align

Bunch(**kwds)
floating alias of float32

Module: align.imaffine

Affine image registration module consisting of the following classes:

AffineMap: encapsulates the necessary information to perform affine
transforms between two domains, defined by a static and a moving image. The domain of the transform is the set of points in the static image’s grid, and the codomain is the set of points in the moving image. When we call the transform method, AffineMap maps each point x of the domain (static grid) to the codomain (moving grid) and interpolates the moving image at that point to obtain the intensity value to be placed at x in the resulting grid. The transform_inverse method performs the opposite operation mapping points in the codomain to points in the domain.
ParzenJointHistogram: computes the marginal and joint distributions of
intensities of a pair of images, using Parzen windows [Parzen62] with a cubic spline kernel, as proposed by Mattes et al. [Mattes03]. It also computes the gradient of the joint histogram w.r.t. the parameters of a given transform.
MutualInformationMetric: computes the value and gradient of the mutual
information metric the way Optimizer needs them. That is, given a set of transform parameters, it will use ParzenJointHistogram to compute the value and gradient of the joint intensity histogram evaluated at the given parameters, and evaluate the the value and gradient of the histogram’s mutual information.
AffineRegistration: it runs the multi-resolution registration, putting
all the pieces together. It needs to create the scale space of the images and run the multi-resolution registration by using the Metric and the Optimizer at each level of the Gaussian pyramid. At each level, it will setup the metric to compute value and gradient of the metric with the input images with different levels of smoothing.

References

[Parzen62] E. Parzen. On the estimation of a probability density
function and the mode. Annals of Mathematical Statistics, 33(3), 1065-1076, 1962.
[Mattes03] Mattes, D., Haynor, D. R., Vesselle, H., Lewellen, T. K.,
& Eubank, W. PET-CT image registration in the chest using free-form deformations. IEEE Transactions on Medical Imaging, 22(1), 120-8, 2003.
AffineInvalidValuesError
AffineInversionError
AffineMap(affine[, domain_grid_shape, ...])

Methods

AffineRegistration([metric, level_iters, ...])

Methods

IsotropicScaleSpace(image, factors, sigmas)

Methods

MutualInformationMetric([nbins, ...])

Methods

Optimizer(fun, x0[, args, method, jac, ...])

Attributes

ParzenJointHistogram

Methods

ScaleSpace(image, num_levels[, ...])

Methods

align_centers_of_mass(static, ...)
align_geometric_centers(static, ...)
align_origins(static, static_grid2world, ...)
compute_parzen_mi Computes the mutual information and its gradient (if requested)
get_direction_and_spacings(affine, dim) Extracts the rotational and spacing components from a matrix
sample_domain_regular Take floor(total_voxels/k) samples from a (2D or 3D) grid
transform_centers_of_mass(static, ...) Transformation to align the center of mass of the input images
transform_geometric_centers(static, ...) Transformation to align the geometric center of the input images
transform_origins(static, static_grid2world, ...) Transformation to align the origins of the input images
warn Issue a warning, or maybe ignore it or raise an exception.

Module: align.imwarp

Classes and functions for Symmetric Diffeomorphic Registration

Bunch(**kwds)
DiffeomorphicMap(dim, disp_shape[, ...])

Methods

DiffeomorphicRegistration([metric])

Methods

ScaleSpace(image, num_levels[, ...])

Methods

SymmetricDiffeomorphicRegistration(metric[, ...])

Methods

floating alias of float32
get_direction_and_spacings(affine, dim) Extracts the rotational and spacing components from a matrix
mult_aff(A, B) Returns the matrix product A.dot(B) considering None as the identity
with_metaclass(meta, *bases) Create a base class with a metaclass.

Module: align.metrics

Metrics for Symmetric Diffeomorphic Registration

CCMetric(dim[, sigma_diff, radius])

Methods

EMMetric(dim[, smooth, inner_iter, ...])

Methods

SSDMetric(dim[, smooth, inner_iter, step_type])

Methods

SimilarityMetric(dim)

Methods

floating alias of float32
gradient(f, *varargs, **kwargs) Return the gradient of an N-dimensional array.
v_cycle_2d(n, k, delta_field, ...[, depth]) Multi-resolution Gauss-Seidel solver using V-type cycles
v_cycle_3d(n, k, delta_field, ...[, depth]) Multi-resolution Gauss-Seidel solver using V-type cycles
with_metaclass(meta, *bases) Create a base class with a metaclass.

Module: align.reslice

Pool Returns a process pool object
affine_transform(input, matrix[, offset, ...]) Apply an affine transformation.
cpu_count Returns the number of CPUs in the system
reslice(data, affine, zooms, new_zooms[, ...]) Reslice data with new voxel resolution defined by new_zooms

Module: align.scalespace

IsotropicScaleSpace(image, factors, sigmas)

Methods

ScaleSpace(image, num_levels[, ...])

Methods

floating alias of float32

Module: align.streamlinear

BundleMinDistanceAsymmetricMetric([num_threads]) Asymmetric Bundle-based Minimum distance
BundleMinDistanceMatrixMetric([num_threads]) Bundle-based Minimum Distance aka BMD
BundleMinDistanceMetric([num_threads]) Bundle-based Minimum Distance aka BMD
BundleSumDistanceMatrixMetric([num_threads]) Bundle-based Sum Distance aka BMD
Optimizer(fun, x0[, args, method, jac, ...])

Attributes

QuickBundles(threshold[, metric, ...]) Clusters streamlines using QuickBundles [Garyfallidis12].
StreamlineDistanceMetric([num_threads])

Methods

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

Methods

StreamlineRegistrationMap(matopt, xopt, ...)

Methods

bundle_min_distance(t, static, moving) MDF-based pairwise distance optimization function (MIN)
bundle_min_distance_asymmetric_fast(t, ...) MDF-based pairwise distance optimization function (MIN)
bundle_min_distance_fast(t, static, moving, ...) MDF-based pairwise distance optimization function (MIN)
bundle_sum_distance(t, static, moving[, ...]) MDF distance optimization function (SUM)
center_streamlines(streamlines) Move streamlines to the origin
compose_matrix([scale, shear, angles, ...]) Return 4x4 transformation matrix from sequence of transformations.
compose_matrix44(t[, dtype]) Compose a 4x4 transformation matrix
compose_transformations(*mats) Compose multiple 4x4 affine transformations in one 4x4 matrix
decompose_matrix(matrix) Return sequence of transformations from transformation matrix.
decompose_matrix44(mat[, size]) Given a 4x4 homogeneous matrix return the parameter vector
distance_matrix_mdf Minimum direct flipped distance matrix between two streamline sets
length Euclidean length of streamlines
progressive_slr(static, moving, metric, x0, ...) Progressive SLR
remove_clusters_by_size(clusters[, min_size])
select_random_set_of_streamlines(...) Select a random set of streamlines
set_number_of_points Change the number of points of streamlines
slr_with_qb(static, moving[, x0, ...]) Utility function for registering large tractograms.
time(() -> floating point number) Return the current time in seconds since the Epoch.
transform_streamlines(streamlines, mat) Apply affine transformation to streamlines
unlist_streamlines(streamlines) Return the streamlines not as a list but as an array and an offset
whole_brain_slr(static, moving[, x0, ...]) Utility function for registering large tractograms.
with_metaclass(meta, *bases) Create a base class with a metaclass.

Bunch

class dipy.align.Bunch(**kwds)

Bases: object

__init__(**kwds)

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

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

floating

dipy.align.floating

alias of float32

AffineInvalidValuesError

class dipy.align.imaffine.AffineInvalidValuesError

Bases: Exception

Attributes

args

Methods

with_traceback Exception.with_traceback(tb) – set self.__traceback__ to tb and return self.
__init__()

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

AffineInversionError

class dipy.align.imaffine.AffineInversionError

Bases: Exception

Attributes

args

Methods

with_traceback Exception.with_traceback(tb) – set self.__traceback__ to tb and return self.
__init__()

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

AffineMap

class dipy.align.imaffine.AffineMap(affine, domain_grid_shape=None, domain_grid2world=None, codomain_grid_shape=None, codomain_grid2world=None)

Bases: object

Methods

get_affine() Returns the value of the transformation, not a reference!
set_affine(affine) Sets the affine transform (operating in physical space)
transform(image[, interp, image_grid2world, ...]) Transforms the input image from co-domain to domain space
transform_inverse(image[, interp, ...]) Transforms the input image from domain to co-domain space
__init__(affine, domain_grid_shape=None, domain_grid2world=None, codomain_grid_shape=None, codomain_grid2world=None)

AffineMap

Implements an affine transformation whose domain is given by domain_grid and domain_grid2world, and whose co-domain is given by codomain_grid and codomain_grid2world.

The actual transform is represented by the affine matrix, which operate in world coordinates. Therefore, to transform a moving image towards a static image, we first map each voxel (i,j,k) of the static image to world coordinates (x,y,z) by applying domain_grid2world. Then we apply the affine transform to (x,y,z) obtaining (x’, y’, z’) in moving image’s world coordinates. Finally, (x’, y’, z’) is mapped to voxel coordinates (i’, j’, k’) in the moving image by multiplying (x’, y’, z’) by the inverse of codomain_grid2world. The codomain_grid_shape is used analogously to transform the static image towards the moving image when calling transform_inverse.

If the domain/co-domain information is not provided (None) then the sampling information needs to be specified each time the transform or transform_inverse is called to transform images. Note that such sampling information is not necessary to transform points defined in physical space, such as stream lines.

Parameters:

affine : array, shape (dim + 1, dim + 1)

the matrix defining the affine transform, where dim is the dimension of the space this map operates in (2 for 2D images, 3 for 3D images). If None, then self represents the identity transformation.

domain_grid_shape : sequence, shape (dim,), optional

the shape of the default domain sampling grid. When transform is called to transform an image, the resulting image will have this shape, unless a different sampling information is provided. If None, then the sampling grid shape must be specified each time the transform method is called.

domain_grid2world : array, shape (dim + 1, dim + 1), optional

the grid-to-world transform associated with the domain grid. If None (the default), then the grid-to-world transform is assumed to be the identity.

codomain_grid_shape : sequence of integers, shape (dim,)

the shape of the default co-domain sampling grid. When transform_inverse is called to transform an image, the resulting image will have this shape, unless a different sampling information is provided. If None (the default), then the sampling grid shape must be specified each time the transform_inverse method is called.

codomain_grid2world : array, shape (dim + 1, dim + 1)

the grid-to-world transform associated with the co-domain grid. If None (the default), then the grid-to-world transform is assumed to be the identity.

get_affine()

Returns the value of the transformation, not a reference!

Returns:

affine : ndarray

Copy of the transform, not a reference.

set_affine(affine)

Sets the affine transform (operating in physical space)

Also sets self.affine_inv - the inverse of affine, or None if there is no inverse.

Parameters:

affine : array, shape (dim + 1, dim + 1)

the matrix representing the affine transform operating in physical space. The domain and co-domain information remains unchanged. If None, then self represents the identity transformation.

transform(image, interp='linear', image_grid2world=None, sampling_grid_shape=None, sampling_grid2world=None, resample_only=False)

Transforms the input image from co-domain to domain space

By default, the transformed image is sampled at a grid defined by self.domain_shape and self.domain_grid2world. If such information was not provided then sampling_grid_shape is mandatory.

Parameters:

image : array, shape (X, Y) or (X, Y, Z)

the image to be transformed

interp : string, either ‘linear’ or ‘nearest’

the type of interpolation to be used, either ‘linear’ (for k-linear interpolation) or ‘nearest’ for nearest neighbor

image_grid2world : array, shape (dim + 1, dim + 1), optional

the grid-to-world transform associated with image. If None (the default), then the grid-to-world transform is assumed to be the identity.

sampling_grid_shape : sequence, shape (dim,), optional

the shape of the grid where the transformed image must be sampled. If None (the default), then self.codomain_shape is used instead (which must have been set at initialization, otherwise an exception will be raised).

sampling_grid2world : array, shape (dim + 1, dim + 1), optional

the grid-to-world transform associated with the sampling grid (specified by sampling_grid_shape, or by default self.codomain_shape). If None (the default), then the grid-to-world transform is assumed to be the identity.

resample_only : Boolean, optional

If False (the default) the affine transform is applied normally. If True, then the affine transform is not applied, and the input image is just re-sampled on the domain grid of this transform.

Returns

——-

transformed : array, shape sampling_grid_shape or

self.codomain_shape

the transformed image, sampled at the requested grid

transform_inverse(image, interp='linear', image_grid2world=None, sampling_grid_shape=None, sampling_grid2world=None, resample_only=False)

Transforms the input image from domain to co-domain space

By default, the transformed image is sampled at a grid defined by self.codomain_shape and self.codomain_grid2world. If such information was not provided then sampling_grid_shape is mandatory.

Parameters:

image : array, shape (X, Y) or (X, Y, Z)

the image to be transformed

interp : string, either ‘linear’ or ‘nearest’

the type of interpolation to be used, either ‘linear’ (for k-linear interpolation) or ‘nearest’ for nearest neighbor

image_grid2world : array, shape (dim + 1, dim + 1), optional

the grid-to-world transform associated with image. If None (the default), then the grid-to-world transform is assumed to be the identity.

sampling_grid_shape : sequence, shape (dim,), optional

the shape of the grid where the transformed image must be sampled. If None (the default), then self.codomain_shape is used instead (which must have been set at initialization, otherwise an exception will be raised).

sampling_grid2world : array, shape (dim + 1, dim + 1), optional

the grid-to-world transform associated with the sampling grid (specified by sampling_grid_shape, or by default self.codomain_shape). If None (the default), then the grid-to-world transform is assumed to be the identity.

resample_only : Boolean, optional

If False (the default) the affine transform is applied normally. If True, then the affine transform is not applied, and the input image is just re-sampled on the domain grid of this transform.

