequential data.

A sequence of N-dimensional points is represented as a 2D array with shape (nb_points, nb_dimensions). A feature object can be specified in order to calculate the distance between extracted features, rather than directly between the sequential data.

Parameters:

feature : Feature object, optional

It is used to extract features before computing the distance.

Notes

When subclassing Metric, one only needs to override the dist and are_compatible methods.

Attributes

feature Feature object used to extract features from sequential data
is_order_invariant Is this metric invariant to the sequence’s ordering

Methods

are_compatible Checks if features can be used by metric.dist based on their shape.
dist Computes a distance between two data points based on their features.
__init__()

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

are_compatible()

Checks if features can be used by metric.dist based on their shape.

Basically this method exists so we don’t have to do this check inside the metric.dist function (speedup).

Parameters:

shape1 : int, 1-tuple or 2-tuple

shape of the first data point’s features

shape2 : int, 1-tuple or 2-tuple

shape of the second data point’s features

Returns:

are_compatible : bool

whether or not shapes are compatible

dist()

Computes a distance between two data points based on their features.

Parameters:

features1 : 2D array

Features of the first data point.

features2 : 2D array

Features of the second data point.

Returns:

double

Distance between two data points.

feature

Feature object used to extract features from sequential data

is_order_invariant

Is this metric invariant to the sequence’s ordering

QB_New

dipy.segment.benchmarks.bench_quickbundles.QB_New

alias of QuickBundles

QB_Old

dipy.segment.benchmarks.bench_quickbundles.QB_Old

alias of QuickBundles

assert_array_equal

dipy.segment.benchmarks.bench_quickbundles.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.

Raises:

AssertionError

If actual and desired objects are not equal.

See also

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)

assert_arrays_equal

dipy.segment.benchmarks.bench_quickbundles.assert_arrays_equal(arrays1, arrays2)

assert_equal

dipy.segment.benchmarks.bench_quickbundles.assert_equal(self, first, second, msg=None)

Fail if the two objects are unequal as determined by the ‘==’ operator.

bench_quickbundles

dipy.segment.benchmarks.bench_quickbundles.bench_quickbundles()

get_data

dipy.segment.benchmarks.bench_quickbundles.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

Returns:

fnames : tuple

filenames for dataset

Examples

>>> import numpy as np
>>> from dipy.data import get_data
>>> fimg,fbvals,fbvecs=get_data('small_101D')
>>> bvals=np.loadtxt(fbvals)
>>> bvecs=np.loadtxt(fbvecs).T
>>> import nibabel as nib
>>> img=nib.load(fimg)
>>> data=img.get_data()
>>> data.shape == (6, 10, 10, 102)
True
>>> bvals.shape == (102,)
True
>>> bvecs.shape == (102, 3)
True

measure

dipy.segment.benchmarks.bench_quickbundles.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).

Returns:

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

BundleMinDistanceAsymmetricMetric

class dipy.segment.bundles.BundleMinDistanceAsymmetricMetric(num_threads=None)

Bases: dipy.align.streamlinear.BundleMinDistanceMetric

Asymmetric Bundle-based Minimum distance

Methods

distance(xopt)
setup(static, moving) Setup static and moving sets of streamlines
__init__(num_threads=None)

An abstract class for the metric used for streamline registration

If the two sets of streamlines match exactly then method distance of this object should be minimum.

Parameters:

num_threads : int

Number of threads. If None (default) then all available threads will be used. Only metrics using OpenMP will use this variable.

distance(xopt)

BundleMinDistanceMetric

class dipy.segment.bundles.BundleMinDistanceMetric(num_threads=None)

Bases: dipy.align.streamlinear.StreamlineDistanceMetric

Bundle-based Minimum Distance aka BMD

This is the cost function used by the StreamlineLinearRegistration

References

[Garyfallidis14]Garyfallidis et al., “Direct native-space fiber bundle alignment for group comparisons”, ISMRM, 2014.

Methods

setup(static, moving)  
distance(xopt)  
__init__(num_threads=None)

An abstract class for the metric used for streamline registration

If the two sets of streamlines match exactly then method distance of this object should be minimum.

Parameters:

num_threads : int

Number of threads. If None (default) then all available threads will be used. Only metrics using OpenMP will use this variable.

distance(xopt)

Distance calculated from this Metric

Parameters:

xopt : sequence

List of affine parameters as an 1D vector,

setup(static, moving)

Setup static and moving sets of streamlines

Parameters:

static : streamlines

Fixed or reference set of streamlines.

moving : streamlines

Moving streamlines.

num_threads : int

Number of threads. If None (default) then all available threads will be used.

Notes

Call this after the object is initiated and before distance.

BundleSumDistanceMatrixMetric

class dipy.segment.bundles.BundleSumDistanceMatrixMetric(num_threads=None)

Bases: dipy.align.streamlinear.BundleMinDistanceMatrixMetric

Bundle-based Sum Distance aka BMD

This is a cost function that can be used by the StreamlineLinearRegistration class.

Notes

The difference with BundleMinDistanceMatrixMetric is that it uses uses the sum of the distance matrix and not the sum of mins.

Methods

setup(static, moving)  
distance(xopt)  
__init__(num_threads=None)

An abstract class for the metric used for streamline registration

If the two sets of streamlines match exactly then method distance of this object should be minimum.

Parameters:

num_threads : int

Number of threads. If None (default) then all available threads will be used. Only metrics using OpenMP will use this variable.

distance(xopt)

Distance calculated from this Metric

Parameters:

xopt : sequence

List of affine parameters as an 1D vector

RecoBundles

class dipy.segment.bundles.RecoBundles(streamlines, cluster_map=None, clust_thr=15, nb_pts=20, seed=42, verbose=True)

Bases: object

Methods

recognize(model_bundle, model_clust_thr[, ...]) Recognize the model_bundle in self.streamlines
__init__(streamlines, cluster_map=None, clust_thr=15, nb_pts=20, seed=42, verbose=True)

Recognition of bundles

Extract bundles from a participants’ tractograms using model bundles segmented from a different subject or an atlas of bundles. See [Garyfallidis17] for the details.

Parameters:

streamlines : Streamlines

The tractogram in which you want to recognize bundles.

cluster_map : QB map

Provide existing clustering to start RB faster (default None).

clust_thr : float

Distance threshold in mm for clustering streamlines

seed : int

Setup for random number generator (default 42).

nb_pts : int

Number of points per streamline (default 20)

Notes

Make sure that before creating this class that the streamlines and the model bundles are roughly in the same space. Also default thresholds are assumed in RAS 1mm^3 space. You may want to adjust those if your streamlines are not in world coordinates.

References

[Garyfallidis17]Garyfallidis et al. Recognition of white matter bundles using local and global streamline-based registration and clustering, Neuroimage, 2017.
recognize(model_bundle, model_clust_thr, reduction_thr=20, reduction_distance='mdf', slr=True, slr_metric=None, slr_x0=None, slr_bounds=None, slr_select=(400, 600), slr_method='L-BFGS-B', pruning_thr=10, pruning_distance='mdf')

Recognize the model_bundle in self.streamlines

Parameters:

model_bundle : Streamlines

model_clust_thr : float

reduction_thr : float

reduction_distance : string

mdf or mam (default mam)

slr : bool

Use Streamline-based Linear Registration (SLR) locally (default True)

slr_metric : BundleMinDistanceMetric

slr_x0 : array

(default None)

slr_bounds : array

(default None)

slr_select : tuple

Select the number of streamlines from model to neirborhood of model to perform the local SLR.

slr_method : string

Optimization method (default ‘L-BFGS-B’)

pruning_thr : float

pruning_distance : string

MDF (‘mdf’) and MAM (‘mam’)

Returns:

recognized_transf : Streamlines

Recognized bundle in the space of the model tractogram

recognized_labels : array

Indices of recognized bundle in the original tractogram

recognized_bundle : Streamlines

Recognized bundle in the space of the original tractogram

References

[Garyfallidis17]Garyfallidis et al. Recognition of white matter bundles using local and global streamline-based registration and clustering, Neuroimage, 2017.

StreamlineLinearRegistration

class dipy.segment.bundles.StreamlineLinearRegistration(metric=None, x0='rigid', method='L-BFGS-B', bounds=None, verbose=False, options=None, evolution=False, num_threads=None)

Bases: object

Methods

optimize(static, moving[, mat]) Find the minimum of the provided metric.
__init__(metric=None, x0='rigid', method='L-BFGS-B', bounds=None, verbose=False, options=None, evolution=False, num_threads=None)

Linear registration of 2 sets of streamlines [Garyfallidis15].

Parameters:

metric : StreamlineDistanceMetric,

If None and fast is False then the BMD distance is used. If fast is True then a faster implementation of BMD is used. Otherwise, use the given distance metric.

x0 : array or int or str

Initial parametrization for the optimization.

If 1D array with:

a) 6 elements then only rigid registration is performed with the 3 first elements for translation and 3 for rotation. b) 7 elements also isotropic scaling is performed (similarity). c) 12 elements then translation, rotation (in degrees), scaling and shearing is performed (affine).