Returns

——-

transformed : array, shape sampling_grid_shape or

self.codomain_shape

the transformed image, sampled at the requested grid

AffineRegistration

class dipy.align.imaffine.AffineRegistration(metric=None, level_iters=None, sigmas=None, factors=None, method='L-BFGS-B', ss_sigma_factor=None, options=None, verbosity=1)

Bases: object

Methods

optimize(static, moving, transform, params0) Starts the optimization process
__init__(metric=None, level_iters=None, sigmas=None, factors=None, method='L-BFGS-B', ss_sigma_factor=None, options=None, verbosity=1)

Initializes an instance of the AffineRegistration class

Parameters:

metric : None or object, optional

an instance of a metric. The default is None, implying the Mutual Information metric with default settings.

level_iters : sequence, optional

the number of iterations at each scale of the scale space. level_iters[0] corresponds to the coarsest scale, level_iters[-1] the finest, where n is the length of the sequence. By default, a 3-level scale space with iterations sequence equal to [10000, 1000, 100] will be used.

sigmas : sequence of floats, optional

custom smoothing parameter to build the scale space (one parameter for each scale). By default, the sequence of sigmas will be [3, 1, 0].

factors : sequence of floats, optional

custom scale factors to build the scale space (one factor for each scale). By default, the sequence of factors will be [4, 2, 1].

method : string, optional

optimization method to be used. If Scipy version < 0.12, then only L-BFGS-B is available. Otherwise, method can be any gradient-based method available in dipy.core.Optimize: CG, BFGS, Newton-CG, dogleg or trust-ncg. The default is ‘L-BFGS-B’.

ss_sigma_factor : float, optional

If None, this parameter is not used and an isotropic scale space with the given factors and sigmas will be built. If not None, an anisotropic scale space will be used by automatically selecting the smoothing sigmas along each axis according to the voxel dimensions of the given image. The ss_sigma_factor is used to scale the automatically computed sigmas. For example, in the isotropic case, the sigma of the kernel will be \(factor * (2 ^ i)\) where \(i = 1, 2, ..., n_scales - 1\) is the scale (the finest resolution image \(i=0\) is never smoothed). The default is None.

options : dict, optional

extra optimization options. The default is None, implying no extra options are passed to the optimizer.

verbosity: int (one of {0, 1, 2, 3}), optional

Set the verbosity level of the algorithm: 0 : do not print anything 1 : print information about the current status of the algorithm 2 : print high level information of the components involved in

the registration that can be used to detect a failing component.

3 : print as much information as possible to isolate the cause

of a bug.

Default: 1

docstring_addendum = 'verbosity: int (one of {0, 1, 2, 3}), optional\n Set the verbosity level of the algorithm:\n 0 : do not print anything\n 1 : print information about the current status of the algorithm\n 2 : print high level information of the components involved in\n the registration that can be used to detect a failing\n component.\n 3 : print as much information as possible to isolate the cause\n of a bug.\n Default: 1\n '
optimize(static, moving, transform, params0, static_grid2world=None, moving_grid2world=None, starting_affine=None)

Starts the optimization process

Parameters:

static : array, shape (S, R, C) or (R, C)

the image to be used as reference during optimization.

moving : array, shape (S’, R’, C’) or (R’, C’)

the image to be used as “moving” during optimization. It is necessary to pre-align the moving image to ensure its domain lies inside the domain of the deformation fields. This is assumed to be accomplished by “pre-aligning” the moving image towards the static using an affine transformation given by the ‘starting_affine’ matrix

transform : instance of Transform

the transformation with respect to whose parameters the gradient must be computed

params0 : array, shape (n,)

parameters from which to start the optimization. If None, the optimization will start at the identity transform. n is the number of parameters of the specified transformation.

static_grid2world : array, shape (dim+1, dim+1), optional

the voxel-to-space transformation associated with the static image. The default is None, implying the transform is the identity.

moving_grid2world : array, shape (dim+1, dim+1), optional

the voxel-to-space transformation associated with the moving image. The default is None, implying the transform is the identity.

starting_affine : string, or matrix, or None, optional

If string:

‘mass’: align centers of gravity ‘voxel-origin’: align physical coordinates of voxel (0,0,0) ‘centers’: align physical coordinates of central voxels

If matrix:

array, shape (dim+1, dim+1).

If None:

Start from identity.

The default is None.

Returns:

affine_map : instance of AffineMap

the affine resulting affine transformation

IsotropicScaleSpace

class dipy.align.imaffine.IsotropicScaleSpace(image, factors, sigmas, image_grid2world=None, input_spacing=None, mask0=False)

Bases: dipy.align.scalespace.ScaleSpace

Methods

get_affine(level) Voxel-to-space transformation at a given level
get_affine_inv(level) Space-to-voxel transformation at a given level
get_domain_shape(level) Shape the sub-sampled image must have at a particular level
get_expand_factors(from_level, to_level) Ratio of voxel size from pyramid level from_level to to_level
get_image(level) Smoothed image at a given level
get_scaling(level) Adjustment factor for input-spacing to reflect voxel sizes at level
get_sigmas(level) Smoothing parameters used at a given level
get_spacing(level) Spacings the sub-sampled image must have at a particular level
print_level(level) Prints properties of a pyramid level
__init__(image, factors, sigmas, image_grid2world=None, input_spacing=None, mask0=False)

IsotropicScaleSpace

Computes the Scale Space representation of an image using isotropic smoothing kernels for all scales. The scale space is simply a list of images produced by smoothing the input image with a Gaussian kernel with different smoothing parameters.

This specialization of ScaleSpace allows the user to provide custom scale and smoothing factors for all scales.

Parameters:

image : array, shape (r,c) or (s, r, c) where s is the number of

slices, r is the number of rows and c is the number of columns of the input image.

factors : list of floats

custom scale factors to build the scale space (one factor for each scale).

sigmas : list of floats

custom smoothing parameter to build the scale space (one parameter for each scale).

image_grid2world : array, shape (dim + 1, dim + 1), optional

the grid-to-space transform of the image grid. The default is the identity matrix.

input_spacing : array, shape (dim,), optional

the spacing (voxel size) between voxels in physical space. The default if 1.0 along all axes.

mask0 : Boolean, optional

if True, all smoothed images will be zero at all voxels that are zero in the input image. The default is False.

MutualInformationMetric

class dipy.align.imaffine.MutualInformationMetric(nbins=32, sampling_proportion=None)

Bases: object

Methods

distance(params) Numeric value of the negative Mutual Information
distance_and_gradient(params) Numeric value of the metric and its gradient at given parameters
gradient(params) Numeric value of the metric’s gradient at the given parameters
setup(transform, static, moving[, ...]) Prepares the metric to compute intensity densities and gradients
__init__(nbins=32, sampling_proportion=None)

Initializes an instance of the Mutual Information metric

This class implements the methods required by Optimizer to drive the registration process.

Parameters:

nbins : int, optional

the number of bins to be used for computing the intensity histograms. The default is 32.

sampling_proportion : None or float in interval (0, 1], optional

There are two types of sampling: dense and sparse. Dense sampling uses all voxels for estimating the (joint and marginal) intensity histograms, while sparse sampling uses a subset of them. If sampling_proportion is None, then dense sampling is used. If sampling_proportion is a floating point value in (0,1] then sparse sampling is used, where sampling_proportion specifies the proportion of voxels to be used. The default is None.

Notes

Since we use linear interpolation, images are not, in general, differentiable at exact voxel coordinates, but they are differentiable between voxel coordinates. When using sparse sampling, selected voxels are slightly moved by adding a small random displacement within one voxel to prevent sampling points from being located exactly at voxel coordinates. When using dense sampling, this random displacement is not applied.

distance(params)

Numeric value of the negative Mutual Information

We need to change the sign so we can use standard minimization algorithms.

Parameters:

params : array, shape (n,)

the parameter vector of the transform currently used by the metric (the transform name is provided when self.setup is called), n is the number of parameters of the transform

Returns:

neg_mi : float

the negative mutual information of the input images after transforming the moving image by the currently set transform with params parameters

distance_and_gradient(params)

Numeric value of the metric and its gradient at given parameters

Parameters:

params : array, shape (n,)

the parameter vector of the transform currently used by the metric (the transform name is provided when self.setup is called), n is the number of parameters of the transform

Returns:

neg_mi : float

the negative mutual information of the input images after transforming the moving image by the currently set transform with params parameters

neg_mi_grad : array, shape (n,)

the gradient of the negative Mutual Information

gradient(params)

Numeric value of the metric’s gradient at the given parameters

Parameters:

params : array, shape (n,)

the parameter vector of the transform currently used by the metric (the transform name is provided when self.setup is called), n is the number of parameters of the transform

Returns:

grad : array, shape (n,)

the gradient of the negative Mutual Information

setup(transform, static, moving, static_grid2world=None, moving_grid2world=None, starting_affine=None)

Prepares the metric to compute intensity densities and gradients

The histograms will be setup to compute probability densities of intensities within the minimum and maximum values of static and moving

Parameters:

transform: instance of Transform

the transformation with respect to whose parameters the gradient must be computed

static : array, shape (S, R, C) or (R, C)

static image

moving : array, shape (S’, R’, C’) or (R’, C’)

moving image. The dimensions of the static (S, R, C) and moving (S’, R’, C’) images do not need to be the same.

static_grid2world : array (dim+1, dim+1), optional

the grid-to-space transform of the static image. The default is None, implying the transform is the identity.

moving_grid2world : array (dim+1, dim+1)

the grid-to-space transform of the moving image. The default is None, implying the spacing along all axes is 1.

starting_affine : array, shape (dim+1, dim+1), optional

the pre-aligning matrix (an affine transform) that roughly aligns the moving image towards the static image. If None, no pre-alignment is performed. If a pre-alignment matrix is available, it is recommended to provide this matrix as starting_affine instead of manually transforming the moving image to reduce interpolation artifacts. The default is None, implying no pre-alignment is performed.

Optimizer

class dipy.align.imaffine.Optimizer(fun, x0, args=(), method='L-BFGS-B', jac=None, hess=None, hessp=None, bounds=None, constraints=(), tol=None, callback=None, options=None, evolution=False)

Bases: object

Attributes

evolution
fopt
message
nfev
nit
xopt

Methods

print_summary()
__init__(fun, x0, args=(), method='L-BFGS-B', jac=None, hess=None, hessp=None, bounds=None, constraints=(), tol=None, callback=None, options=None, evolution=False)

A class for handling minimization of scalar function of one or more variables.

Parameters:

fun : callable

Objective function.

x0 : ndarray

Initial guess.

args : tuple, optional

Extra arguments passed to the objective function and its derivatives (Jacobian, Hessian).

method : str, optional

Type of solver. Should be one of

  • ‘Nelder-Mead’
  • ‘Powell’
  • ‘CG’
  • ‘BFGS’
  • ‘Newton-CG’
  • ‘Anneal’
  • ‘L-BFGS-B’
  • ‘TNC’
  • ‘COBYLA’
  • ‘SLSQP’
  • ‘dogleg’
  • ‘trust-ncg’

jac : bool or callable, optional

Jacobian of objective function. Only for CG, BFGS, Newton-CG, dogleg, trust-ncg. If jac is a Boolean and is True, fun is assumed to return the value of Jacobian along with the objective function. If False, the Jacobian will be estimated numerically. jac can also be a callable returning the Jacobian of the objective. In this case, it must accept the same arguments as fun.

hess, hessp : callable, optional

Hessian of objective function or Hessian of objective function times an arbitrary vector p. Only for Newton-CG, dogleg, trust-ncg. Only one of hessp or hess needs to be given. If hess is provided, then hessp will be ignored. If neither hess nor hessp is provided, then the hessian product will be approximated using finite differences on jac. hessp must compute the Hessian times an arbitrary vector.

bounds : sequence, optional

Bounds for variables (only for L-BFGS-B, TNC and SLSQP). (min, max) pairs for each element in x, defining the bounds on that parameter. Use None for one of min or max when there is no bound in that direction.

constraints : dict or sequence of dict, optional

Constraints definition (only for COBYLA and SLSQP). Each constraint is defined in a dictionary with fields:

type : str

Constraint type: ‘eq’ for equality, ‘ineq’ for inequality.

fun : callable

The function defining the constraint.

jac : callable, optional

The Jacobian of fun (only for SLSQP).

args : sequence, optional

Extra arguments to be passed to the function and Jacobian.

Equality constraint means that the constraint function result is to be zero whereas inequality means that it is to be non-negative. Note that COBYLA only supports inequality constraints.

tol : float, optional

Tolerance for termination. For detailed control, use solver-specific options.

callback : callable, optional

Called after each iteration, as callback(xk), where xk is the current parameter vector. Only available using Scipy >= 0.12.

options : dict, optional

A dictionary of solver options. All methods accept the following generic options:

maxiter : int

Maximum number of iterations to perform.

disp : bool

Set to True to print convergence messages.

For method-specific options, see show_options(‘minimize’, method).

evolution : bool, optional

save history of x for each iteration. Only available using Scipy >= 0.12.

See also

scipy.optimize.minimize

evolution
fopt
message
nfev
nit
print_summary()
xopt

ParzenJointHistogram

class dipy.align.imaffine.ParzenJointHistogram

Bases: object

Methods

bin_index Bin index associated with the given normalized intensity
bin_normalize_moving Maps intensity x to the range covered by the moving histogram
bin_normalize_static Maps intensity x to the range covered by the static histogram
setup Compute histogram settings to store the PDF of input images
update_gradient_dense Computes the Gradient of the joint PDF w.r.t.
update_gradient_sparse Computes the Gradient of the joint PDF w.r.t.
update_pdfs_dense Computes the Probability Density Functions of two images
update_pdfs_sparse Computes the Probability Density Functions from a set of samples
__init__()

Computes joint histogram and derivatives with Parzen windows

Base class to compute joint and marginal probability density functions and their derivatives with respect to a transform’s parameters. The smooth histograms are computed by using Parzen windows [Parzen62] with a cubic spline kernel, as proposed by Mattes et al. [Mattes03]. This implementation is not tied to any optimization (registration) method, the idea is that information-theoretic matching functionals (such as Mutual Information) can inherit from this class to perform the low-level computations of the joint intensity distributions and its gradient w.r.t. the transform parameters. The derived class can then compute the similarity/dissimilarity measure and gradient, and finally communicate the results to the appropriate optimizer.

Parameters:

nbins : int

the number of bins of the joint and marginal probability density functions (the actual number of bins of the joint PDF is nbins**2)

Notes

We need this class in cython to allow _joint_pdf_gradient_dense_2d and _joint_pdf_gradient_dense_3d to use a nogil Jacobian function (obtained from an instance of the Transform class), which allows us to evaluate Jacobians at all the sampling points (maybe the full grid) inside a nogil loop.

The reason we need a class is to encapsulate all the parameters related to the joint and marginal distributions.

References

[Parzen62] E. Parzen. On the estimation of a probability density
function and the mode. Annals of Mathematical Statistics, 33(3), 1065-1076, 1962.
[Mattes03] Mattes, D., Haynor, D. R., Vesselle, H., Lewellen, T. K.,
& Eubank, W. PET-CT image registration in the chest using free-form deformations. IEEE Transactions on Medical Imaging, 22(1), 120-8, 2003.
bin_index()

Bin index associated with the given normalized intensity

The return value is an integer in [padding, nbins - 1 - padding]

Parameters:

xnorm : float

intensity value normalized to the range covered by the histogram

Returns:

bin : int

the bin index associated with the given normalized intensity

bin_normalize_moving()

Maps intensity x to the range covered by the moving histogram

If the input intensity is in [self.mmin, self.mmax] then the normalized intensity will be in [self.padding, self.nbins - self.padding]

Parameters:

x : float

the intensity to be normalized

Returns:

xnorm : float

normalized intensity to the range covered by the moving histogram

bin_normalize_static()

Maps intensity x to the range covered by the static histogram

If the input intensity is in [self.smin, self.smax] then the normalized intensity will be in [self.padding, self.nbins - self.padding]

Parameters:

x : float

the intensity to be normalized

Returns:

xnorm : float

normalized intensity to the range covered by the static histogram

setup()

Compute histogram settings to store the PDF of input images

Parameters:

static : array

static image

moving : array

moving image

smask : array

mask of static object being registered (a binary array with 1’s inside the object of interest and 0’s along the background). If None, the behaviour is equivalent to smask=ones_like(static)

mmask : array

mask of moving object being registered (a binary array with 1’s inside the object of interest and 0’s along the background). If None, the behaviour is equivalent to mmask=ones_like(static)

update_gradient_dense()

Computes the Gradient of the joint PDF w.r.t. transform parameters

Computes the vector of partial derivatives of the joint histogram w.r.t. each transformation parameter.

The gradient is stored in self.joint_grad.

Parameters:

theta : array, shape (n,)

parameters of the transformation to compute the gradient from

transform : instance of Transform

the transformation with respect to whose parameters the gradient must be computed

static : array, shape (S, R, C)

static image

moving : array, shape (S, R, C)

moving image

grid2world : array, shape (4, 4)

we assume that both images have already been sampled at a common grid. This transform must map voxel coordinates of this common grid to physical coordinates of its corresponding voxel in the moving image. For example, if the moving image was sampled on the static image’s grid (this is the typical setting) using an aligning matrix A, then

  1. grid2world = A.dot(static_affine)

where static_affine is the transformation mapping static image’s grid coordinates to physical space.

mgradient : array, shape (S, R, C, 3)

the gradient of the moving image

smask : array, shape (S, R, C), optional

mask of static object being registered (a binary array with 1’s inside the object of interest and 0’s along the background). The default is None, indicating all voxels are considered.

mmask : array, shape (S, R, C), optional

mask of moving object being registered (a binary array with 1’s inside the object of interest and 0’s along the background). The default is None, indicating all voxels are considered.

update_gradient_sparse()

Computes the Gradient of the joint PDF w.r.t. transform parameters

Computes the vector of partial derivatives of the joint histogram w.r.t. each transformation parameter.

The list of intensities sval and mval are assumed to be sampled from the static and moving images, respectively, at the same physical points. Of course, the images may not be perfectly aligned at the moment the sampling was performed. The resulting gradient corresponds to the paired intensities according to the alignment at the moment the images were sampled.

The gradient is stored in self.joint_grad.

Parameters:

theta : array, shape (n,)

parameters to compute the gradient at

transform : instance of Transform

the transformation with respect to whose parameters the gradient must be computed

sval : array, shape (m,)

sampled intensities from the static image at sampled_points

mval : array, shape (m,)

sampled intensities from the moving image at sampled_points

sample_points : array, shape (m, 3)

coordinates (in physical space) of the points the images were sampled at

mgradient : array, shape (m, 3)

the gradient of the moving image at the sample points

update_pdfs_dense()

Computes the Probability Density Functions of two images

The joint PDF is stored in self.joint. The marginal distributions corresponding to the static and moving images are computed and stored in self.smarginal and self.mmarginal, respectively.

Parameters:

static : array, shape (S, R, C)

static image

moving : array, shape (S, R, C)

moving image

smask : array, shape (S, R, C)

mask of static object being registered (a binary array with 1’s inside the object of interest and 0’s along the background). If None, ones_like(static) is used as mask.

mmask : array, shape (S, R, C)

mask of moving object being registered (a binary array with 1’s inside the object of interest and 0’s along the background). If None, ones_like(moving) is used as mask.

update_pdfs_sparse()

Computes the Probability Density Functions from a set of samples

The list of intensities sval and mval are assumed to be sampled from the static and moving images, respectively, at the same physical points. Of course, the images may not be perfectly aligned at the moment the sampling was performed. The resulting distributions corresponds to the paired intensities according to the alignment at the moment the images were sampled.

The joint PDF is stored in self.joint. The marginal distributions corresponding to the static and moving images are computed and stored in self.smarginal and self.mmarginal, respectively.

Parameters:

sval : array, shape (n,)

sampled intensities from the static image at sampled_points

mval : array, shape (n,)

sampled intensities from the moving image at sampled_points

ScaleSpace

class dipy.align.imaffine.ScaleSpace(image, num_levels, image_grid2world=None, input_spacing=None, sigma_factor=0.2, mask0=False)

Bases: object

Methods

get_affine(level) Voxel-to-space transformation at a given level
get_affine_inv(level) Space-to-voxel transformation at a given level
get_domain_shape(level) Shape the sub-sampled image must have at a particular level
get_expand_factors(from_level, to_level) Ratio of voxel size from pyramid level from_level to to_level
get_image(level) Smoothed image at a given level
get_scaling(level) Adjustment factor for input-spacing to reflect voxel sizes at level
get_sigmas(level) Smoothing parameters used at a given level
get_spacing(level) Spacings the sub-sampled image must have at a particular level
print_level(level) Prints properties of a pyramid level
__init__(image, num_levels, image_grid2world=None, input_spacing=None, sigma_factor=0.2, mask0=False)

ScaleSpace

Computes the Scale Space representation of an image. The scale space is simply a list of images produced by smoothing the input image with a Gaussian kernel with increasing smoothing parameter. If the image’s voxels are isotropic, the smoothing will be the same along all directions: at level L = 0, 1, ..., the sigma is given by \(s * ( 2^L - 1 )\). If the voxel dimensions are not isotropic, then the smoothing is weaker along low resolution directions.

Parameters:

image : array, shape (r,c) or (s, r, c) where s is the number of

slices, r is the number of rows and c is the number of columns of the input image.

num_levels : int

the desired number of levels (resolutions) of the scale space

image_grid2world : array, shape (dim + 1, dim + 1), optional

the grid-to-space transform of the image grid. The default is the identity matrix

input_spacing : array, shape (dim,), optional

the spacing (voxel size) between voxels in physical space. The default is 1.0 along all axes

sigma_factor : float, optional

the smoothing factor to be used in the construction of the scale space. The default is 0.2

mask0 : Boolean, optional

if True, all smoothed images will be zero at all voxels that are zero in the input image. The default is False.

get_affine(level)

Voxel-to-space transformation at a given level

Returns the voxel-to-space transformation associated with the sub-sampled image at a particular resolution of the scale space (note that this object does not explicitly subsample the smoothed images, but only provides the properties the sub-sampled images must have).

Parameters:

level : int, 0 <= from_level < L, (L = number of resolutions)

the scale space level to get affine transform from

Returns:

the affine (voxel-to-space) transform at the requested resolution

or None if an invalid level was requested

get_affine_inv(level)

Space-to-voxel transformation at a given level

Returns the space-to-voxel transformation associated with the sub-sampled image at a particular resolution of the scale space (note that this object does not explicitly subsample the smoothed images, but only provides the properties the sub-sampled images must have).

Parameters:

level : int, 0 <= from_level < L, (L = number of resolutions)

the scale space level to get the inverse transform from

Returns:

the inverse (space-to-voxel) transform at the requested resolution or

None if an invalid level was requested

get_domain_shape(level)

Shape the sub-sampled image must have at a particular level

Returns the shape the sub-sampled image must have at a particular resolution of the scale space (note that this object does not explicitly subsample the smoothed images, but only provides the properties the sub-sampled images must have).

Parameters:

level : int, 0 <= from_level < L, (L = number of resolutions)

the scale space level to get the sub-sampled shape from

Returns:

the sub-sampled shape at the requested resolution or None if an

invalid level was requested

get_expand_factors(from_level, to_level)

Ratio of voxel size from pyramid level from_level to to_level

Given two scale space resolutions a = from_level, b = to_level, returns the ratio of voxels size at level b to voxel size at level a (the factor that must be used to multiply voxels at level a to ‘expand’ them to level b).

Parameters:

from_level : int, 0 <= from_level < L, (L = number of resolutions)

the resolution to expand voxels from

to_level : int, 0 <= to_level < from_level

the resolution to expand voxels to

Returns:

factors : array, shape (k,), k = 2, 3

the expand factors (a scalar for each voxel dimension)

get_image(level)

Smoothed image at a given level

Returns the smoothed image at the requested level in the Scale Space.

Parameters:

level : int, 0 <= from_level < L, (L = number of resolutions)

the scale space level to get the smooth image from

Returns:

the smooth image at the requested resolution or None if an invalid

level was requested

get_scaling(level)

Adjustment factor for input-spacing to reflect voxel sizes at level

Returns the scaling factor that needs to be applied to the input spacing (the voxel sizes of the image at level 0 of the scale space) to transform them to voxel sizes at the requested level.

Parameters:

level : int, 0 <= from_level < L, (L = number of resolutions)

the scale space level to get the scalings from

Returns:

the scaling factors from the original spacing to the spacings at the

requested level

get_sigmas(level)

Smoothing parameters used at a given level

Returns the smoothing parameters (a scalar for each axis) used at the requested level of the scale space

Parameters:

level : int, 0 <= from_level < L, (L = number of resolutions)

the scale space level to get the smoothing parameters from

Returns:

the smoothing parameters at the requested level

get_spacing(level)

Spacings the sub-sampled image must have at a particular level

Returns the spacings (voxel sizes) the sub-sampled image must have at a particular resolution of the scale space (note that this object does not explicitly subsample the smoothed images, but only provides the properties the sub-sampled images must have).

Parameters:

level : int, 0 <= from_level < L, (L = number of resolutions)

the scale space level to get the sub-sampled shape from

Returns:

the spacings (voxel sizes) at the requested resolution or None if an

invalid level was requested

print_level(level)

Prints properties of a pyramid level

Prints the properties of a level of this scale space to standard output

Parameters:

level : int, 0 <= from_level < L, (L = number of resolutions)

the scale space level to be printed

align_centers_of_mass

dipy.align.imaffine.align_centers_of_mass(static, static_grid2world, moving, moving_grid2world)

align_geometric_centers

dipy.align.imaffine.align_geometric_centers(static, static_grid2world, moving, moving_grid2world)

align_origins

dipy.align.imaffine.align_origins(static, static_grid2world, moving, moving_grid2world)

compute_parzen_mi

dipy.align.imaffine.compute_parzen_mi()

Computes the mutual information and its gradient (if requested)

Parameters:

joint : array, shape (nbins, nbins)

the joint intensity distribution

joint_gradient : array, shape (nbins, nbins, n)

the gradient of the joint distribution w.r.t. the transformation parameters

smarginal : array, shape (nbins,)

the marginal intensity distribution of the static image

mmarginal : array, shape (nbins,)

the marginal intensity distribution of the moving image

mi_gradient : array, shape (n,)

the buffer in which to write the gradient of the mutual information. If None, the gradient is not computed

get_direction_and_spacings

dipy.align.imaffine.get_direction_and_spacings(affine, dim)

Extracts the rotational and spacing components from a matrix

Extracts the rotational and spacing (voxel dimensions) components from a matrix. An image gradient represents the local variation of the image’s gray values per voxel. Since we are iterating on the physical space, we need to compute the gradients as variation per millimeter, so we need to divide each gradient’s component by the voxel size along the corresponding axis, that’s what the spacings are used for. Since the image’s gradients are oriented along the grid axes, we also need to re-orient the gradients to be given in physical space coordinates.

Parameters:

affine : array, shape (k, k), k = 3, 4

the matrix transforming grid coordinates to physical space.