Here is an example of x0 with 12 elements: x0=np.array([0, 10, 0, 40, 0, 0, 2., 1.5, 1, 0.1, -0.5, 0])

This has translation (0, 10, 0), rotation (40, 0, 0) in degrees, scaling (2., 1.5, 1) and shearing (0.1, -0.5, 0).

If int:
  1. 6
    x0 = np.array([0, 0, 0, 0, 0, 0])
  2. 7
    x0 = np.array([0, 0, 0, 0, 0, 0, 1.])
  3. 12
    x0 = np.array([0, 0, 0, 0, 0, 0, 1., 1., 1, 0, 0, 0])
If str:
  1. “rigid”
    x0 = np.array([0, 0, 0, 0, 0, 0])
  2. “similarity”
    x0 = np.array([0, 0, 0, 0, 0, 0, 1.])
  3. “affine”
    x0 = np.array([0, 0, 0, 0, 0, 0, 1., 1., 1, 0, 0, 0])

method : str,

‘L_BFGS_B’ or ‘Powell’ optimizers can be used. Default is ‘L_BFGS_B’.

bounds : list of tuples or None,

If method == ‘L_BFGS_B’ then we can use bounded optimization. For example for the six parameters of rigid rotation we can set the bounds = [(-30, 30), (-30, 30), (-30, 30),

(-45, 45), (-45, 45), (-45, 45)]

That means that we have set the bounds for the three translations and three rotation axes (in degrees).

verbose : bool,

If True then information about the optimization is shown.

options : None or dict,

Extra options to be used with the selected method.

evolution : boolean

If True save the transformation for each iteration of the optimizer. Default is False. Supported only with Scipy >= 0.11.

num_threads : int

Number of threads. If None (default) then all available threads will be used. Only metrics using OpenMP will use this variable.

References

[Garyfallidis15](1, 2) Garyfallidis et al. “Robust and efficient linear registration of white-matter fascicles in the space of streamlines”, NeuroImage, 117, 124–140, 2015
[Garyfallidis14]Garyfallidis et al., “Direct native-space fiber bundle alignment for group comparisons”, ISMRM, 2014.
[Garyfallidis17]Garyfallidis et al. Recognition of white matter bundles using local and global streamline-based registration and clustering, Neuroimage, 2017.
optimize(static, moving, mat=None)

Find the minimum of the provided metric.

Parameters:

static : streamlines

Reference or fixed set of streamlines.

moving : streamlines

Moving set of streamlines.

mat : array

Transformation (4, 4) matrix to start the registration. mat is applied to moving. Default value None which means that initial transformation will be generated by shifting the centers of moving and static sets of streamlines to the origin.

Returns:

map : StreamlineRegistrationMap

Streamlines

class dipy.segment.bundles.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.

chain

class dipy.segment.bundles.chain

Bases: object

chain(*iterables) –> chain object

Return a chain object whose .__next__() method returns elements from the first iterable until it is exhausted, then elements from the next iterable, until all of the iterables are exhausted.

Methods

from_iterable chain.from_iterable(iterable) –> chain object
__init__()

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

from_iterable()

chain.from_iterable(iterable) –> chain object

Alternate chain() constructor taking a single iterable argument that evaluates lazily.

apply_affine

dipy.segment.bundles.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.

Returns:

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]]]...)

bundles_distances_mam

dipy.segment.bundles.bundles_distances_mam()

Calculate distances between list of tracks A and list of tracks B

Parameters:

tracksA : sequence

of tracks as arrays, shape (N1,3) .. (Nm,3)

tracksB : sequence

of tracks as arrays, shape (N1,3) .. (Nm,3)

metric : str

‘avg’, ‘min’, ‘max’

Returns:

DM : array, shape (len(tracksA), len(tracksB))

distances between tracksA and tracksB according to metric

bundles_distances_mdf

dipy.segment.bundles.bundles_distances_mdf()

Calculate distances between list of tracks A and list of tracks B

All tracks need to have the same number of points

Parameters:

tracksA : sequence

of tracks as arrays, [(N,3) .. (N,3)]

tracksB : sequence

of tracks as arrays, [(N,3) .. (N,3)]

Returns:

DM : array, shape (len(tracksA), len(tracksB))

distances between tracksA and tracksB according to metric

See also

dipy.metrics.downsample

nbytes

dipy.segment.bundles.nbytes(streamlines)

qbx_and_merge

dipy.segment.bundles.qbx_and_merge(streamlines, thresholds, nb_pts=20, select_randomly=None, rng=None, verbose=True)

Run QuickBundlesX and then run again on the centroids of the last layer

Running again QuickBundles at a layer has the effect of merging some of the clusters that maybe originally devided because of branching. This function help obtain a result at a QuickBundles quality but with QuickBundlesX speed. The merging phase has low cost because it is applied only on the centroids rather than the entire dataset.

Parameters:

streamlines : Streamlines

thresholds : sequence

List of distance thresholds for QuickBundlesX.

nb_pts : int

Number of points for discretizing each streamline

select_randomly : int

Randomly select a specific number of streamlines. If None all the streamlines are used.

rng : RandomState

If None then RandomState is initialized internally.

verbose : bool

If True print information in stdout.

Returns:

clusters : obj

Contains the clusters of the last layer of QuickBundlesX after merging.

References

[Garyfallidis12]Garyfallidis E. et al., QuickBundles a method for tractography simplification, Frontiers in Neuroscience, vol 6, no 175, 2012.
[Garyfallidis16]Garyfallidis E. et al. QuickBundlesX: Sequential clustering of millions of streamlines in multiple levels of detail at record execution time. Proceedings of the, International Society of Magnetic Resonance in Medicine (ISMRM). Singapore, 4187, 2016.

select_random_set_of_streamlines

dipy.segment.bundles.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).

Returns:

selected_streamlines : list

Notes

The same streamline will not be selected twice.

set_number_of_points

dipy.segment.bundles.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.

Returns:

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]

time

dipy.segment.bundles.time() → floating point number

Return the current time in seconds since the Epoch. Fractions of a second may be present if the system clock provides them.

ABCMeta

class dipy.segment.clustering.ABCMeta

Bases: type

Metaclass for defining Abstract Base Classes (ABCs).

Use this metaclass to create an ABC. An ABC can be subclassed directly, and then acts as a mix-in class. You can also register unrelated concrete classes (even built-in classes) and unrelated ABCs as ‘virtual subclasses’ – these and their descendants will be considered subclasses of the registering ABC by the built-in issubclass() function, but the registering ABC won’t show up in their MRO (Method Resolution Order) nor will method implementations defined by the registering ABC be callable (not even via super()).

Methods

__call__ Call self as a function.
mro(() -> list) return a type’s method resolution order
register(subclass) Register a virtual subclass of an ABC.
__init__()

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

register(subclass)

Register a virtual subclass of an ABC.

Returns the subclass, to allow usage as a class decorator.

AveragePointwiseEuclideanMetric

class dipy.segment.clustering.AveragePointwiseEuclideanMetric

Bases: dipy.segment.metricspeed.SumPointwiseEuclideanMetric

Computes the average of pointwise Euclidean distances between two sequential data.

A sequence of N-dimensional points is represented as a 2D array with shape (nb_points, nb_dimensions). A feature object can be specified in order to calculate the distance between the features, rather than directly between the sequential data.

Parameters:

feature : Feature object, optional

It is used to extract features before computing the distance.

Notes

The distance between two 2D sequential data:

s1       s2

0*   a    *0
  \       |
   \      |
   1*     |
    |  b  *1
    |      \
    2*      \
        c    *2

is equal to \((a+b+c)/3\) where \(a\) is the Euclidean distance between s1[0] and s2[0], \(b\) between s1[1] and s2[1] and \(c\) between s1[2] and s2[2].

Attributes

feature Feature object used to extract features from sequential data
is_order_invariant Is this metric invariant to the sequence’s ordering

Methods

are_compatible Checks if features can be used by metric.dist based on their shape.
dist Computes a distance between two data points based on their features.
__init__()

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

Cluster

class dipy.segment.clustering.Cluster(id=0, indices=None, refdata=<dipy.segment.clustering.Identity object>)

Bases: object

Provides functionalities for interacting with a cluster.

Useful container to retrieve index of elements grouped together. If a reference to the data is provided to cluster_map, elements will be returned instead of their index when possible.

Parameters:

cluster_map : ClusterMap object

Reference to the set of clusters this cluster is being part of.

id : int

Id of this cluster in its associated cluster_map object.

refdata : list (optional)

Actual elements that clustered indices refer to.

Notes

A cluster does not contain actual data but instead knows how to retrieve them using its ClusterMap object.

Methods

assign(*indices) Assigns indices to this cluster.
__init__(id=0, indices=None, refdata=<dipy.segment.clustering.Identity object>)
assign(*indices)

Assigns indices to this cluster.

Parameters:

*indices : list of indices

Indices to add to this cluster.

ClusterCentroid

class dipy.segment.clustering.ClusterCentroid(centroid, id=0, indices=None, refdata=<dipy.segment.clustering.Identity object>)

Bases: dipy.segment.clustering.Cluster

Provides functionalities for interacting with a cluster.

Useful container to retrieve the indices of elements grouped together and the cluster’s centroid. If a reference to the data is provided to cluster_map, elements will be returned instead of their index when possible.