Returns:

direction : array, shape (k-1, k-1)

the rotational component of the input matrix

spacings : array, shape (k-1,)

the scaling component (voxel size) of the matrix

sample_domain_regular

dipy.align.imaffine.sample_domain_regular()

Take floor(total_voxels/k) samples from a (2D or 3D) grid

The sampling is made by taking all pixels whose index (in lexicographical order) is a multiple of k. Each selected point is slightly perturbed by adding a realization of a normally distributed random variable and then mapped to physical space by the given grid-to-space transform.

The lexicographical order of a pixels in a grid of shape (a, b, c) is defined by assigning to each voxel position (i, j, k) the integer index

F((i, j, k)) = i * (b * c) + j * (c) + k

and sorting increasingly by this index.

Parameters:

k : int

the sampling rate, as described before

shape : array, shape (dim,)

the shape of the grid to be sampled

grid2world : array, shape (dim+1, dim+1)

the grid-to-space transform

sigma : float

the standard deviation of the Normal random distortion to be applied to the sampled points

Returns:

samples : array, shape (total_pixels//k, dim)

the matrix whose rows are the sampled points

transform_centers_of_mass

dipy.align.imaffine.transform_centers_of_mass(static, static_grid2world, moving, moving_grid2world)

Transformation to align the center of mass of the input images

Parameters:

static : array, shape (S, R, C)

static image

static_grid2world : array, shape (dim+1, dim+1)

the voxel-to-space transformation of the static image

moving : array, shape (S, R, C)

moving image

moving_grid2world : array, shape (dim+1, dim+1)

the voxel-to-space transformation of the moving image

Returns:

affine_map : instance of AffineMap

the affine transformation (translation only, in this case) aligning the center of mass of the moving image towards the one of the static image

transform_geometric_centers

dipy.align.imaffine.transform_geometric_centers(static, static_grid2world, moving, moving_grid2world)

Transformation to align the geometric center of the input images

With “geometric center” of a volume we mean the physical coordinates of its central voxel

Parameters:

static : array, shape (S, R, C)

static image

static_grid2world : array, shape (dim+1, dim+1)

the voxel-to-space transformation of the static image

moving : array, shape (S, R, C)

moving image

moving_grid2world : array, shape (dim+1, dim+1)

the voxel-to-space transformation of the moving image

Returns:

affine_map : instance of AffineMap

the affine transformation (translation only, in this case) aligning the geometric center of the moving image towards the one of the static image

transform_origins

dipy.align.imaffine.transform_origins(static, static_grid2world, moving, moving_grid2world)

Transformation to align the origins of the input images

With “origin” of a volume we mean the physical coordinates of voxel (0,0,0)

Parameters:

static : array, shape (S, R, C)

static image

static_grid2world : array, shape (dim+1, dim+1)

the voxel-to-space transformation of the static image

moving : array, shape (S, R, C)

moving image

moving_grid2world : array, shape (dim+1, dim+1)

the voxel-to-space transformation of the moving image

Returns:

affine_map : instance of AffineMap

the affine transformation (translation only, in this case) aligning the origin of the moving image towards the one of the static image

warn

dipy.align.imaffine.warn()

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

Bunch

class dipy.align.imwarp.Bunch(**kwds)

Bases: object

__init__(**kwds)

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

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

DiffeomorphicMap

class dipy.align.imwarp.DiffeomorphicMap(dim, disp_shape, disp_grid2world=None, domain_shape=None, domain_grid2world=None, codomain_shape=None, codomain_grid2world=None, prealign=None)

Bases: object

Methods

allocate() Creates a zero displacement field
compute_inversion_error() Inversion error of the displacement fields
expand_fields(expand_factors, new_shape) Expands the displacement fields from current shape to new_shape
get_backward_field() Deformation field to transform an image in the backward direction
get_forward_field() Deformation field to transform an image in the forward direction
get_simplified_transform() Constructs a simplified version of this Diffeomorhic Map
interpret_matrix(obj) Try to interpret obj as a matrix
inverse() Inverse of this DiffeomorphicMap instance
shallow_copy() Shallow copy of this DiffeomorphicMap instance
transform(image[, interpolation, ...]) Warps an image in the forward direction
transform_inverse(image[, interpolation, ...]) Warps an image in the backward direction
warp_endomorphism(phi) Composition of this DiffeomorphicMap with a given endomorphism
__init__(dim, disp_shape, disp_grid2world=None, domain_shape=None, domain_grid2world=None, codomain_shape=None, codomain_grid2world=None, prealign=None)

DiffeomorphicMap

Implements a diffeomorphic transformation on the physical space. The deformation fields encoding the direct and inverse transformations share the same domain discretization (both the discretization grid shape and voxel-to-space matrix). The input coordinates (physical coordinates) are first aligned using prealign, and then displaced using the corresponding vector field interpolated at the aligned coordinates.

Parameters:

dim : int, 2 or 3

the transformation’s dimension

disp_shape : array, shape (dim,)

the number of slices (if 3D), rows and columns of the deformation field’s discretization

disp_grid2world : the voxel-to-space transform between the def. fields

grid and space

domain_shape : array, shape (dim,)

the number of slices (if 3D), rows and columns of the default discretizatio of this map’s domain

domain_grid2world : array, shape (dim+1, dim+1)

the default voxel-to-space transformation between this map’s discretization and physical space

codomain_shape : array, shape (dim,)

the number of slices (if 3D), rows and columns of the images that are ‘normally’ warped using this transformation in the forward direction (this will provide default transformation parameters to warp images under this transformation). By default, we assume that the inverse transformation is ‘normally’ used to warp images with the same discretization and voxel-to-space transformation as the deformation field grid.

codomain_grid2world : array, shape (dim+1, dim+1)

the voxel-to-space transformation of images that are ‘normally’ warped using this transformation (in the forward direction).

prealign : array, shape (dim+1, dim+1)

the linear transformation to be applied to align input images to the reference space before warping under the deformation field.

allocate()

Creates a zero displacement field

Creates a zero displacement field (the identity transformation).

compute_inversion_error()

Inversion error of the displacement fields

Estimates the inversion error of the displacement fields by computing statistics of the residual vectors obtained after composing the forward and backward displacement fields.

Returns:

residual : array, shape (R, C) or (S, R, C)

the displacement field resulting from composing the forward and backward displacement fields of this transformation (the residual should be zero for a perfect diffeomorphism)

stats : array, shape (3,)

statistics from the norms of the vectors of the residual displacement field: maximum, mean and standard deviation

Notes

Since the forward and backward displacement fields have the same discretization, the final composition is given by

comp[i] = forward[ i + Dinv * backward[i]]

where Dinv is the space-to-grid transformation of the displacement fields

expand_fields(expand_factors, new_shape)

Expands the displacement fields from current shape to new_shape

Up-samples the discretization of the displacement fields to be of new_shape shape.

Parameters:

expand_factors : array, shape (dim,)

the factors scaling current spacings (voxel sizes) to spacings in the expanded discretization.

new_shape : array, shape (dim,)

the shape of the arrays holding the up-sampled discretization

get_backward_field()

Deformation field to transform an image in the backward direction

Returns the deformation field that must be used to warp an image under this transformation in the backward direction (note the ‘is_inverse’ flag).

get_forward_field()

Deformation field to transform an image in the forward direction

Returns the deformation field that must be used to warp an image under this transformation in the forward direction (note the ‘is_inverse’ flag).

get_simplified_transform()

Constructs a simplified version of this Diffeomorhic Map

The simplified version incorporates the pre-align transform, as well as the domain and codomain affine transforms into the displacement field. The resulting transformation may be regarded as operating on the image spaces given by the domain and codomain discretization. As a result, self.prealign, self.disp_grid2world, self.domain_grid2world and self.codomain affine will be None (denoting Identity) in the resulting diffeomorphic map.

interpret_matrix(obj)

Try to interpret obj as a matrix

Some operations are performed faster if we know in advance if a matrix is the identity (so we can skip the actual matrix-vector multiplication). This function returns None if the given object is None or the ‘identity’ string. It returns the same object if it is a numpy array. It raises an exception otherwise.

Parameters:

obj : object

any object

Returns:

obj : object

the same object given as argument if obj is None or a numpy array. None if obj is the ‘identity’ string.

inverse()

Inverse of this DiffeomorphicMap instance

Returns a diffeomorphic map object representing the inverse of this transformation. The internal arrays are not copied but just referenced.

Returns:

inv : DiffeomorphicMap object

the inverse of this diffeomorphic map.

shallow_copy()

Shallow copy of this DiffeomorphicMap instance

Creates a shallow copy of this diffeomorphic map (the arrays are not copied but just referenced)

Returns:

new_map : DiffeomorphicMap object

the shallow copy of this diffeomorphic map

transform(image, interpolation='linear', image_world2grid=None, out_shape=None, out_grid2world=None)

Warps an image in the forward direction

Transforms the input image under this transformation in the forward direction. It uses the “is_inverse” flag to switch between “forward” and “backward” (if is_inverse is False, then transform(...) warps the image forwards, else it warps the image backwards).

Parameters:

image : array, shape (s, r, c) if dim = 3 or (r, c) if dim = 2

the image to be warped under this transformation in the forward direction

interpolation : string, either ‘linear’ or ‘nearest’

the type of interpolation to be used for warping, either ‘linear’ (for k-linear interpolation) or ‘nearest’ for nearest neighbor

image_world2grid : array, shape (dim+1, dim+1)

the transformation bringing world (space) coordinates to voxel coordinates of the image given as input

out_shape : array, shape (dim,)

the number of slices, rows and columns of the desired warped image

out_grid2world : the transformation bringing voxel coordinates of the

warped image to physical space

Returns:

warped : array, shape = out_shape or self.codomain_shape if None

the warped image under this transformation in the forward direction

Notes

See _warp_forward and _warp_backward documentation for further information.

transform_inverse(image, interpolation='linear', image_world2grid=None, out_shape=None, out_grid2world=None)

Warps an image in the backward direction

Transforms the input image under this transformation in the backward direction. It uses the “is_inverse” flag to switch between “forward” and “backward” (if is_inverse is False, then transform_inverse(...) warps the image backwards, else it warps the image forwards)

Parameters:

image : array, shape (s, r, c) if dim = 3 or (r, c) if dim = 2

the image to be warped under this transformation in the forward direction

interpolation : string, either ‘linear’ or ‘nearest’

the type of interpolation to be used for warping, either ‘linear’ (for k-linear interpolation) or ‘nearest’ for nearest neighbor

image_world2grid : array, shape (dim+1, dim+1)

the transformation bringing world (space) coordinates to voxel coordinates of the image given as input

out_shape : array, shape (dim,)

the number of slices, rows and columns of the desired warped image

out_grid2world : the transformation bringing voxel coordinates of the

warped image to physical space

Returns:

warped : array, shape = out_shape or self.codomain_shape if None

warped image under this transformation in the backward direction

Notes

See _warp_forward and _warp_backward documentation for further information.

warp_endomorphism(phi)

Composition of this DiffeomorphicMap with a given endomorphism

Creates a new DiffeomorphicMap C with the same properties as self and composes its displacement fields with phi’s corresponding fields. The resulting diffeomorphism is of the form C(x) = phi(self(x)) with inverse C^{-1}(y) = self^{-1}(phi^{-1}(y)). We assume that phi is an endomorphism with the same discretization and domain affine as self to ensure that the composition inherits self’s properties (we also assume that the pre-aligning matrix of phi is None or identity).

Parameters:

phi : DiffeomorphicMap object

the endomorphism to be warped by this diffeomorphic map

Returns:

composition : the composition of this diffeomorphic map with the

endomorphism given as input

Notes

The problem with our current representation of a DiffeomorphicMap is that the set of Diffeomorphism that can be represented this way (a pre-aligning matrix followed by a non-linear endomorphism given as a displacement field) is not closed under the composition operation.

Supporting a general DiffeomorphicMap class, closed under composition, may be extremely costly computationally, and the kind of transformations we actually need for Avants’ mid-point algorithm (SyN) are much simpler.

DiffeomorphicRegistration

class dipy.align.imwarp.DiffeomorphicRegistration(metric=None)

Bases: abc.NewBase

Methods

get_map() Returns the resulting diffeomorphic map after optimization
optimize() Starts the metric optimization
set_level_iters(level_iters) Sets the number of iterations at each pyramid level
__init__(metric=None)

Diffeomorphic Registration

This abstract class defines the interface to be implemented by any optimization algorithm for diffeomorphic registration.

Parameters:

metric : SimilarityMetric object

the object measuring the similarity of the two images. The registration algorithm will minimize (or maximize) the provided similarity.

get_map()

Returns the resulting diffeomorphic map after optimization

optimize()

Starts the metric optimization

This is the main function each specialized class derived from this must implement. Upon completion, the deformation field must be available from the forward transformation model.

set_level_iters(level_iters)

Sets the number of iterations at each pyramid level

Establishes the maximum number of iterations to be performed at each level of the Gaussian pyramid, similar to ANTS.

Parameters:

level_iters : list

the number of iterations at each level of the Gaussian pyramid. level_iters[0] corresponds to the finest level, level_iters[n-1] the coarsest, where n is the length of the list

ScaleSpace

class dipy.align.imwarp.ScaleSpace(image, num_levels, image_grid2world=None, input_spacing=None, sigma_factor=0.2, mask0=False)

Bases: object

Methods

get_affine(level) Voxel-to-space transformation at a given level
get_affine_inv(level) Space-to-voxel transformation at a given level
get_domain_shape(level) Shape the sub-sampled image must have at a particular level
get_expand_factors(from_level, to_level) Ratio of voxel size from pyramid level from_level to to_level
get_image(level) Smoothed image at a given level
get_scaling(level) Adjustment factor for input-spacing to reflect voxel sizes at level
get_sigmas(level) Smoothing parameters used at a given level
get_spacing(level) Spacings the sub-sampled image must have at a particular level
print_level(level) Prints properties of a pyramid level
__init__(image, num_levels, image_grid2world=None, input_spacing=None, sigma_factor=0.2, mask0=False)

ScaleSpace

Computes the Scale Space representation of an image. The scale space is simply a list of images produced by smoothing the input image with a Gaussian kernel with increasing smoothing parameter. If the image’s voxels are isotropic, the smoothing will be the same along all directions: at level L = 0, 1, ..., the sigma is given by \(s * ( 2^L - 1 )\). If the voxel dimensions are not isotropic, then the smoothing is weaker along low resolution directions.