Parameters:

cluster_map : ClusterMapCentroid object

Reference to the set of clusters this cluster is being part of.

id : int

Id of this cluster in its associated cluster_map object.

refdata : list (optional)

Actual elements that clustered indices refer to.

Notes

A cluster does not contain actual data but instead knows how to retrieve them using its ClusterMapCentroid object.

Methods

assign(id_datum, features) Assigns a data point to this cluster.
update() Update centroid of this cluster.
__init__(centroid, id=0, indices=None, refdata=<dipy.segment.clustering.Identity object>)
assign(id_datum, features)

Assigns a data point to this cluster.

Parameters:

id_datum : int

Index of the data point to add to this cluster.

features : 2D array

Data point’s features to modify this cluster’s centroid.

update()

Update centroid of this cluster.

Returns:

converged : bool

Tells if the centroid has moved.

ClusterMap

class dipy.segment.clustering.ClusterMap(refdata=<dipy.segment.clustering.Identity object>)

Bases: object

Provides functionalities for interacting with clustering outputs.

Useful container to create, remove, retrieve and filter clusters. If refdata is given, elements will be returned instead of their index when using Cluster objects.

Parameters:

refdata : list

Actual elements that clustered indices refer to.

Attributes

clusters
refdata

Methods

add_cluster(*clusters) Adds one or multiple clusters to this cluster map.
clear() Remove all clusters from this cluster map.
clusters_sizes() Gets the size of every cluster contained in this cluster map.
get_large_clusters(min_size) Gets clusters which contains at least min_size elements.
get_small_clusters(max_size) Gets clusters which contains at most max_size elements.
remove_cluster(*clusters) Remove one or multiple clusters from this cluster map.
size() Gets number of clusters contained in this cluster map.
__init__(refdata=<dipy.segment.clustering.Identity object>)
add_cluster(*clusters)

Adds one or multiple clusters to this cluster map.

Parameters:

*clusters : Cluster object, ...

Cluster(s) to be added in this cluster map.

clear()

Remove all clusters from this cluster map.

clusters
clusters_sizes()

Gets the size of every cluster contained in this cluster map.

Returns:

list of int

Sizes of every cluster in this cluster map.

get_large_clusters(min_size)

Gets clusters which contains at least min_size elements.

Parameters:

min_size : int

Minimum number of elements a cluster needs to have to be selected.

Returns:

list of Cluster objects

Clusters having at least min_size elements.

get_small_clusters(max_size)

Gets clusters which contains at most max_size elements.

Parameters:

max_size : int

Maximum number of elements a cluster can have to be selected.

Returns:

list of Cluster objects

Clusters having at most max_size elements.

refdata
remove_cluster(*clusters)

Remove one or multiple clusters from this cluster map.

Parameters:

*clusters : Cluster object, ...

Cluster(s) to be removed from this cluster map.

size()

Gets number of clusters contained in this cluster map.

ClusterMapCentroid

class dipy.segment.clustering.ClusterMapCentroid(refdata=<dipy.segment.clustering.Identity object>)

Bases: dipy.segment.clustering.ClusterMap

Provides functionalities for interacting with clustering outputs that have centroids.

Allows to retrieve easely the centroid of every cluster. Also, it is a useful container to create, remove, retrieve and filter clusters. If refdata is given, elements will be returned instead of their index when using ClusterCentroid objects.

Parameters:

refdata : list

Actual elements that clustered indices refer to.

Attributes

centroids
clusters
refdata

Methods

add_cluster(*clusters) Adds one or multiple clusters to this cluster map.
clear() Remove all clusters from this cluster map.
clusters_sizes() Gets the size of every cluster contained in this cluster map.
get_large_clusters(min_size) Gets clusters which contains at least min_size elements.
get_small_clusters(max_size) Gets clusters which contains at most max_size elements.
remove_cluster(*clusters) Remove one or multiple clusters from this cluster map.
size() Gets number of clusters contained in this cluster map.
__init__(refdata=<dipy.segment.clustering.Identity object>)
centroids

Clustering

class dipy.segment.clustering.Clustering

Bases: object

Methods

cluster(data[, ordering]) Clusters data.
__init__()

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

cluster(data, ordering=None)

Clusters data.

Subclasses will perform their clustering algorithm here.

Parameters:

data : list of N-dimensional arrays

Each array represents a data point.

ordering : iterable of indices, optional

Specifies the order in which data points will be clustered.

Returns:

ClusterMap object

Result of the clustering.

Identity

class dipy.segment.clustering.Identity

Bases: object

Provides identity indexing functionality.

This can replace any class supporting indexing used for referencing (e.g. list, tuple). Indexing an instance of this class will return the index provided instead of the element. It does not support slicing.

__init__()

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

Metric

class dipy.segment.clustering.Metric

Bases: object

Computes a distance between two sequential data.

A sequence of N-dimensional points is represented as a 2D array with shape (nb_points, nb_dimensions). A feature object can be specified in order to calculate the distance between extracted features, rather than directly between the sequential data.

Parameters:

feature : Feature object, optional

It is used to extract features before computing the distance.

Notes

When subclassing Metric, one only needs to override the dist and are_compatible methods.

Attributes

feature Feature object used to extract features from sequential data
is_order_invariant Is this metric invariant to the sequence’s ordering

Methods

are_compatible Checks if features can be used by metric.dist based on their shape.
dist Computes a distance between two data points based on their features.
__init__()

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

are_compatible()

Checks if features can be used by metric.dist based on their shape.

Basically this method exists so we don’t have to do this check inside the metric.dist function (speedup).

Parameters:

shape1 : int, 1-tuple or 2-tuple

shape of the first data point’s features

shape2 : int, 1-tuple or 2-tuple

shape of the second data point’s features

Returns:

are_compatible : bool

whether or not shapes are compatible

dist()

Computes a distance between two data points based on their features.

Parameters:

features1 : 2D array

Features of the first data point.

features2 : 2D array

Features of the second data point.

Returns:

double

Distance between two data points.

feature

Feature object used to extract features from sequential data

is_order_invariant

Is this metric invariant to the sequence’s ordering

MinimumAverageDirectFlipMetric

class dipy.segment.clustering.MinimumAverageDirectFlipMetric

Bases: dipy.segment.metricspeed.AveragePointwiseEuclideanMetric

Computes the MDF distance (minimum average direct-flip) between two sequential data.

A sequence of N-dimensional points is represented as a 2D array with shape (nb_points, nb_dimensions).

Notes

The distance between two 2D sequential data:

s1       s2

0*   a    *0
  \       |
   \      |
   1*     |
    |  b  *1
    |      \
    2*      \
        c    *2

is equal to \(\min((a+b+c)/3, (a'+b'+c')/3)\) where \(a\) is the Euclidean distance between s1[0] and s2[0], \(b\) between s1[1] and s2[1], \(c\) between s1[2] and s2[2], \(a'\) between s1[0] and s2[2], \(b'\) between s1[1] and s2[1] and \(c'\) between s1[2] and s2[0].

Attributes

feature Feature object used to extract features from sequential data
is_order_invariant Is this metric invariant to the sequence’s ordering

Methods

are_compatible Checks if features can be used by metric.dist based on their shape.
dist Computes a distance between two data points based on their features.
__init__()

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

is_order_invariant

Is this metric invariant to the sequence’s ordering

QuickBundles

class dipy.segment.clustering.QuickBundles(threshold, metric='MDF_12points', max_nb_clusters=2147483647)

Bases: dipy.segment.clustering.Clustering

Clusters streamlines using QuickBundles [Garyfallidis12].

Given a list of streamlines, the QuickBundles algorithm sequentially assigns each streamline to its closest bundle in \(\mathcal{O}(Nk)\) where \(N\) is the number of streamlines and \(k\) is the final number of bundles. If for a given streamline its closest bundle is farther than threshold, a new bundle is created and the streamline is assigned to it except if the number of bundles has already exceeded max_nb_clusters.

Parameters:

threshold : float

The maximum distance from a bundle for a streamline to be still considered as part of it.

metric : str or Metric object (optional)

The distance metric to use when comparing two streamlines. By default, the Minimum average Direct-Flip (MDF) distance [Garyfallidis12] is used and streamlines are automatically resampled so they have 12 points.

max_nb_clusters : int

Limits the creation of bundles.

References

[Garyfallidis12]Garyfallidis E. et al., QuickBundles a method for tractography simplification, Frontiers in Neuroscience, vol 6, no 175, 2012.

Examples

>>> from dipy.segment.clustering import QuickBundles
>>> from dipy.data import get_data
>>> from nibabel import trackvis as tv
>>> streams, hdr = tv.read(get_data('fornix'))
>>> streamlines = [i[0] for i in streams]
>>> # Segment fornix with a treshold of 10mm and streamlines resampled
>>> # to 12 points.
>>> qb = QuickBundles(threshold=10.)
>>> clusters = qb.cluster(streamlines)
>>> len(clusters)
4
>>> list(map(len, clusters))
[61, 191, 47, 1]
>>> # Resampling streamlines differently is done explicitly as follows.
>>> # Note this has an impact on the speed and the accuracy (tradeoff).
>>> from dipy.segment.metric import ResampleFeature
>>> from dipy.segment.metric import AveragePointwiseEuclideanMetric
>>> feature = ResampleFeature(nb_points=2)
>>> metric = AveragePointwiseEuclideanMetric(feature)
>>> qb = QuickBundles(threshold=10., metric=metric)
>>> clusters = qb.cluster(streamlines)
>>> len(clusters)
4
>>> list(map(len, clusters))
[58, 142, 72, 28]

Methods

cluster(streamlines[, ordering]) Clusters streamlines into bundles.
__init__(threshold, metric='MDF_12points', max_nb_clusters=2147483647)
cluster(streamlines, ordering=None)

Clusters streamlines into bundles.