Parameters:

image : array, shape (r,c) or (s, r, c) where s is the number of

slices, r is the number of rows and c is the number of columns of the input image.

num_levels : int

the desired number of levels (resolutions) of the scale space

image_grid2world : array, shape (dim + 1, dim + 1), optional

the grid-to-space transform of the image grid. The default is the identity matrix

input_spacing : array, shape (dim,), optional

the spacing (voxel size) between voxels in physical space. The default is 1.0 along all axes

sigma_factor : float, optional

the smoothing factor to be used in the construction of the scale space. The default is 0.2

mask0 : Boolean, optional

if True, all smoothed images will be zero at all voxels that are zero in the input image. The default is False.

get_affine(level)

Voxel-to-space transformation at a given level

Returns the voxel-to-space transformation associated with the sub-sampled image at a particular resolution of the scale space (note that this object does not explicitly subsample the smoothed images, but only provides the properties the sub-sampled images must have).

Parameters:

level : int, 0 <= from_level < L, (L = number of resolutions)

the scale space level to get affine transform from

Returns:

the affine (voxel-to-space) transform at the requested resolution

or None if an invalid level was requested

get_affine_inv(level)

Space-to-voxel transformation at a given level

Returns the space-to-voxel transformation associated with the sub-sampled image at a particular resolution of the scale space (note that this object does not explicitly subsample the smoothed images, but only provides the properties the sub-sampled images must have).

Parameters:

level : int, 0 <= from_level < L, (L = number of resolutions)

the scale space level to get the inverse transform from

Returns:

the inverse (space-to-voxel) transform at the requested resolution or

None if an invalid level was requested

get_domain_shape(level)

Shape the sub-sampled image must have at a particular level

Returns the shape the sub-sampled image must have at a particular resolution of the scale space (note that this object does not explicitly subsample the smoothed images, but only provides the properties the sub-sampled images must have).

Parameters:

level : int, 0 <= from_level < L, (L = number of resolutions)

the scale space level to get the sub-sampled shape from

Returns:

the sub-sampled shape at the requested resolution or None if an

invalid level was requested

get_expand_factors(from_level, to_level)

Ratio of voxel size from pyramid level from_level to to_level

Given two scale space resolutions a = from_level, b = to_level, returns the ratio of voxels size at level b to voxel size at level a (the factor that must be used to multiply voxels at level a to ‘expand’ them to level b).

Parameters:

from_level : int, 0 <= from_level < L, (L = number of resolutions)

the resolution to expand voxels from

to_level : int, 0 <= to_level < from_level

the resolution to expand voxels to

Returns:

factors : array, shape (k,), k = 2, 3

the expand factors (a scalar for each voxel dimension)

get_image(level)

Smoothed image at a given level

Returns the smoothed image at the requested level in the Scale Space.

Parameters:

level : int, 0 <= from_level < L, (L = number of resolutions)

the scale space level to get the smooth image from

Returns:

the smooth image at the requested resolution or None if an invalid

level was requested

get_scaling(level)

Adjustment factor for input-spacing to reflect voxel sizes at level

Returns the scaling factor that needs to be applied to the input spacing (the voxel sizes of the image at level 0 of the scale space) to transform them to voxel sizes at the requested level.

Parameters:

level : int, 0 <= from_level < L, (L = number of resolutions)

the scale space level to get the scalings from

Returns:

the scaling factors from the original spacing to the spacings at the

requested level

get_sigmas(level)

Smoothing parameters used at a given level

Returns the smoothing parameters (a scalar for each axis) used at the requested level of the scale space

Parameters:

level : int, 0 <= from_level < L, (L = number of resolutions)

the scale space level to get the smoothing parameters from

Returns:

the smoothing parameters at the requested level

get_spacing(level)

Spacings the sub-sampled image must have at a particular level

Returns the spacings (voxel sizes) the sub-sampled image must have at a particular resolution of the scale space (note that this object does not explicitly subsample the smoothed images, but only provides the properties the sub-sampled images must have).

Parameters:

level : int, 0 <= from_level < L, (L = number of resolutions)

the scale space level to get the sub-sampled shape from

Returns:

the spacings (voxel sizes) at the requested resolution or None if an

invalid level was requested

print_level(level)

Prints properties of a pyramid level

Prints the properties of a level of this scale space to standard output

Parameters:

level : int, 0 <= from_level < L, (L = number of resolutions)

the scale space level to be printed

SymmetricDiffeomorphicRegistration

class dipy.align.imwarp.SymmetricDiffeomorphicRegistration(metric, level_iters=None, step_length=0.25, ss_sigma_factor=0.2, opt_tol=1e-05, inv_iter=20, inv_tol=0.001, callback=None)

Bases: dipy.align.imwarp.DiffeomorphicRegistration

Methods

get_map() Returns the resulting diffeomorphic map Returns the DiffeomorphicMap registering the moving image towards the static image.
optimize(static, moving[, ...]) Starts the optimization
set_level_iters(level_iters) Sets the number of iterations at each pyramid level
update(current_displacement, ...) Composition of the current displacement field with the given field
__init__(metric, level_iters=None, step_length=0.25, ss_sigma_factor=0.2, opt_tol=1e-05, inv_iter=20, inv_tol=0.001, callback=None)

Symmetric Diffeomorphic Registration (SyN) Algorithm

Performs the multi-resolution optimization algorithm for non-linear registration using a given similarity metric.

Parameters:

metric : SimilarityMetric object

the metric to be optimized

level_iters : list of int

the number of iterations at each level of the Gaussian Pyramid (the length of the list defines the number of pyramid levels to be used)

opt_tol : float

the optimization will stop when the estimated derivative of the energy profile w.r.t. time falls below this threshold

inv_iter : int

the number of iterations to be performed by the displacement field inversion algorithm

step_length : float

the length of the maximum displacement vector of the update displacement field at each iteration

ss_sigma_factor : float

parameter of the scale-space smoothing kernel. For example, the std. dev. of the kernel will be factor*(2^i) in the isotropic case where i = 0, 1, ..., n_scales is the scale

inv_tol : float

the displacement field inversion algorithm will stop iterating when the inversion error falls below this threshold

callback : function(SymmetricDiffeomorphicRegistration)

a function receiving a SymmetricDiffeomorphicRegistration object to be called after each iteration (this optimizer will call this function passing self as parameter)

get_map()

Returns the resulting diffeomorphic map Returns the DiffeomorphicMap registering the moving image towards the static image.

optimize(static, moving, static_grid2world=None, moving_grid2world=None, prealign=None)

Starts the optimization

Parameters:

static : array, shape (S, R, C) or (R, C)

the image to be used as reference during optimization. The displacement fields will have the same discretization as the static image.

moving : array, shape (S, R, C) or (R, C)

the image to be used as “moving” during optimization. Since the deformation fields’ discretization is the same as the static image, it is necessary to pre-align the moving image to ensure its domain lies inside the domain of the deformation fields. This is assumed to be accomplished by “pre-aligning” the moving image towards the static using an affine transformation given by the ‘prealign’ matrix

static_grid2world : array, shape (dim+1, dim+1)

the voxel-to-space transformation associated to the static image

moving_grid2world : array, shape (dim+1, dim+1)

the voxel-to-space transformation associated to the moving image

prealign : array, shape (dim+1, dim+1)

the affine transformation (operating on the physical space) pre-aligning the moving image towards the static

Returns:

static_to_ref : DiffeomorphicMap object

the diffeomorphic map that brings the moving image towards the static one in the forward direction (i.e. by calling static_to_ref.transform) and the static image towards the moving one in the backward direction (i.e. by calling static_to_ref.transform_inverse).

update(current_displacement, new_displacement, disp_world2grid, time_scaling)

Composition of the current displacement field with the given field

Interpolates new displacement at the locations defined by current_displacement. Equivalently, computes the composition C of the given displacement fields as C(x) = B(A(x)), where A is current_displacement and B is new_displacement. This function is intended to be used with deformation fields of the same sampling (e.g. to be called by a registration algorithm).

Parameters:

current_displacement : array, shape (R’, C’, 2) or (S’, R’, C’, 3)

the displacement field defining where to interpolate new_displacement

new_displacement : array, shape (R, C, 2) or (S, R, C, 3)

the displacement field to be warped by current_displacement

disp_world2grid : array, shape (dim+1, dim+1)

the space-to-grid transform associated with the displacements’ grid (we assume that both displacements are discretized over the same grid)

time_scaling : float

scaling factor applied to d2. The effect may be interpreted as moving d1 displacements along a factor (time_scaling) of d2.

Returns:

updated : array, shape (the same as new_displacement)

the warped displacement field

mean_norm : the mean norm of all vectors in current_displacement

floating

dipy.align.imwarp.floating

alias of float32

get_direction_and_spacings

dipy.align.imwarp.get_direction_and_spacings(affine, dim)

Extracts the rotational and spacing components from a matrix

Extracts the rotational and spacing (voxel dimensions) components from a matrix. An image gradient represents the local variation of the image’s gray values per voxel. Since we are iterating on the physical space, we need to compute the gradients as variation per millimeter, so we need to divide each gradient’s component by the voxel size along the corresponding axis, that’s what the spacings are used for. Since the image’s gradients are oriented along the grid axes, we also need to re-orient the gradients to be given in physical space coordinates.

Parameters:

affine : array, shape (k, k), k = 3, 4

the matrix transforming grid coordinates to physical space.

Returns:

direction : array, shape (k-1, k-1)

the rotational component of the input matrix

spacings : array, shape (k-1,)

the scaling component (voxel size) of the matrix

mult_aff

dipy.align.imwarp.mult_aff(A, B)

Returns the matrix product A.dot(B) considering None as the identity

Parameters:

A : array, shape (n,k)

B : array, shape (k,m)

Returns:

The matrix product A.dot(B). If any of the input matrices is None, it is

treated as the identity matrix. If both matrices are None, None is returned

with_metaclass

dipy.align.imwarp.with_metaclass(meta, *bases)

Create a base class with a metaclass.

CCMetric

class dipy.align.metrics.CCMetric(dim, sigma_diff=2.0, radius=4)

Bases: dipy.align.metrics.SimilarityMetric

Methods

compute_backward() Computes one step bringing the static image towards the moving.
compute_forward() Computes one step bringing the moving image towards the static.
free_iteration() Frees the resources allocated during initialization
get_energy() Numerical value assigned by this metric to the current image pair
initialize_iteration() Prepares the metric to compute one displacement field iteration.
set_levels_above(levels) Informs the metric how many pyramid levels are above the current one
set_levels_below(levels) Informs the metric how many pyramid levels are below the current one
set_moving_image(moving_image, ...) Sets the moving image being compared against the static one.
set_static_image(static_image, ...) Sets the static image being compared against the moving one.
use_moving_image_dynamics(...) This is called by the optimizer just after setting the moving image
use_static_image_dynamics(...) This is called by the optimizer just after setting the static image.
__init__(dim, sigma_diff=2.0, radius=4)

Normalized Cross-Correlation Similarity metric.

Parameters:

dim : int (either 2 or 3)

the dimension of the image domain

sigma_diff : the standard deviation of the Gaussian smoothing kernel to

be applied to the update field at each iteration

radius : int

the radius of the squared (cubic) neighborhood at each voxel to be considered to compute the cross correlation

compute_backward()

Computes one step bringing the static image towards the moving.

Computes the update displacement field to be used for registration of the static image towards the moving image

compute_forward()

Computes one step bringing the moving image towards the static.

Computes the update displacement field to be used for registration of the moving image towards the static image

free_iteration()

Frees the resources allocated during initialization

get_energy()

Numerical value assigned by this metric to the current image pair

Returns the Cross Correlation (data term) energy computed at the largest iteration

initialize_iteration()

Prepares the metric to compute one displacement field iteration.

Pre-computes the cross-correlation factors for efficient computation of the gradient of the Cross Correlation w.r.t. the displacement field. It also pre-computes the image gradients in the physical space by re-orienting the gradients in the voxel space using the corresponding affine transformations.

EMMetric

class dipy.align.metrics.EMMetric(dim, smooth=1.0, inner_iter=5, q_levels=256, double_gradient=True, step_type='gauss_newton')

Bases: dipy.align.metrics.SimilarityMetric

Methods

compute_backward() Computes one step bringing the static image towards the moving.
compute_demons_step([forward_step]) Demons step for EM metric
compute_forward() Computes one step bringing the reference image towards the static.
compute_gauss_newton_step([forward_step]) Computes the Gauss-Newton energy minimization step
free_iteration() Frees the resources allocated during initialization
get_energy() The numerical value assigned by this metric to the current image pair
initialize_iteration() Prepares the metric to compute one displacement field iteration.
set_levels_above(levels) Informs the metric how many pyramid levels are above the current one
set_levels_below(levels) Informs the metric how many pyramid levels are below the current one
set_moving_image(moving_image, ...) Sets the moving image being compared against the static one.
set_static_image(static_image, ...) Sets the static image being compared against the moving one.
use_moving_image_dynamics(...) This is called by the optimizer just after setting the moving image.
use_static_image_dynamics(...) This is called by the optimizer just after setting the static image.
__init__(dim, smooth=1.0, inner_iter=5, q_levels=256, double_gradient=True, step_type='gauss_newton')

Expectation-Maximization Metric

Similarity metric based on the Expectation-Maximization algorithm to handle multi-modal images. The transfer function is modeled as a set of hidden random variables that are estimated at each iteration of the algorithm.