Performs quickbundles algorithm using predefined metric and threshold.

Parameters:

streamlines : list of 2D arrays

Each 2D array represents a sequence of 3D points (points, 3).

ordering : iterable of indices

Specifies the order in which data points will be clustered.

Returns:

ClusterMapCentroid object

Result of the clustering.

QuickBundlesX

class dipy.segment.clustering.QuickBundlesX(thresholds, metric='MDF_12points')

Bases: dipy.segment.clustering.Clustering

Clusters streamlines using QuickBundlesX.

Parameters:

thresholds : list of float

Thresholds to use for each clustering layer. A threshold represents the maximum distance from a cluster for a streamline to be still considered as part of it.

metric : str or Metric object (optional)

The distance metric to use when comparing two streamlines. By default, the Minimum average Direct-Flip (MDF) distance [Garyfallidis12] is used and streamlines are automatically resampled so they have 12 points.

References

[Garyfallidis12]Garyfallidis E. et al., QuickBundles a method for tractography simplification, Frontiers in Neuroscience, vol 6, no 175, 2012.
[Garyfallidis16]Garyfallidis E. et al. QuickBundlesX: Sequential clustering of millions of streamlines in multiple levels of detail at record execution time. Proceedings of the, International Society of Magnetic Resonance in Medicine (ISMRM). Singapore, 4187, 2016.

Methods

cluster(streamlines[, ordering]) Clusters streamlines into bundles.
__init__(thresholds, metric='MDF_12points')
cluster(streamlines, ordering=None)

Clusters streamlines into bundles.

Performs QuickbundleX using a predefined metric and thresholds.

Parameters:

streamlines : list of 2D arrays

Each 2D array represents a sequence of 3D points (points, 3).

ordering : iterable of indices

Specifies the order in which data points will be clustered.

Returns:

TreeClusterMap object

Result of the clustering.

ResampleFeature

class dipy.segment.clustering.ResampleFeature

Bases: dipy.segment.featurespeed.CythonFeature

Extracts features from a sequential datum.

A sequence of N-dimensional points is represented as a 2D array with shape (nb_points, nb_dimensions).

The features being extracted are the points of the sequence once resampled. This is useful for metrics requiring a constant number of points for all

streamlines.

Attributes

is_order_invariant Is this feature invariant to the sequence’s ordering

Methods

extract Extracts features from a sequential datum.
infer_shape Infers the shape of features extracted from a sequential datum.
__init__()

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

TreeCluster

class dipy.segment.clustering.TreeCluster(threshold, centroid, indices=None)

Bases: dipy.segment.clustering.ClusterCentroid

Attributes

is_leaf

Methods

add(child)
assign(id_datum, features) Assigns a data point to this cluster.
update() Update centroid of this cluster.
__init__(threshold, centroid, indices=None)
add(child)
is_leaf

TreeClusterMap

class dipy.segment.clustering.TreeClusterMap(root)

Bases: dipy.segment.clustering.ClusterMap

Attributes

clusters
refdata

Methods

add_cluster(*clusters) Adds one or multiple clusters to this cluster map.
clear() Remove all clusters from this cluster map.
clusters_sizes() Gets the size of every cluster contained in this cluster map.
get_clusters(wanted_level)
get_large_clusters(min_size) Gets clusters which contains at least min_size elements.
get_small_clusters(max_size) Gets clusters which contains at most max_size elements.
iter_preorder(node)
remove_cluster(*clusters) Remove one or multiple clusters from this cluster map.
size() Gets number of clusters contained in this cluster map.
traverse_postorder(node, visit)
__init__(root)
get_clusters(wanted_level)
iter_preorder(node)
refdata
traverse_postorder(node, visit)

abstractmethod

dipy.segment.clustering.abstractmethod(funcobj)

A decorator indicating abstract methods.

Requires that the metaclass is ABCMeta or derived from it. A class that has a metaclass derived from ABCMeta cannot be instantiated unless all of its abstract methods are overridden. The abstract methods can be called using any of the normal ‘super’ call mechanisms.

Usage:

class C(metaclass=ABCMeta):

@abstractmethod def my_abstract_method(self, ...):

...

nbytes

dipy.segment.clustering.nbytes(streamlines)

qbx_and_merge

dipy.segment.clustering.qbx_and_merge(streamlines, thresholds, nb_pts=20, select_randomly=None, rng=None, verbose=True)

Run QuickBundlesX and then run again on the centroids of the last layer

Running again QuickBundles at a layer has the effect of merging some of the clusters that maybe originally devided because of branching. This function help obtain a result at a QuickBundles quality but with QuickBundlesX speed. The merging phase has low cost because it is applied only on the centroids rather than the entire dataset.

Parameters:

streamlines : Streamlines

thresholds : sequence

List of distance thresholds for QuickBundlesX.

nb_pts : int

Number of points for discretizing each streamline

select_randomly : int

Randomly select a specific number of streamlines. If None all the streamlines are used.

rng : RandomState

If None then RandomState is initialized internally.

verbose : bool

If True print information in stdout.

Returns:

clusters : obj

Contains the clusters of the last layer of QuickBundlesX after merging.

References

[Garyfallidis12]Garyfallidis E. et al., QuickBundles a method for tractography simplification, Frontiers in Neuroscience, vol 6, no 175, 2012.
[Garyfallidis16]Garyfallidis E. et al. QuickBundlesX: Sequential clustering of millions of streamlines in multiple levels of detail at record execution time. Proceedings of the, International Society of Magnetic Resonance in Medicine (ISMRM). Singapore, 4187, 2016.

set_number_of_points

dipy.segment.clustering.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.

Returns:

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]

time

dipy.segment.clustering.time() → floating point number

Return the current time in seconds since the Epoch. Fractions of a second may be present if the system clock provides them.

applymask

dipy.segment.mask.applymask(vol, mask)

Mask vol with mask.

Parameters:

vol : ndarray

Array with \(V\) dimensions

mask : ndarray

Binary mask. Has \(M\) dimensions where \(M <= V\). When \(M < V\), we append \(V - M\) dimensions with axis length 1 to mask so that mask will broadcast against vol. In the typical case vol can be 4D, mask can be 3D, and we append a 1 to the mask shape which (via numpy broadcasting) has the effect of appling the 3D mask to each 3D slice in vol (vol[..., 0] to vol[..., -1).

Returns:

masked_vol : ndarray

vol multiplied by mask where mask may have been extended to match extra dimensions in vol

binary_dilation

dipy.segment.mask.binary_dilation(input, structure=None, iterations=1, mask=None, output=None, border_value=0, origin=0, brute_force=False)

Multi-dimensional binary dilation with the given structuring element.

Parameters:

input : array_like

Binary array_like to be dilated. Non-zero (True) elements form the subset to be dilated.

structure : array_like, optional

Structuring element used for the dilation. Non-zero elements are considered True. If no structuring element is provided an element is generated with a square connectivity equal to one.

iterations : {int, float}, optional

The dilation is repeated iterations times (one, by default). If iterations is less than 1, the dilation is repeated until the result does not change anymore.

mask : array_like, optional

If a mask is given, only those elements with a True value at the corresponding mask element are modified at each iteration.

output : ndarray, optional

Array of the same shape as input, into which the output is placed. By default, a new array is created.

origin : int or tuple of ints, optional

Placement of the filter, by default 0.

border_value : int (cast to 0 or 1), optional

Value at the border in the output array.

Returns:

binary_dilation : ndarray of bools

Dilation of the input by the structuring element.

See also

grey_dilation, binary_erosion, binary_closing, binary_opening, generate_binary_structure

Notes

Dilation [R424] is a mathematical morphology operation [R425] that uses a structuring element for expanding the shapes in an image. The binary dilation of an image by a structuring element is the locus of the points covered by the structuring element, when its center lies within the non-zero points of the image.

References

[R424](1, 2) http://en.wikipedia.org/wiki/Dilation_%28morphology%29
[R425](1, 2) http://en.wikipedia.org/wiki/Mathematical_morphology

Examples

>>> from scipy import ndimage
>>> a = np.zeros((5, 5))
>>> a[2, 2] = 1
>>> a
array([[ 0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  1.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.]])
>>> ndimage.binary_dilation(a)
array([[False, False, False, False, False],
       [False, False,  True, False, False],
       [False,  True,  True,  True, False],
       [False, False,  True, False, False],
       [False, False, False, False, False]], dtype=bool)
>>> ndimage.binary_dilation(a).astype(a.dtype)
array([[ 0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  1.,  0.,  0.],
       [ 0.,  1.,  1.,  1.,  0.],
       [ 0.,  0.,  1.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.]])
>>> # 3x3 structuring element with connectivity 1, used by default
>>> struct1 = ndimage.generate_binary_structure(2, 1)
>>> struct1
array([[False,  True, False],
       [ True,  True,  True],
       [False,  True, False]], dtype=bool)
>>> # 3x3 structuring element with connectivity 2
>>> struct2 = ndimage.generate_binary_structure(2, 2)
>>> struct2
array([[ True,  True,  True],
       [ True,  True,  True],
       [ True,  True,  True]], dtype=bool)
>>> ndimage.binary_dilation(a, structure=struct1).astype(a.dtype)
array([[ 0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  1.,  0.,  0.],
       [ 0.,  1.,  1.,  1.,  0.],
       [ 0.,  0.,  1.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.]])
>>> ndimage.binary_dilation(a, structure=struct2).astype(a.dtype)
array([[ 0.,  0.,  0.,  0.,  0.],
       [ 0.,  1.,  1.,  1.,  0.],
       [ 0.,  1.,  1.,  1.,  0.],
       [ 0.,  1.,  1.,  1.,  0.],
       [ 0.,  0.,  0.,  0.,  0.]])
>>> ndimage.binary_dilation(a, structure=struct1,\
... iterations=2).astype(a.dtype)
array([[ 0.,  0.,  1.,  0.,  0.],
       [ 0.,  1.,  1.,  1.,  0.],
       [ 1.,  1.,  1.,  1.,  1.],
       [ 0.,  1.,  1.,  1.,  0.],
       [ 0.,  0.,  1.,  0.,  0.]])

bounding_box

dipy.segment.mask.bounding_box(vol)

Compute the bounding box of nonzero intensity voxels in the volume.

Parameters:

vol : ndarray

Volume to compute bounding box on.

Returns:

npmins : list

Array containg minimum index of each dimension

npmaxs : list

Array containg maximum index of each dimension

clean_cc_mask

dipy.segment.mask.clean_cc_mask(mask)

Cleans a segmentation of the corpus callosum so no random pixels are included.

Parameters:

mask : ndarray

Binary mask of the coarse segmentation.

Returns:

new_cc_mask : ndarray

Binary mask of the cleaned segmentation.

color_fa

dipy.segment.mask.color_fa(fa, evecs)

Color fractional anisotropy of diffusion tensor

Parameters:

fa : array-like

Array of the fractional anisotropy (can be 1D, 2D or 3D)

evecs : array-like

eigen vectors from the tensor model

Returns:

rgb : Array with 3 channels for each color as the last dimension.

Colormap of the FA with red for the x value, y for the green value and z for the blue value.

ec{e})) imes fa

crop

dipy.segment.mask.crop(vol, mins, maxs)

Crops the input volume.

Parameters:

vol : ndarray

Volume to crop.

mins : array

Array containg minimum index of each dimension.

maxs : array

Array containg maximum index of each dimension.

Returns:

vol : ndarray

The cropped volume.

fractional_anisotropy

dipy.segment.mask.fractional_anisotropy(evals, axis=-1)
Fractional anisotropy (FA) of a diffusion tensor.
Parameters:

evals : array-like

Eigenvalues of a diffusion tensor.

axis : int

Axis of evals which contains 3 eigenvalues.

Returns:

fa : array

Calculated FA. Range is 0 <= FA <= 1.

rac{1}{2} rac{(lambda_1-lambda_2)^2+(lambda_1-

lambda_3)^2+(lambda_2-lambda_3)^2}{lambda_1^2+ lambda_2^2+lambda_3^2}}

generate_binary_structure

dipy.segment.mask.generate_binary_structure(rank, connectivity)

Generate a binary structure for binary morphological operations.

Parameters:

rank : int

Number of dimensions of the array to which the structuring element will be applied, as returned by np.ndim.

connectivity : int

connectivity determines which elements of the output array belong to the structure, i.e. are considered as neighbors of the central element. Elements up to a squared distance of connectivity from the center are considered neighbors. connectivity may range from 1 (no diagonal elements are neighbors) to rank (all elements are neighbors).

Returns:

output : ndarray of bools

Structuring element which may be used for binary morphological operations, with rank dimensions and all dimensions equal to 3.

See also

iterate_structure, binary_dilation, binary_erosion

Notes

generate_binary_structure can only create structuring elements with dimensions equal to 3, i.e. minimal dimensions. For larger structuring elements, that are useful e.g. for eroding large objects, one may either use iterate_structure, or create directly custom arrays with numpy functions such as numpy.ones.

Examples

>>> from scipy import ndimage
>>> struct = ndimage.generate_binary_structure(2, 1)
>>> struct
array([[False,  True, False],
       [ True,  True,  True],
       [False,  True, False]], dtype=bool)
>>> a = np.zeros((5,5))
>>> a[2, 2] = 1
>>> a
array([[ 0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  1.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.]])
>>> b = ndimage.binary_dilation(a, structure=struct).astype(a.dtype)
>>> b
array([[ 0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  1.,  0.,  0.],
       [ 0.,  1.,  1.,  1.,  0.],
       [ 0.,  0.,  1.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.]])
>>> ndimage.binary_dilation(b, structure=struct).astype(a.dtype)
array([[ 0.,  0.,  1.,  0.,  0.],
       [ 0.,  1.,  1.,  1.,  0.],
       [ 1.,  1.,  1.,  1.,  1.],
       [ 0.,  1.,  1.,  1.,  0.],
       [ 0.,  0.,  1.,  0.,  0.]])
>>> struct = ndimage.generate_binary_structure(2, 2)
>>> struct
array([[ True,  True,  True],
       [ True,  True,  True],
       [ True,  True,  True]], dtype=bool)
>>> struct = ndimage.generate_binary_structure(3, 1)
>>> struct # no diagonal elements
array([[[False, False, False],
        [False,  True, False],
        [False, False, False]],
       [[False,  True, False],
        [ True,  True,  True],
        [False,  True, False]],
       [[False, False, False],
        [False,  True, False],
        [False, False, False]]], dtype=bool)

median_filter

dipy.segment.mask.median_filter(input, size=None, footprint=None, output=None, mode='reflect', cval=0.0, origin=0)

Calculates a multidimensional median filter.

Parameters:

input : array_like

Input array to filter.

size : scalar or tuple, optional

See footprint, below

footprint : array, optional

Either size or footprint must be defined. size gives the shape that is taken from the input array, at every element position, to define the input to the filter function. footprint is a boolean array that specifies (implicitly) a shape, but also which of the elements within this shape will get passed to the filter function. Thus size=(n,m) is equivalent to footprint=np.ones((n,m)). We adjust size to the number of dimensions of the input array, so that, if the input array is shape (10,10,10), and size is 2, then the actual size used is (2,2,2).

output : array, optional

The output parameter passes an array in which to store the filter output. Output array should have different name as compared to input array to avoid aliasing errors.

mode : {‘reflect’, ‘constant’, ‘nearest’, ‘mirror’, ‘wrap’}, optional

The mode parameter determines how the array borders are handled, where cval is the value when mode is equal to ‘constant’. Default is ‘reflect’

cval : scalar, optional

Value to fill past edges of input if mode is ‘constant’. Default is 0.0

origin : scalar, optional

The origin parameter controls the placement of the filter. Default 0.0.

Returns:

median_filter : ndarray

Filtered array. Has the same shape as input.

Examples

>>> from scipy import ndimage, misc
>>> import matplotlib.pyplot as plt
>>> fig = plt.figure()
>>> plt.gray()  # show the filtered result in grayscale
>>> ax1 = fig.add_subplot(121)  # left side
>>> ax2 = fig.add_subplot(122)  # right side
>>> ascent = misc.ascent()
>>> result = ndimage.median_filter(ascent, size=20)
>>> ax1.imshow(ascent)
>>> ax2.imshow(result)
>>> plt.show()

median_otsu

dipy.segment.mask.median_otsu(input_volume, median_radius=4, numpass=4, autocrop=False, vol_idx=None, dilate=None)

Simple brain extraction tool method for images from DWI data.

It uses a median filter smoothing of the input_volumes vol_idx and an automatic histogram Otsu thresholding technique, hence the name median_otsu.

This function is inspired from Mrtrix’s bet which has default values median_radius=3, numpass=2. However, from tests on multiple 1.5T and 3T data from GE, Philips, Siemens, the most robust choice is median_radius=4, numpass=4.

Parameters:

input_volume : ndarray

ndarray of the brain volume

median_radius : int

Radius (in voxels) of the applied median filter (default: 4).

numpass: int

Number of pass of the median filter (default: 4).

autocrop: bool, optional

if True, the masked input_volume will also be cropped using the bounding box defined by the masked data. Should be on if DWI is upsampled to 1x1x1 resolution. (default: False).

vol_idx : None or array, optional

1D array representing indices of axis=3 of a 4D input_volume None (the default) corresponds to (0,) (assumes first volume in 4D array).

dilate : None or int, optional

number of iterations for binary dilation

Returns:

maskedvolume : ndarray

Masked input_volume

mask : 3D ndarray

The binary brain mask

Notes

Copyright (C) 2011, the scikit-image team All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

  1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
  2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
  3. Neither the name of skimage nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS’’ AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

multi_median

dipy.segment.mask.multi_median(input, median_radius, numpass)

Applies median filter multiple times on input data.