Parameters:

dim : int (either 2 or 3)

the dimension of the image domain

smooth : float

smoothness parameter, the larger the value the smoother the deformation field

inner_iter : int

number of iterations to be performed at each level of the multi- resolution Gauss-Seidel optimization algorithm (this is not the number of steps per Gaussian Pyramid level, that parameter must be set for the optimizer, not the metric)

q_levels : number of quantization levels (equal to the number of hidden

variables in the EM algorithm)

double_gradient : boolean

if True, the gradient of the expected static image under the moving modality will be added to the gradient of the moving image, similarly, the gradient of the expected moving image under the static modality will be added to the gradient of the static image.

step_type : string (‘gauss_newton’, ‘demons’)

the optimization schedule to be used in the multi-resolution Gauss-Seidel optimization algorithm (not used if Demons Step is selected)

compute_backward()

Computes one step bringing the static image towards the moving.

Computes the update displacement field to be used for registration of the static image towards the moving image

compute_demons_step(forward_step=True)

Demons step for EM metric

Parameters:

forward_step : boolean

if True, computes the Demons step in the forward direction (warping the moving towards the static image). If False, computes the backward step (warping the static image to the moving image)

Returns:

displacement : array, shape (R, C, 2) or (S, R, C, 3)

the Demons step

compute_forward()

Computes one step bringing the reference image towards the static.

Computes the forward update field to register the moving image towards the static image in a gradient-based optimization algorithm

compute_gauss_newton_step(forward_step=True)

Computes the Gauss-Newton energy minimization step

Computes the Newton step to minimize this energy, i.e., minimizes the linearized energy function with respect to the regularized displacement field (this step does not require post-smoothing, as opposed to the demons step, which does not include regularization). To accelerate convergence we use the multi-grid Gauss-Seidel algorithm proposed by Bruhn and Weickert et al [Bruhn05]

Parameters:

forward_step : boolean

if True, computes the Newton step in the forward direction (warping the moving towards the static image). If False, computes the backward step (warping the static image to the moving image)

Returns:

displacement : array, shape (R, C, 2) or (S, R, C, 3)

the Newton step

References

[Bruhn05] Andres Bruhn and Joachim Weickert, “Towards ultimate motion
estimation: combining highest accuracy with real-time performance”, 10th IEEE International Conference on Computer Vision, 2005. ICCV 2005.
free_iteration()

Frees the resources allocated during initialization

get_energy()

The numerical value assigned by this metric to the current image pair

Returns the EM (data term) energy computed at the largest iteration

initialize_iteration()

Prepares the metric to compute one displacement field iteration.

Pre-computes the transfer functions (hidden random variables) and variances of the estimators. Also pre-computes the gradient of both input images. Note that once the images are transformed to the opposite modality, the gradient of the transformed images can be used with the gradient of the corresponding modality in the same fashion as diff-demons does for mono-modality images. If the flag self.use_double_gradient is True these gradients are averaged.

use_moving_image_dynamics(original_moving_image, transformation)

This is called by the optimizer just after setting the moving image.

EMMetric takes advantage of the image dynamics by computing the current moving image mask from the original_moving_image mask (warped by nearest neighbor interpolation)

Parameters:

original_moving_image : array, shape (R, C) or (S, R, C)

the original moving image from which the current moving image was generated, the current moving image is the one that was provided via ‘set_moving_image(...)’, which may not be the same as the original moving image but a warped version of it.

transformation : DiffeomorphicMap object

the transformation that was applied to the original_moving_image to generate the current moving image

use_static_image_dynamics(original_static_image, transformation)

This is called by the optimizer just after setting the static image.

EMMetric takes advantage of the image dynamics by computing the current static image mask from the originalstaticImage mask (warped by nearest neighbor interpolation)

Parameters:

original_static_image : array, shape (R, C) or (S, R, C)

the original static image from which the current static image was generated, the current static image is the one that was provided via ‘set_static_image(...)’, which may not be the same as the original static image but a warped version of it (even the static image changes during Symmetric Normalization, not only the moving one).

transformation : DiffeomorphicMap object

the transformation that was applied to the original_static_image to generate the current static image

SSDMetric

class dipy.align.metrics.SSDMetric(dim, smooth=4, inner_iter=10, step_type='demons')

Bases: dipy.align.metrics.SimilarityMetric

Methods

compute_backward() Computes one step bringing the static image towards the moving.
compute_demons_step([forward_step]) Demons step for SSD metric
compute_forward() Computes one step bringing the reference image towards the static.
compute_gauss_newton_step([forward_step]) Computes the Gauss-Newton energy minimization step
free_iteration() Nothing to free for the SSD metric
get_energy() The numerical value assigned by this metric to the current image pair
initialize_iteration() Prepares the metric to compute one displacement field iteration.
set_levels_above(levels) Informs the metric how many pyramid levels are above the current one
set_levels_below(levels) Informs the metric how many pyramid levels are below the current one
set_moving_image(moving_image, ...) Sets the moving image being compared against the static one.
set_static_image(static_image, ...) Sets the static image being compared against the moving one.
use_moving_image_dynamics(...) This is called by the optimizer just after setting the moving image
use_static_image_dynamics(...) This is called by the optimizer just after setting the static image.
__init__(dim, smooth=4, inner_iter=10, step_type='demons')

Sum of Squared Differences (SSD) Metric

Similarity metric for (mono-modal) nonlinear image registration defined by the sum of squared differences (SSD)

Parameters:

dim : int (either 2 or 3)

the dimension of the image domain

smooth : float

smoothness parameter, the larger the value the smoother the deformation field

inner_iter : int

number of iterations to be performed at each level of the multi- resolution Gauss-Seidel optimization algorithm (this is not the number of steps per Gaussian Pyramid level, that parameter must be set for the optimizer, not the metric)

step_type : string

the displacement field step to be computed when ‘compute_forward’ and ‘compute_backward’ are called. Either ‘demons’ or ‘gauss_newton’

compute_backward()

Computes one step bringing the static image towards the moving.

Computes the update displacement field to be used for registration of the static image towards the moving image

compute_demons_step(forward_step=True)

Demons step for SSD metric

Computes the demons step proposed by Vercauteren et al.[Vercauteren09] for the SSD metric.

Parameters:

forward_step : boolean

if True, computes the Demons step in the forward direction (warping the moving towards the static image). If False, computes the backward step (warping the static image to the moving image)

Returns:

displacement : array, shape (R, C, 2) or (S, R, C, 3)

the Demons step

References

[Vercauteren09] Tom Vercauteren, Xavier Pennec, Aymeric Perchant,
Nicholas Ayache, “Diffeomorphic Demons: Efficient Non-parametric Image Registration”, Neuroimage 2009
compute_forward()

Computes one step bringing the reference image towards the static.

Computes the update displacement field to be used for registration of the moving image towards the static image

compute_gauss_newton_step(forward_step=True)

Computes the Gauss-Newton energy minimization step

Minimizes the linearized energy function (Newton step) defined by the sum of squared differences of corresponding pixels of the input images with respect to the displacement field.

Parameters:

forward_step : boolean

if True, computes the Newton step in the forward direction (warping the moving towards the static image). If False, computes the backward step (warping the static image to the moving image)

Returns:

displacement : array, shape = static_image.shape + (3,)

if forward_step==True, the forward SSD Gauss-Newton step, else, the backward step

free_iteration()

Nothing to free for the SSD metric

get_energy()

The numerical value assigned by this metric to the current image pair

Returns the Sum of Squared Differences (data term) energy computed at the largest iteration

initialize_iteration()

Prepares the metric to compute one displacement field iteration.

Pre-computes the gradient of the input images to be used in the computation of the forward and backward steps.

SimilarityMetric

class dipy.align.metrics.SimilarityMetric(dim)

Bases: abc.NewBase

Methods

compute_backward() Computes one step bringing the static image towards the moving.
compute_forward() Computes one step bringing the reference image towards the static.
free_iteration() Releases the resources no longer needed by the metric
get_energy() Numerical value assigned by this metric to the current image pair
initialize_iteration() Prepares the metric to compute one displacement field iteration.
set_levels_above(levels) Informs the metric how many pyramid levels are above the current one
set_levels_below(levels) Informs the metric how many pyramid levels are below the current one
set_moving_image(moving_image, ...) Sets the moving image being compared against the static one.
set_static_image(static_image, ...) Sets the static image being compared against the moving one.
use_moving_image_dynamics(...) This is called by the optimizer just after setting the moving image
use_static_image_dynamics(...) This is called by the optimizer just after setting the static image.
__init__(dim)

Similarity Metric abstract class

A similarity metric is in charge of keeping track of the numerical value of the similarity (or distance) between the two given images. It also computes the update field for the forward and inverse displacement fields to be used in a gradient-based optimization algorithm. Note that this metric does not depend on any transformation (affine or non-linear) so it assumes the static and moving images are already warped

Parameters:

dim : int (either 2 or 3)

the dimension of the image domain

compute_backward()

Computes one step bringing the static image towards the moving.

Computes the backward update field to register the static image towards the moving image in a gradient-based optimization algorithm

compute_forward()

Computes one step bringing the reference image towards the static.

Computes the forward update field to register the moving image towards the static image in a gradient-based optimization algorithm

free_iteration()

Releases the resources no longer needed by the metric

This method is called by the RegistrationOptimizer after the required iterations have been computed (forward and / or backward) so that the SimilarityMetric can safely delete any data it computed as part of the initialization

get_energy()

Numerical value assigned by this metric to the current image pair

Must return the numeric value of the similarity between the given static and moving images

initialize_iteration()

Prepares the metric to compute one displacement field iteration.

This method will be called before any compute_forward or compute_backward call, this allows the Metric to pre-compute any useful information for speeding up the update computations. This initialization was needed in ANTS because the updates are called once per voxel. In Python this is unpractical, though.

set_levels_above(levels)

Informs the metric how many pyramid levels are above the current one

Informs this metric the number of pyramid levels above the current one. The metric may change its behavior (e.g. number of inner iterations) accordingly

Parameters:

levels : int

the number of levels above the current Gaussian Pyramid level

set_levels_below(levels)

Informs the metric how many pyramid levels are below the current one

Informs this metric the number of pyramid levels below the current one. The metric may change its behavior (e.g. number of inner iterations) accordingly

Parameters:

levels : int

the number of levels below the current Gaussian Pyramid level

set_moving_image(moving_image, moving_affine, moving_spacing, moving_direction)

Sets the moving image being compared against the static one.

Sets the moving image. The default behavior (of this abstract class) is simply to assign the reference to an attribute, but generalizations of the metric may need to perform other operations

Parameters:

moving_image : array, shape (R, C) or (S, R, C)

the moving image

set_static_image(static_image, static_affine, static_spacing, static_direction)

Sets the static image being compared against the moving one.

Sets the static image. The default behavior (of this abstract class) is simply to assign the reference to an attribute, but generalizations of the metric may need to perform other operations

Parameters:

static_image : array, shape (R, C) or (S, R, C)

the static image

use_moving_image_dynamics(original_moving_image, transformation)

This is called by the optimizer just after setting the moving image

This method allows the metric to compute any useful information from knowing how the current static image was generated (as the transformation of an original static image). This method is called by the optimizer just after it sets the static image. Transformation will be an instance of DiffeomorficMap or None if the original_moving_image equals self.moving_image.

Parameters:

original_moving_image : array, shape (R, C) or (S, R, C)

original image from which the current moving image was generated

transformation : DiffeomorphicMap object

the transformation that was applied to original image to generate the current moving image

use_static_image_dynamics(original_static_image, transformation)

This is called by the optimizer just after setting the static image.

This method allows the metric to compute any useful information from knowing how the current static image was generated (as the transformation of an original static image). This method is called by the optimizer just after it sets the static image. Transformation will be an instance of DiffeomorficMap or None if the original_static_image equals self.moving_image.

Parameters:

original_static_image : array, shape (R, C) or (S, R, C)

original image from which the current static image was generated

transformation : DiffeomorphicMap object

the transformation that was applied to original image to generate the current static image

floating

dipy.align.metrics.floating

alias of float32

gradient

dipy.align.metrics.gradient(f, *varargs, **kwargs)

Return the gradient of an N-dimensional array.

The gradient is computed using second order accurate central differences in the interior and either first differences or second order accurate one-sides (forward or backwards) differences at the boundaries. The returned gradient hence has the same shape as the input array.

Parameters:

f : array_like

An N-dimensional array containing samples of a scalar function.

varargs : scalar or list of scalar, optional

N scalars specifying the sample distances for each dimension, i.e. dx, dy, dz, ... Default distance: 1. single scalar specifies sample distance for all dimensions. if axis is given, the number of varargs must equal the number of axes.

edge_order : {1, 2}, optional

Gradient is calculated using N-th order accurate differences at the boundaries. Default: 1.

New in version 1.9.1.

axis : None or int or tuple of ints, optional

Gradient is calculated only along the given axis or axes The default (axis = None) is to calculate the gradient for all the axes of the input array. axis may be negative, in which case it counts from the last to the first axis.

New in version 1.11.0.

Returns:

gradient : ndarray or list of ndarray

A set of ndarrays (or a single ndarray if there is only one dimension) correposnding to the derivatives of f with respect to each dimension. Each derivative has the same shape as f.

Examples

>>> x = np.array([1, 2, 4, 7, 11, 16], dtype=np.float)
>>> np.gradient(x)
array([ 1. ,  1.5,  2.5,  3.5,  4.5,  5. ])
>>> np.gradient(x, 2)
array([ 0.5 ,  0.75,  1.25,  1.75,  2.25,  2.5 ])

For two dimensional arrays, the return will be two arrays ordered by axis. In this example the first array stands for the gradient in rows and the second one in columns direction:

>>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=np.float))
[array([[ 2.,  2., -1.],
        [ 2.,  2., -1.]]), array([[ 1. ,  2.5,  4. ],
        [ 1. ,  1. ,  1. ]])]
>>> x = np.array([0, 1, 2, 3, 4])
>>> y = x**2
>>> np.gradient(y, edge_order=2)
array([-0.,  2.,  4.,  6.,  8.])

The axis keyword can be used to specify a subset of axes of which the gradient is calculated >>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=np.float), axis=0) array([[ 2., 2., -1.],

[ 2., 2., -1.]])

v_cycle_2d

dipy.align.metrics.v_cycle_2d(n, k, delta_field, sigma_sq_field, gradient_field, target, lambda_param, displacement, depth=0)

Multi-resolution Gauss-Seidel solver using V-type cycles

Multi-resolution Gauss-Seidel solver: solves the Gauss-Newton linear system by first filtering (GS-iterate) the current level, then solves for the residual at a coarser resolution and finally refines the solution at the current resolution. This scheme corresponds to the V-cycle proposed by Bruhn and Weickert[Bruhn05].

Parameters:

n : int

number of levels of the multi-resolution algorithm (it will be called recursively until level n == 0)

k : int

the number of iterations at each multi-resolution level

delta_field : array, shape (R, C)

the difference between the static and moving image (the ‘derivative w.r.t. time’ in the optical flow model)

sigma_sq_field : array, shape (R, C)

the variance of the gray level value at each voxel, according to the EM model (for SSD, it is 1 for all voxels). Inf and 0 values are processed specially to support infinite and zero variance.

gradient_field : array, shape (R, C, 2)

the gradient of the moving image

target : array, shape (R, C, 2)

right-hand side of the linear system to be solved in the Weickert’s multi-resolution algorithm

lambda_param : float

smoothness parameter, the larger its value the smoother the displacement field

displacement : array, shape (R, C, 2)

the displacement field to start the optimization from

Returns:

energy : the energy of the EM (or SSD if sigmafield[...]==1) metric at this

iteration

References

[Bruhn05] Andres Bruhn and Joachim Weickert, “Towards ultimate motion
estimation: combining highest accuracy with real-time performance”, 10th IEEE International Conference on Computer Vision, 2005. ICCV 2005.

v_cycle_3d

dipy.align.metrics.v_cycle_3d(n, k, delta_field, sigma_sq_field, gradient_field, target, lambda_param, displacement, depth=0)

Multi-resolution Gauss-Seidel solver using V-type cycles

Multi-resolution Gauss-Seidel solver: solves the linear system by first filtering (GS-iterate) the current level, then solves for the residual at a coarser resolution and finally refines the solution at the current resolution. This scheme corresponds to the V-cycle proposed by Bruhn and Weickert[1]. [1] Andres Bruhn and Joachim Weickert, “Towards ultimate motion estimation:

combining highest accuracy with real-time performance”, 10th IEEE International Conference on Computer Vision, 2005. ICCV 2005.
Parameters:

n : int

number of levels of the multi-resolution algorithm (it will be called recursively until level n == 0)

k : int

the number of iterations at each multi-resolution level

delta_field : array, shape (S, R, C)

the difference between the static and moving image (the ‘derivative w.r.t. time’ in the optical flow model)

sigma_sq_field : array, shape (S, R, C)

the variance of the gray level value at each voxel, according to the EM model (for SSD, it is 1 for all voxels). Inf and 0 values are processed specially to support infinite and zero variance.

gradient_field : array, shape (S, R, C, 3)

the gradient of the moving image

target : array, shape (S, R, C, 3)

right-hand side of the linear system to be solved in the Weickert’s multi-resolution algorithm

lambda_param : float

smoothness parameter, the larger its value the smoother the displacement field

displacement : array, shape (S, R, C, 3)

the displacement field to start the optimization from

Returns:

energy : the energy of the EM (or SSD if sigmafield[...]==1) metric at this

iteration

with_metaclass

dipy.align.metrics.with_metaclass(meta, *bases)

Create a base class with a metaclass.

Pool

dipy.align.reslice.Pool(self, processes=None, initializer=None, initargs=(), maxtasksperchild=None)

Returns a process pool object

affine_transform

dipy.align.reslice.affine_transform(input, matrix, offset=0.0, output_shape=None, output=None, order=3, mode='constant', cval=0.0, prefilter=True)

Apply an affine transformation.

The given matrix and offset are used to find for each point in the output the corresponding coordinates in the input by an affine transformation. The value of the input at those coordinates is determined by spline interpolation of the requested order. Points outside the boundaries of the input are filled according to the given mode.

Given an output image pixel index vector o, the pixel value is determined from the input image at position np.dot(matrix,o) + offset.

A diagonal matrix can be specified by supplying a one-dimensional array-like to the matrix parameter, in which case a more efficient algorithm is applied.

Changed in version 0.18.0: Previously, the exact interpretation of the affine transformation depended on whether the matrix was supplied as a one-dimensional or two-dimensional array. If a one-dimensional array was supplied to the matrix parameter, the output pixel value at index o was determined from the input image at position matrix * (o + offset).

Parameters:

input : ndarray

The input array.

matrix : ndarray

The matrix must be two-dimensional or can also be given as a one-dimensional sequence or array. In the latter case, it is assumed that the matrix is diagonal. A more efficient algorithms is then applied that exploits the separability of the problem.

offset : float or sequence, optional

The offset into the array where the transform is applied. If a float, offset is the same for each axis. If a sequence, offset should contain one value for each axis.

output_shape : tuple of ints, optional

Shape tuple.

output : ndarray or dtype, optional

The array in which to place the output, or the dtype of the returned array.

order : int, optional

The order of the spline interpolation, default is 3. The order has to be in the range 0-5.

mode : str, optional

Points outside the boundaries of the input are filled according to the given mode (‘constant’, ‘nearest’, ‘reflect’, ‘mirror’ or ‘wrap’). Default is ‘constant’.

cval : scalar, optional

Value used for points outside the boundaries of the input if mode='constant'. Default is 0.0

prefilter : bool, optional

The parameter prefilter determines if the input is pre-filtered with spline_filter before interpolation (necessary for spline interpolation of order > 1). If False, it is assumed that the input is already filtered. Default is True.

Returns:

affine_transform : ndarray or None

The transformed input. If output is given as a parameter, None is returned.

cpu_count

dipy.align.reslice.cpu_count(self)

Returns the number of CPUs in the system

reslice

dipy.align.reslice.reslice(data, affine, zooms, new_zooms, order=1, mode='constant', cval=0, num_processes=1)

Reslice data with new voxel resolution defined by new_zooms

Parameters:

data : array, shape (I,J,K) or (I,J,K,N)

3d volume or 4d volume with datasets

affine : array, shape (4,4)

mapping from voxel coordinates to world coordinates

zooms : tuple, shape (3,)

voxel size for (i,j,k) dimensions

new_zooms : tuple, shape (3,)

new voxel size for (i,j,k) after resampling

order : int, from 0 to 5

order of interpolation for resampling/reslicing, 0 nearest interpolation, 1 trilinear etc.. if you don’t want any smoothing 0 is the option you need.

mode : string (‘constant’, ‘nearest’, ‘reflect’ or ‘wrap’)

Points outside the boundaries of the input are filled according to the given mode.

cval : float

Value used for points outside the boundaries of the input if mode=’constant’.

num_processes : int

Split the calculation to a pool of children processes. This only applies to 4D data arrays. If a positive integer then it defines the size of the multiprocessing pool that will be used. If 0, then the size of the pool will equal the number of cores available.

Returns:

data2 : array, shape (I,J,K) or (I,J,K,N)

datasets resampled into isotropic voxel size

affine2 : array, shape (4,4)

new affine for the resampled image

Examples

>>> import nibabel as nib
>>> from dipy.align.reslice import reslice
>>> from dipy.data import get_data
>>> fimg = get_data('aniso_vox')
>>> img = nib.load(fimg)
>>> data = img.get_data()
>>> data.shape == (58, 58, 24)
True
>>> affine = img.affine
>>> zooms = img.header.get_zooms()[:3]
>>> zooms
(4.0, 4.0, 5.0)
>>> new_zooms = (3.,3.,3.)
>>> new_zooms
(3.0, 3.0, 3.0)
>>> data2, affine2 = reslice(data, affine, zooms, new_zooms)
>>> data2.shape == (77, 77, 40)
True

IsotropicScaleSpace

class dipy.align.scalespace.IsotropicScaleSpace(image, factors, sigmas, image_grid2world=None, input_spacing=None, mask0=False)

Bases: dipy.align.scalespace.ScaleSpace

Methods

get_affine(level) Voxel-to-space transformation at a given level
get_affine_inv(level) Space-to-voxel transformation at a given level
get_domain_shape(level) Shape the sub-sampled image must have at a particular level
get_expand_factors(from_level, to_level) Ratio of voxel size from pyramid level from_level to to_level
get_image(level) Smoothed image at a given level
get_scaling(level) Adjustment factor for input-spacing to reflect voxel sizes at level
get_sigmas(level) Smoothing parameters used at a given level
get_spacing(level) Spacings the sub-sampled image must have at a particular level
print_level(level) Prints properties of a pyramid level
__init__(image, factors, sigmas, image_grid2world=None, input_spacing=None, mask0=False)

IsotropicScaleSpace

Computes the Scale Space representation of an image using isotropic smoothing kernels for all scales. The scale space is simply a list of images produced by smoothing the input image with a Gaussian kernel with different smoothing parameters.

This specialization of ScaleSpace allows the user to provide custom scale and smoothing factors for all scales.

Parameters:

image : array, shape (r,c) or (s, r, c) where s is the number of

slices, r is the number of rows and c is the number of columns of the input image.

factors : list of floats

custom scale factors to build the scale space (one factor for each scale).

sigmas : list of floats

custom smoothing parameter to build the scale space (one parameter for each scale).

image_grid2world : array, shape (dim + 1, dim + 1), optional

the grid-to-space transform of the image grid. The default is the identity matrix.

input_spacing : array, shape (dim,), optional

the spacing (voxel size) between voxels in physical space. The default if 1.0 along all axes.

mask0 : Boolean, optional

if True, all smoothed images will be zero at all voxels that are zero in the input image. The default is False.

ScaleSpace

class dipy.align.scalespace.ScaleSpace(image, num_levels, image_grid2world=None, input_spacing=None, sigma_factor=0.2, mask0=False)

Bases: object

Methods

get_affine(level) Voxel-to-space transformation at a given level
get_affine_inv(level) Space-to-voxel transformation at a given level
get_domain_shape(level) Shape the sub-sampled image must have at a particular level
get_expand_factors(from_level, to_level) Ratio of voxel size from pyramid level from_level to to_level
get_image(level) Smoothed image at a given level
get_scaling(level) Adjustment factor for input-spacing to reflect voxel sizes at level
get_sigmas(level) Smoothing parameters used at a given level
get_spacing(level) Spacings the sub-sampled image must have at a particular level
print_level(level) Prints properties of a pyramid level
__init__(image, num_levels, image_grid2world=None, input_spacing=None, sigma_factor=0.2, mask0=False)

ScaleSpace

Computes the Scale Space representation of an image. The scale space is simply a list of images produced by smoothing the input image with a Gaussian kernel with increasing smoothing parameter. If the image’s voxels are isotropic, the smoothing will be the same along all directions: at level L = 0, 1, ..., the sigma is given by \(s * ( 2^L - 1 )\). If the voxel dimensions are not isotropic, then the smoothing is weaker along low resolution directions.

Parameters:

image : array, shape (r,c) or (s, r, c) where s is the number of

slices, r is the number of rows and c is the number of columns of the input image.

num_levels : int

the desired number of levels (resolutions) of the scale space

image_grid2world : array, shape (dim + 1, dim + 1), optional

the grid-to-space transform of the image grid. The default is the identity matrix

input_spacing : array, shape (dim,), optional

the spacing (voxel size) between voxels in physical space. The default is 1.0 along all axes

sigma_factor : float, optional

the smoothing factor to be used in the construction of the scale space. The default is 0.2

mask0 : Boolean, optional

if True, all smoothed images will be zero at all voxels that are zero in the input image. The default is False.

get_affine(level)

Voxel-to-space transformation at a given level

Returns the voxel-to-space transformation associated with the sub-sampled image at a particular resolution of the scale space (note that this object does not explicitly subsample the smoothed images, but only provides the properties the sub-sampled images must have).

Parameters:

level : int, 0 <= from_level < L, (L = number of resolutions)

the scale space level to get affine transform from

Returns:

the affine (voxel-to-space) transform at the requested resolution

or None if an invalid level was requested

get_affine_inv(level)

Space-to-voxel transformation at a given level

Returns the space-to-voxel transformation associated with the sub-sampled image at a particular resolution of the scale space (note that this object does not explicitly subsample the smoothed images, but only provides the properties the sub-sampled images must have).

Parameters:

level : int, 0 <= from_level < L, (L = number of resolutions)

the scale space level to get the inverse transform from

Returns:

the inverse (space-to-voxel) transform at the requested resolution or

None if an invalid level was requested

get_domain_shape(level)

Shape the sub-sampled image must have at a particular level

Returns the shape the sub-sampled image must have at a particular resolution of the scale space (note that this object does not explicitly subsample the smoothed images, but only provides the properties the sub-sampled images must have).