Parameters:

input : ndarray

The input volume to apply filter on.

median_radius : int

Radius (in voxels) of the applied median filter

numpass: int

Number of pass of the median filter

Returns:

input : ndarray

Filtered input volume.

otsu

dipy.segment.mask.otsu(image, nbins=256)

Return threshold value based on Otsu’s method. Copied from scikit-image to remove dependency.

Parameters:

image : array

Input image.

nbins : int

Number of bins used to calculate histogram. This value is ignored for integer arrays.

Returns:

threshold : float

Threshold value.

segment_from_cfa

dipy.segment.mask.segment_from_cfa(tensor_fit, roi, threshold, return_cfa=False)

Segment the cfa inside roi using the values from threshold as bounds.

Parameters:

tensor_fit : TensorFit object

TensorFit object

roi : ndarray

A binary mask, which contains the bounding box for the segmentation.

threshold : array-like

An iterable that defines the min and max values to use for the thresholding. The values are specified as (R_min, R_max, G_min, G_max, B_min, B_max)

return_cfa : bool, optional

If True, the cfa is also returned.

Returns:

mask : ndarray

Binary mask of the segmentation.

cfa : ndarray, optional

Array with shape = (..., 3), where ... is the shape of tensor_fit. The color fractional anisotropy, ordered as a nd array with the last dimension of size 3 for the R, G and B channels.

warn

dipy.segment.mask.warn()

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

ArcLengthFeature

class dipy.segment.metric.ArcLengthFeature

Bases: dipy.segment.featurespeed.CythonFeature

Extracts features from a sequential datum.

A sequence of N-dimensional points is represented as a 2D array with shape (nb_points, nb_dimensions).

The feature being extracted consists of one scalar representing the arc length of the sequence (i.e. the sum of the length of all segments).

Attributes

is_order_invariant Is this feature invariant to the sequence’s ordering

Methods

extract Extracts features from a sequential datum.
infer_shape Infers the shape of features extracted from a sequential datum.
__init__()

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

AveragePointwiseEuclideanMetric

class dipy.segment.metric.AveragePointwiseEuclideanMetric

Bases: dipy.segment.metricspeed.SumPointwiseEuclideanMetric

Computes the average of pointwise Euclidean distances between two sequential data.

A sequence of N-dimensional points is represented as a 2D array with shape (nb_points, nb_dimensions). A feature object can be specified in order to calculate the distance between the features, rather than directly between the sequential data.

Parameters:

feature : Feature object, optional

It is used to extract features before computing the distance.

Notes

The distance between two 2D sequential data:

s1       s2

0*   a    *0
  \       |
   \      |
   1*     |
    |  b  *1
    |      \
    2*      \
        c    *2

is equal to \((a+b+c)/3\) where \(a\) is the Euclidean distance between s1[0] and s2[0], \(b\) between s1[1] and s2[1] and \(c\) between s1[2] and s2[2].

Attributes

feature Feature object used to extract features from sequential data
is_order_invariant Is this metric invariant to the sequence’s ordering

Methods

are_compatible Checks if features can be used by metric.dist based on their shape.
dist Computes a distance between two data points based on their features.
__init__()

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

CenterOfMassFeature

class dipy.segment.metric.CenterOfMassFeature

Bases: dipy.segment.featurespeed.CythonFeature

Extracts features from a sequential datum.

A sequence of N-dimensional points is represented as a 2D array with shape (nb_points, nb_dimensions).

The feature being extracted consists of one N-dimensional point representing the mean of the points, i.e. the center of mass.

Attributes

is_order_invariant Is this feature invariant to the sequence’s ordering

Methods

extract Extracts features from a sequential datum.
infer_shape Infers the shape of features extracted from a sequential datum.
__init__()

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

CosineMetric

class dipy.segment.metric.CosineMetric

Bases: dipy.segment.metricspeed.CythonMetric

Computes the cosine distance between two vectors.

A vector (i.e. a N-dimensional point) is represented as a 2D array with shape (1, nb_dimensions).

Notes

The distance between two vectors \(v_1\) and \(v_2\) is equal to \(\frac{1}{\pi} \arccos\left(\frac{v_1 \cdot v_2}{\|v_1\| \|v_2\|}\right)\) and is bounded within \([0,1]\).

Attributes

feature Feature object used to extract features from sequential data
is_order_invariant Is this metric invariant to the sequence’s ordering

Methods

are_compatible Checks if features can be used by metric.dist based on their shape.
dist Computes a distance between two data points based on their features.
__init__()

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

EuclideanMetric

dipy.segment.metric.EuclideanMetric

alias of SumPointwiseEuclideanMetric

Feature

class dipy.segment.metric.Feature

Bases: object

Extracts features from a sequential datum.

A sequence of N-dimensional points is represented as a 2D array with shape (nb_points, nb_dimensions).

Parameters:

is_order_invariant : bool (optional)

tells if this feature is invariant to the sequence’s ordering. This means starting from either extremities produces the same features. (Default: True)

Notes

When subclassing Feature, one only needs to override the extract and infer_shape methods.

Attributes

is_order_invariant Is this feature invariant to the sequence’s ordering

Methods

extract Extracts features from a sequential datum.
infer_shape Infers the shape of features extracted from a sequential datum.
__init__()

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

extract()

Extracts features from a sequential datum.

Parameters:

datum : 2D array

Sequence of N-dimensional points.

Returns:

2D array

Features extracted from datum.

infer_shape()

Infers the shape of features extracted from a sequential datum.

Parameters:

datum : 2D array

Sequence of N-dimensional points.

Returns:

int, 1-tuple or 2-tuple

Shape of the features.

is_order_invariant

Is this feature invariant to the sequence’s ordering

IdentityFeature

class dipy.segment.metric.IdentityFeature

Bases: dipy.segment.featurespeed.CythonFeature

Extracts features from a sequential datum.

A sequence of N-dimensional points is represented as a 2D array with shape (nb_points, nb_dimensions).

The features being extracted are the actual sequence’s points. This is useful for metric that does not require any pre-processing.

Attributes

is_order_invariant Is this feature invariant to the sequence’s ordering

Methods

extract Extracts features from a sequential datum.
infer_shape Infers the shape of features extracted from a sequential datum.
__init__()

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

Metric

class dipy.segment.metric.Metric

Bases: object

Computes a distance between two sequential data.

A sequence of N-dimensional points is represented as a 2D array with shape (nb_points, nb_dimensions). A feature object can be specified in order to calculate the distance between extracted features, rather than directly between the sequential data.

Parameters:

feature : Feature object, optional

It is used to extract features before computing the distance.

Notes

When subclassing Metric, one only needs to override the dist and are_compatible methods.

Attributes

feature Feature object used to extract features from sequential data
is_order_invariant Is this metric invariant to the sequence’s ordering

Methods

are_compatible Checks if features can be used by metric.dist based on their shape.
dist Computes a distance between two data points based on their features.
__init__()

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

are_compatible()

Checks if features can be used by metric.dist based on their shape.

Basically this method exists so we don’t have to do this check inside the metric.dist function (speedup).

Parameters:

shape1 : int, 1-tuple or 2-tuple

shape of the first data point’s features

shape2 : int, 1-tuple or 2-tuple

shape of the second data point’s features

Returns:

are_compatible : bool

whether or not shapes are compatible

dist()

Computes a distance between two data points based on their features.

Parameters:

features1 : 2D array

Features of the first data point.

features2 : 2D array

Features of the second data point.

Returns:

double

Distance between two data points.

feature

Feature object used to extract features from sequential data

is_order_invariant

Is this metric invariant to the sequence’s ordering

MidpointFeature

class dipy.segment.metric.MidpointFeature

Bases: dipy.segment.featurespeed.CythonFeature

Extracts features from a sequential datum.

A sequence of N-dimensional points is represented as a 2D array with shape (nb_points, nb_dimensions).

The feature being extracted consists of one N-dimensional point representing the middle point of the sequence (i.e. `nb_points//2`th point).

Attributes

is_order_invariant Is this feature invariant to the sequence’s ordering

Methods

extract Extracts features from a sequential datum.
infer_shape Infers the shape of features extracted from a sequential datum.
__init__()

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

MinimumAverageDirectFlipMetric

class dipy.segment.metric.MinimumAverageDirectFlipMetric

Bases: dipy.segment.metricspeed.AveragePointwiseEuclideanMetric

Computes the MDF distance (minimum average direct-flip) between two sequential data.

A sequence of N-dimensional points is represented as a 2D array with shape (nb_points, nb_dimensions).

Notes

The distance between two 2D sequential data:

s1       s2

0*   a    *0
  \       |
   \      |
   1*     |
    |  b  *1
    |      \
    2*      \
        c    *2

is equal to \(\min((a+b+c)/3, (a'+b'+c')/3)\) where \(a\) is the Euclidean distance between s1[0] and s2[0], \(b\) between s1[1] and s2[1], \(c\) between s1[2] and s2[2], \(a'\) between s1[0] and s2[2], \(b'\) between s1[1] and s2[1] and \(c'\) between s1[2] and s2[0].

Attributes

feature Feature object used to extract features from sequential data
is_order_invariant Is this metric invariant to the sequence’s ordering

Methods

are_compatible Checks if features can be used by metric.dist based on their shape.
dist Computes a distance between two data points based on their features.
__init__()

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

is_order_invariant

Is this metric invariant to the sequence’s ordering

ResampleFeature

class dipy.segment.metric.ResampleFeature

Bases: dipy.segment.featurespeed.CythonFeature

Extracts features from a sequential datum.

A sequence of N-dimensional points is represented as a 2D array with shape (nb_points, nb_dimensions).

The features being extracted are the points of the sequence once resampled. This is useful for metrics requiring a constant number of points for all

streamlines.

Attributes

is_order_invariant Is this feature invariant to the sequence’s ordering

Methods

extract Extracts features from a sequential datum.
infer_shape Infers the shape of features extracted from a sequential datum.
__init__()

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

SumPointwiseEuclideanMetric

class dipy.segment.metric.SumPointwiseEuclideanMetric

Bases: dipy.segment.metricspeed.CythonMetric

Computes the sum of pointwise Euclidean distances between two sequential data.

A sequence of N-dimensional points is represented as a 2D array with shape (nb_points, nb_dimensions). A feature object can be specified in order to calculate the distance between the features, rather than directly between the sequential data.

Parameters:

feature : Feature object, optional

It is used to extract features before computing the distance.

Notes

The distance between two 2D sequential data:

s1       s2

0*   a    *0
  \       |
   \      |
   1*     |
    |  b  *1
    |      \
    2*      \
        c    *2

is equal to \(a+b+c\) where \(a\) is the Euclidean distance between s1[0] and s2[0], \(b\) between s1[1] and s2[1] and \(c\) between s1[2] and s2[2].

Attributes

feature Feature object used to extract features from sequential data
is_order_invariant Is this metric invariant to the sequence’s ordering

Methods

are_compatible Checks if features can be used by metric.dist based on their shape.
dist Computes a distance between two data points based on their features.
__init__()

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

VectorOfEndpointsFeature

class dipy.segment.metric.VectorOfEndpointsFeature

Bases: dipy.segment.featurespeed.CythonFeature

Extracts features from a sequential datum.

A sequence of N-dimensional points is represented as a 2D array with shape (nb_points, nb_dimensions).

The feature being extracted consists of one vector in the N-dimensional space pointing from one end-point of the sequence to the other (i.e. S[-1]-S[0]).

Attributes

is_order_invariant Is this feature invariant to the sequence’s ordering

Methods

extract Extracts features from a sequential datum.
infer_shape Infers the shape of features extracted from a sequential datum.
__init__()

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

dist

dipy.segment.metric.dist()

Computes a distance between datum1 and datum2.

A sequence of N-dimensional points is represented as a 2D array with shape (nb_points, nb_dimensions).

Parameters:

metric : Metric object

Tells how to compute the distance between datum1 and datum2.

datum1 : 2D array

Sequence of N-dimensional points.

datum2 : 2D array

Sequence of N-dimensional points.

Returns:

double

Distance between two data points.

distance_matrix

dipy.segment.metric.distance_matrix()

Computes the distance matrix between two lists of sequential data.

The distance matrix is obtained by computing the pairwise distance of all tuples spawn by the Cartesian product of data1 with data2. If data2 is not provided, the Cartesian product of data1 with itself is used instead. A sequence of N-dimensional points is represented as a 2D array with shape (nb_points, nb_dimensions).

Parameters:

metric : Metric object

Tells how to compute the distance between two sequential data.

data1 : list of 2D arrays

List of sequences of N-dimensional points.

data2 : list of 2D arrays

Llist of sequences of N-dimensional points.

Returns:

2D array (double)

Distance matrix.

mdf

dipy.segment.metric.mdf(s1, s2)

Computes the MDF (Minimum average Direct-Flip) distance [Garyfallidis12] between two streamlines.

Streamlines must have the same number of points.

Parameters:

s1 : 2D array

A streamline (sequence of N-dimensional points).

s2 : 2D array

A streamline (sequence of N-dimensional points).

Returns:

double

Distance between two streamlines.

References

[Garyfallidis12]Garyfallidis E. et al., QuickBundles a method for tractography simplification, Frontiers in Neuroscience, vol 6, no 175, 2012.

QuickBundles

class dipy.segment.quickbundles.QuickBundles(tracks, dist_thr=4.0, pts=12)

Bases: object

Attributes

centroids
total_clusters

Methods

clusters()
clusters_sizes()
downsampled_tracks()
exemplars([tracks])
label2cluster(id)
label2tracks(tracks, id)
label2tracksids(id)
partitions()
points_per_track()
remove_cluster(id)
remove_clusters(list_ids)
remove_small_clusters(size) Remove clusters with small size
remove_tracks()
virtuals()
__init__(tracks, dist_thr=4.0, pts=12)

Highly efficient trajectory clustering [Garyfallidis12].

Parameters:

tracks : sequence of (N,3) ... (M,3) arrays

trajectories (or tractography or streamlines)

dist_thr : float

distance threshold in the space of the tracks

pts : int

number of points for simplifying the tracks

References

[Garyfallidis12]Garyfallidis E. et al., QuickBundles a method for tractography simplification, Frontiers in Neuroscience, vol 6, no 175, 2012.

Methods

clustering() returns a dict holding with the clustering result  
virtuals() gives the virtuals (track centroids) of the clusters  
exemplars() gives the exemplars (track medoids) of the clusters  
centroids
clusters()
clusters_sizes()
downsampled_tracks()
exemplars(tracks=None)
label2cluster(id)
label2tracks(tracks, id)
label2tracksids(id)
partitions()
points_per_track()
remove_cluster(id)
remove_clusters(list_ids)
remove_small_clusters(size)

Remove clusters with small size

Parameters:size : int, threshold for minimum number of tracks allowed
remove_tracks()
total_clusters
virtuals()

bundles_distances_mdf

dipy.segment.quickbundles.bundles_distances_mdf()

Calculate distances between list of tracks A and list of tracks B

All tracks need to have the same number of points

Parameters:

tracksA : sequence

of tracks as arrays, [(N,3) .. (N,3)]

tracksB : sequence

of tracks as arrays, [(N,3) .. (N,3)]

Returns:

DM : array, shape (len(tracksA), len(tracksB))

distances between tracksA and tracksB according to metric

See also

dipy.metrics.downsample

downsample

dipy.segment.quickbundles.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.

Returns:

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

local_skeleton_clustering

dipy.segment.quickbundles.local_skeleton_clustering()

Efficient tractography clustering

Every track can needs to have the same number of points. Use dipy.tracking.metrics.downsample to restrict the number of points

Parameters:

tracks : sequence

of tracks as arrays, shape (N,3) .. (N,3) where N=points

d_thr : float

average euclidean distance threshold

Returns:

C : dict

Clusters.

Notes

The distance calculated between two tracks:

t_1       t_2

0*   a    *0
  \       |
   \      |
   1*     |
    |  b  *1
    |      \
    2*      \
        c    *2

is equal to \((a+b+c)/3\) where \(a\) the euclidean distance between t_1[0] and t_2[0], \(b\) between t_1[1] and t_2[1] and \(c\) between t_1[2] and t_2[2]. Also the same with t2 flipped (so t_1[0] compared to t_2[2] etc).

Visualization:

It is possible to visualize the clustering C from the example above using the fvtk module:

from dipy.viz import fvtk
r=fvtk.ren()
for c in C:
    color=np.random.rand(3)
    for i in C[c]['indices']:
        fvtk.add(r,fvtk.line(tracks[i],color))
fvtk.show(r)

Examples

>>> tracks=[np.array([[0,0,0],[1,0,0,],[2,0,0]]),
...         np.array([[3,0,0],[3.5,1,0],[4,2,0]]),
...         np.array([[3.2,0,0],[3.7,1,0],[4.4,2,0]]),
...         np.array([[3.4,0,0],[3.9,1,0],[4.6,2,0]]),
...         np.array([[0,0.2,0],[1,0.2,0],[2,0.2,0]]),
...         np.array([[2,0.2,0],[1,0.2,0],[0,0.2,0]]),
...         np.array([[0,0,0],[0,1,0],[0,2,0]])]
>>> C = local_skeleton_clustering(tracks, d_thr=0.5)

warn

dipy.segment.quickbundles.warn()

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

otsu

dipy.segment.threshold.otsu(image, nbins=256)

Return threshold value based on Otsu’s method. Copied from scikit-image to remove dependency.

Parameters:

image : array

Input image.

nbins : int

Number of bins used to calculate histogram. This value is ignored for integer arrays.

Returns:

threshold : float

Threshold value.

upper_bound_by_percent

dipy.segment.threshold.upper_bound_by_percent(data, percent=1)

Find the upper bound for visualization of medical images

Calculate the histogram of the image and go right to left until you find the bound that contains more than a percentage of the image.

Parameters:

data : ndarray

percent : float

Returns:

upper_bound : float

upper_bound_by_rate

dipy.segment.threshold.upper_bound_by_rate(data, rate=0.05)

Adjusts upper intensity boundary using rates

It calculates the image intensity histogram, and based on the rate value it decide what is the upperbound value for intensity normalization, usually lower bound is 0. The rate is the ratio between the amount of pixels in every bins and the bins with highest pixel amount

Parameters:

data : float

Input intensity value data

rate : float

representing the threshold whether a spicific histogram bin that should be count in the normalization range

Returns:

high : float

the upper_bound value for normalization

ConstantObservationModel

class dipy.segment.tissue.ConstantObservationModel

Bases: object

Observation model assuming that the intensity of each class is constant. The model parameters are the means \(\mu_{k}\) and variances \(\sigma_{k}\) associated with each tissue class. According to this model, the observed intensity at voxel \(x\) is given by \(I(x) = \mu_{k} + \eta_{k}\) where \(k\) is the tissue class of voxel \(x\), and \(\eta_{k}\) is a Gaussian random variable with zero mean and variance \(\sigma_{k}^{2}\). The observation model is responsible for computing the negative log-likelihood of observing any given intensity \(z\) at each voxel \(x\) assuming the voxel belongs to each class \(k\). It also provides a default parameter initialization.

Methods

initialize_param_uniform Initializes the means and variances uniformly
negloglikelihood Computes the gaussian negative log-likelihood of each class at each voxel of image assuming a gaussian distribution with means and variances given by mu and sigmasq, respectively (constant models along the full volume).
prob_image Conditional probability of the label given the image
seg_stats Mean and standard variation for N desired tissue classes
update_param Updates the means and the variances in each iteration for all the labels.
update_param_new Updates the means and the variances in each iteration for all the labels.
__init__()

Initializes an instance of the ConstantObservationModel class

initialize_param_uniform()

Initializes the means and variances uniformly

The means are initialized uniformly along the dynamic range of image. The variances are set to 1 for all classes

Parameters:

image : array,

3D structural image

nclasses : int,

number of desired classes

Returns:

mu : array,

1 x nclasses, mean for each class

sigma : array,

1 x nclasses, standard deviation for each class. Set up to 1.0 for all classes.

negloglikelihood()

Computes the gaussian negative log-likelihood of each class at each voxel of image assuming a gaussian distribution with means and variances given by mu and sigmasq, respectively (constant models along the full volume). The negative log-likelihood will be written in nloglike.

Parameters:

image : ndarray,

3D gray scale structural image

mu : ndarray,

mean of each class

sigmasq : ndarray,

variance of each class

nclasses : int

number of classes

Returns:

nloglike : ndarray,

4D negloglikelihood for each class in each volume

prob_image()

Conditional probability of the label given the image

Parameters:

img : ndarray,

3D structural gray-scale image

nclasses : int,

number of tissue classes

mu : ndarray,

1 x nclasses, current estimate of the mean of each tissue class

sigmasq : ndarray,

1 x nclasses, current estimate of the variance of each tissue class

P_L_N : ndarray,

4D probability map of the label given the neighborhood.

Previously computed by function prob_neighborhood

Returns:

P_L_Y : ndarray,

4D probability of the label given the input image

seg_stats()

Mean and standard variation for N desired tissue classes

Parameters:

input_image : ndarray,

3D structural image

seg_image : ndarray,

3D segmented image

nclass : int,

number of classes (3 in most cases)

Returns:

mu, std: ndarrays,

1 x nclasses dimension Mean and standard deviation for each class

update_param()

Updates the means and the variances in each iteration for all the labels. This is for equations 25 and 26 of Zhang et. al., IEEE Trans. Med. Imag, Vol. 20, No. 1, Jan 2001.

Parameters:

image : ndarray,

3D structural gray-scale image

P_L_Y : ndarray,

4D probability map of the label given the input image computed by the expectation maximization (EM) algorithm

mu : ndarray,

1 x nclasses, current estimate of the mean of each tissue class.

nclasses : int,

number of tissue classes

Returns:

mu_upd : ndarray,

1 x nclasses, updated mean of each tissue class

var_upd : ndarray,

1 x nclasses, updated variance of each tissue class

update_param_new()

Updates the means and the variances in each iteration for all the labels. This is for equations 25 and 26 of the Zhang et al. paper

Parameters:

image : ndarray,

3D structural gray-scale image

P_L_Y : ndarray,

4D probability map of the label given the input image computed by the expectation maximization (EM) algorithm

mu : ndarray,

1 x nclasses, current estimate of the mean of each tissue class.

nclasses : int,

number of tissue classes

Returns:

mu_upd : ndarray,

1 x nclasses, updated mean of each tissue class

var_upd : ndarray,

1 x nclasses, updated variance of each tissue class

IteratedConditionalModes

class dipy.segment.tissue.IteratedConditionalModes

Bases: object

Methods

icm_ising Executes one iteration of the ICM algorithm for MRF MAP estimation.
initialize_maximum_likelihood Initializes the segmentation of an image with given
prob_neighborhood Conditional probability of the label given the neighborhood Equation 2.18 of the Stan Z.
__init__()
icm_ising()

Executes one iteration of the ICM algorithm for MRF MAP estimation. The prior distribution of the MRF is a Gibbs distribution with the Potts/Ising model with parameter beta:

https://en.wikipedia.org/wiki/Potts_model

Parameters:

nloglike : ndarray,

4D shape, nloglike[x,y,z,k] is the negative log likelihood of class k at voxel (x,y,z)

beta : float,

positive scalar, it is the parameter of the Potts/Ising model. Determines the smoothness of the output segmentation.

seg : ndarray,

3D initial segmentation. This segmentation will change by one iteration of the ICM algorithm

Returns:

new_seg : ndarray,

3D final segmentation

energy : ndarray,

3D final energy

initialize_maximum_likelihood()
Initializes the segmentation of an image with given
neg-loglikelihood

Initializes the segmentation of an image with neglog-likelihood field given by nloglike. The class of each voxel is selected as the one with the minimum neglog-likelihood (i.e. maximum-likelihood segmentation).

Parameters:

nloglike : ndarray,

4D shape, nloglike[x,y,z,k] is the likelihhood of class k for voxel (x, y, z)

Returns:

seg : ndarray,

3D initial segmentation

prob_neighborhood()

Conditional probability of the label given the neighborhood Equation 2.18 of the Stan Z. Li book (Stan Z. Li, Markov Random Field Modeling in Image Analysis, 3rd ed., Advances in Pattern Recognition Series, Springer Verlag 2009.)

Parameters:

seg : ndarray,

3D tissue segmentation derived from the ICM model

beta : float,

scalar that determines the importance of the neighborhood and the spatial smoothness of the segmentation. Usually between 0 to 0.5

nclasses : int,

number of tissue classes

Returns:

PLN : ndarray,

4D probability map of the label given the neighborhood of the voxel.

TissueClassifierHMRF

class dipy.segment.tissue.TissueClassifierHMRF(save_history=False, verbose=True)

Bases: object

This class contains the methods for tissue classification using the Markov Random Fields modeling approach

Methods

classify(image, nclasses, beta[, tolerance, ...]) This method uses the Maximum a posteriori - Markov Random Field approach for segmentation by using the Iterative Conditional Modes and Expectation Maximization to estimate the parameters.
__init__(save_history=False, verbose=True)
classify(image, nclasses, beta, tolerance=None, max_iter=None)

This method uses the Maximum a posteriori - Markov Random Field approach for segmentation by using the Iterative Conditional Modes and Expectation Maximization to estimate the parameters.

Parameters:

image : ndarray,

3D structural image.

nclasses : int,

number of desired classes.

beta : float,

smoothing parameter, the higher this number the smoother the output will be.

tolerance: float,

value that defines the percentage of change tolerated to prevent the ICM loop to stop. Default is 1e-05.

max_iter : float,

fixed number of desired iterations. Default is 100. If the user only specifies this parameter, the tolerance value will not be considered. If none of these two parameters

Returns:

initial_segmentation : ndarray,

3D segmented image with all tissue types specified in nclasses.

final_segmentation : ndarray,

3D final refined segmentation containing all tissue types.

PVE : ndarray,

3D probability map of each tissue type.

add_noise

dipy.segment.tissue.add_noise(signal, snr, S0, noise_type='rician')

Add noise of specified distribution to the signal from a single voxel.

Parameters:

signal : 1-d ndarray

The signal in the voxel.

snr : float

The desired signal-to-noise ratio. (See notes below.) If snr is None, return the signal as-is.

S0 : float

Reference signal for specifying snr.

noise_type : string, optional

The distribution of noise added. Can be either ‘gaussian’ for Gaussian distributed noise, ‘rician’ for Rice-distributed noise (default) or ‘rayleigh’ for a Rayleigh distribution.

Returns:

signal : array, same shape as the input

Signal with added noise.

Notes

SNR is defined here, following [R426], as S0 / sigma, where sigma is the standard deviation of the two Gaussian distributions forming the real and imaginary components of the Rician noise distribution (see [R427]).

References

[R426](1, 2) Descoteaux, Angelino, Fitzgibbons and Deriche (2007) Regularized, fast and robust q-ball imaging. MRM, 58: 497-510
[R427](1, 2) Gudbjartson and Patz (2008). The Rician distribution of noisy MRI data. MRM 34: 910-914.

Examples

>>> signal = np.arange(800).reshape(2, 2, 2, 100)
>>> signal_w_noise = add_noise(signal, 10., 100., noise_type='rician')