Parameters:

level : int, 0 <= from_level < L, (L = number of resolutions)

the scale space level to get the sub-sampled shape from

Returns:

the sub-sampled shape at the requested resolution or None if an

invalid level was requested

get_expand_factors(from_level, to_level)

Ratio of voxel size from pyramid level from_level to to_level

Given two scale space resolutions a = from_level, b = to_level, returns the ratio of voxels size at level b to voxel size at level a (the factor that must be used to multiply voxels at level a to ‘expand’ them to level b).

Parameters:

from_level : int, 0 <= from_level < L, (L = number of resolutions)

the resolution to expand voxels from

to_level : int, 0 <= to_level < from_level

the resolution to expand voxels to

Returns:

factors : array, shape (k,), k = 2, 3

the expand factors (a scalar for each voxel dimension)

get_image(level)

Smoothed image at a given level

Returns the smoothed image at the requested level in the Scale Space.

Parameters:

level : int, 0 <= from_level < L, (L = number of resolutions)

the scale space level to get the smooth image from

Returns:

the smooth image at the requested resolution or None if an invalid

level was requested

get_scaling(level)

Adjustment factor for input-spacing to reflect voxel sizes at level

Returns the scaling factor that needs to be applied to the input spacing (the voxel sizes of the image at level 0 of the scale space) to transform them to voxel sizes at the requested level.

Parameters:

level : int, 0 <= from_level < L, (L = number of resolutions)

the scale space level to get the scalings from

Returns:

the scaling factors from the original spacing to the spacings at the

requested level

get_sigmas(level)

Smoothing parameters used at a given level

Returns the smoothing parameters (a scalar for each axis) used at the requested level of the scale space

Parameters:

level : int, 0 <= from_level < L, (L = number of resolutions)

the scale space level to get the smoothing parameters from

Returns:

the smoothing parameters at the requested level

get_spacing(level)

Spacings the sub-sampled image must have at a particular level

Returns the spacings (voxel sizes) the sub-sampled image must have at a particular resolution of the scale space (note that this object does not explicitly subsample the smoothed images, but only provides the properties the sub-sampled images must have).

Parameters:

level : int, 0 <= from_level < L, (L = number of resolutions)

the scale space level to get the sub-sampled shape from

Returns:

the spacings (voxel sizes) at the requested resolution or None if an

invalid level was requested

print_level(level)

Prints properties of a pyramid level

Prints the properties of a level of this scale space to standard output

Parameters:

level : int, 0 <= from_level < L, (L = number of resolutions)

the scale space level to be printed

floating

dipy.align.scalespace.floating

alias of float32

BundleMinDistanceAsymmetricMetric

class dipy.align.streamlinear.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)

BundleMinDistanceMatrixMetric

class dipy.align.streamlinear.BundleMinDistanceMatrixMetric(num_threads=None)

Bases: dipy.align.streamlinear.StreamlineDistanceMetric

Bundle-based Minimum Distance aka BMD

This is the cost function used by the StreamlineLinearRegistration

Notes

The difference with BundleMinDistanceMetric is that this creates the entire distance matrix and therefore requires more memory.

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.

Notes

Call this after the object is initiated and before distance.

Num_threads is not used in this class. Use BundleMinDistanceMetric for a faster, threaded and less memory hungry metric

BundleMinDistanceMetric

class dipy.align.streamlinear.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.align.streamlinear.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

Optimizer

class dipy.align.streamlinear.Optimizer(fun, x0, args=(), method='L-BFGS-B', jac=None, hess=None, hessp=None, bounds=None, constraints=(), tol=None, callback=None, options=None, evolution=False)

Bases: object

Attributes

evolution
fopt
message
nfev
nit
xopt

Methods

print_summary()
__init__(fun, x0, args=(), method='L-BFGS-B', jac=None, hess=None, hessp=None, bounds=None, constraints=(), tol=None, callback=None, options=None, evolution=False)

A class for handling minimization of scalar function of one or more variables.

Parameters:

fun : callable

Objective function.

x0 : ndarray

Initial guess.

args : tuple, optional

Extra arguments passed to the objective function and its derivatives (Jacobian, Hessian).

method : str, optional

Type of solver. Should be one of

  • ‘Nelder-Mead’
  • ‘Powell’
  • ‘CG’
  • ‘BFGS’
  • ‘Newton-CG’
  • ‘Anneal’
  • ‘L-BFGS-B’
  • ‘TNC’
  • ‘COBYLA’
  • ‘SLSQP’
  • ‘dogleg’
  • ‘trust-ncg’

jac : bool or callable, optional

Jacobian of objective function. Only for CG, BFGS, Newton-CG, dogleg, trust-ncg. If jac is a Boolean and is True, fun is assumed to return the value of Jacobian along with the objective function. If False, the Jacobian will be estimated numerically. jac can also be a callable returning the Jacobian of the objective. In this case, it must accept the same arguments as fun.

hess, hessp : callable, optional

Hessian of objective function or Hessian of objective function times an arbitrary vector p. Only for Newton-CG, dogleg, trust-ncg. Only one of hessp or hess needs to be given. If hess is provided, then hessp will be ignored. If neither hess nor hessp is provided, then the hessian product will be approximated using finite differences on jac. hessp must compute the Hessian times an arbitrary vector.

bounds : sequence, optional

Bounds for variables (only for L-BFGS-B, TNC and SLSQP). (min, max) pairs for each element in x, defining the bounds on that parameter. Use None for one of min or max when there is no bound in that direction.

constraints : dict or sequence of dict, optional

Constraints definition (only for COBYLA and SLSQP). Each constraint is defined in a dictionary with fields:

type : str

Constraint type: ‘eq’ for equality, ‘ineq’ for inequality.

fun : callable

The function defining the constraint.

jac : callable, optional

The Jacobian of fun (only for SLSQP).

args : sequence, optional

Extra arguments to be passed to the function and Jacobian.

Equality constraint means that the constraint function result is to be zero whereas inequality means that it is to be non-negative. Note that COBYLA only supports inequality constraints.

tol : float, optional

Tolerance for termination. For detailed control, use solver-specific options.

callback : callable, optional

Called after each iteration, as callback(xk), where xk is the current parameter vector. Only available using Scipy >= 0.12.

options : dict, optional

A dictionary of solver options. All methods accept the following generic options:

maxiter : int

Maximum number of iterations to perform.

disp : bool

Set to True to print convergence messages.

For method-specific options, see show_options(‘minimize’, method).

evolution : bool, optional

save history of x for each iteration. Only available using Scipy >= 0.12.

See also

scipy.optimize.minimize

evolution
fopt
message
nfev
nit
print_summary()
xopt

QuickBundles

class dipy.align.streamlinear.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](1, 2, 3, 4) 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.

StreamlineDistanceMetric

class dipy.align.streamlinear.StreamlineDistanceMetric(num_threads=None)

Bases: abc.NewBase

Methods

distance(xopt) calculate distance for current set of parameters
setup(static, moving)
__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)

calculate distance for current set of parameters

setup(static, moving)

StreamlineLinearRegistration

class dipy.align.streamlinear.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]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

StreamlineRegistrationMap

class dipy.align.streamlinear.StreamlineRegistrationMap(matopt, xopt, fopt, matopt_history, funcs, iterations)

Bases: object

Methods

transform(moving) Transform moving streamlines to the static.
__init__(matopt, xopt, fopt, matopt_history, funcs, iterations)

A map holding the optimum affine matrix and some other parameters of the optimization

Parameters:

matrix : array,

4x4 affine matrix which transforms the moving to the static streamlines

xopt : array,

1d array with the parameters of the transformation after centering

fopt : float,

final value of the metric

matrix_history : array

All transformation matrices created during the optimization

funcs : int,

Number of function evaluations of the optimizer

iterations : int

Number of iterations of the optimizer

transform(moving)

Transform moving streamlines to the static.

Parameters:moving : streamlines
Returns:moved : streamlines

Notes

All this does is apply self.matrix to the input streamlines.

bundle_min_distance

dipy.align.streamlinear.bundle_min_distance(t, static, moving)

MDF-based pairwise distance optimization function (MIN)

We minimize the distance between moving streamlines as they align with the static streamlines.

Parameters:

t : ndarray

t is a vector of of affine transformation parameters with size at least 6. If size is 6, t is interpreted as translation + rotation. If size is 7, t is interpreted as translation + rotation + isotropic scaling. If size is 12, t is interpreted as translation + rotation + scaling + shearing.

static : list

Static streamlines

moving : list

Moving streamlines.

num_threads : int

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

Returns:

cost: float

bundle_min_distance_asymmetric_fast

dipy.align.streamlinear.bundle_min_distance_asymmetric_fast(t, static, moving, block_size)

MDF-based pairwise distance optimization function (MIN)

We minimize the distance between moving streamlines as they align with the static streamlines.

Parameters:

t : array

1D array. t is a vector of of affine transformation parameters with size at least 6. If size is 6, t is interpreted as translation + rotation. If size is 7, t is interpreted as translation + rotation + isotropic scaling. If size is 12, t is interpreted as translation + rotation + scaling + shearing.

static : array

N*M x 3 array. All the points of the static streamlines. With order of streamlines intact. Where N is the number of streamlines and M is the number of points per streamline.

moving : array

K*M x 3 array. All the points of the moving streamlines. With order of streamlines intact. Where K is the number of streamlines and M is the number of points per streamline.

block_size : int

Number of points per streamline. All streamlines in static and moving should have the same number of points M.

Returns:

cost: float

bundle_min_distance_fast

dipy.align.streamlinear.bundle_min_distance_fast(t, static, moving, block_size, num_threads)

MDF-based pairwise distance optimization function (MIN)

We minimize the distance between moving streamlines as they align with the static streamlines.

Parameters:

t : array

1D array. t is a vector of of affine transformation parameters with size at least 6. If size is 6, t is interpreted as translation + rotation. If size is 7, t is interpreted as translation + rotation + isotropic scaling. If size is 12, t is interpreted as translation + rotation + scaling + shearing.

static : array

N*M x 3 array. All the points of the static streamlines. With order of streamlines intact. Where N is the number of streamlines and M is the number of points per streamline.

moving : array

K*M x 3 array. All the points of the moving streamlines. With order of streamlines intact. Where K is the number of streamlines and M is the number of points per streamline.

block_size : int

Number of points per streamline. All streamlines in static and moving should have the same number of points M.

num_threads : int

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

Returns:

cost: float

Notes

This is a faster implementation of bundle_min_distance, which requires that all the points of each streamline are allocated into an ndarray (of shape N*M by 3, with N the number of points per streamline and M the number of streamlines). This can be done by calling dipy.tracking.streamlines.unlist_streamlines.

bundle_sum_distance

dipy.align.streamlinear.bundle_sum_distance(t, static, moving, num_threads=None)

MDF distance optimization function (SUM)

We minimize the distance between moving streamlines as they align with the static streamlines.

Parameters:

t : ndarray

t is a vector of of affine transformation parameters with size at least 6. If size is 6, t is interpreted as translation + rotation. If size is 7, t is interpreted as translation + rotation + isotropic scaling. If size is 12, t is interpreted as translation + rotation + scaling + shearing.

static : list

Static streamlines

moving : list

Moving streamlines. These will be transform to align with the static streamlines

Returns:

cost: float

center_streamlines

dipy.align.streamlinear.center_streamlines(streamlines)

Move streamlines to the origin

Parameters:

streamlines : list

List of 2D ndarrays of shape[-1]==3

Returns:

new_streamlines : list

List of 2D ndarrays of shape[-1]==3

inv_shift : ndarray

Translation in x,y,z to go back in the initial position

compose_matrix

dipy.align.streamlinear.compose_matrix(scale=None, shear=None, angles=None, translate=None, perspective=None)

Return 4x4 transformation matrix from sequence of transformations.

Code modified from the work of Christoph Gohlke link provided here http://www.lfd.uci.edu/~gohlke/code/transformations.py.html

This is the inverse of the decompose_matrix function.

Parameters:

scale : (3,) array_like

Scaling factors.

shear : array_like

Shear factors for x-y, x-z, y-z axes.

angles : array_like

Euler angles about static x, y, z axes.

translate : array_like

Translation vector along x, y, z axes.

perspective : array_like

Perspective partition of matrix.

Returns:

matrix : 4x4 array

Examples

>>> import math
>>> import numpy as np
>>> import dipy.core.geometry as gm
>>> scale = np.random.random(3) - 0.5
>>> shear = np.random.random(3) - 0.5
>>> angles = (np.random.random(3) - 0.5) * (2*math.pi)
>>> trans = np.random.random(3) - 0.5
>>> persp = np.random.random(4) - 0.5
>>> M0 = gm.compose_matrix(scale, shear, angles, trans, persp)

compose_matrix44

dipy.align.streamlinear.compose_matrix44(t, dtype=<class 'numpy.float64'>)

Compose a 4x4 transformation matrix

Parameters:

t : ndarray

This is a 1D vector of of affine transformation parameters with size at least 3. If size is 3, t is interpreted as translation. If size is 6, t is interpreted as translation + rotation. If size is 7, t is interpreted as translation + rotation + isotropic scaling. If size is 9, t is interpreted as translation + rotation + anisotropic scaling. If size is 12, t is interpreted as translation + rotation + scaling + shearing.

Returns:

T : ndarray

Homogeneous transformation matrix of size 4x4.

compose_transformations

dipy.align.streamlinear.compose_transformations(*mats)

Compose multiple 4x4 affine transformations in one 4x4 matrix

Parameters:

mat1 : array, (4, 4)

mat2 : array, (4, 4)

...

matN : array, (4, 4)

Returns:

matN x ... x mat2 x mat1 : array, (4, 4)

decompose_matrix

dipy.align.streamlinear.decompose_matrix(matrix)

Return sequence of transformations from transformation matrix.

Code modified from the excellent work of Christoph Gohlke link provided here: http://www.lfd.uci.edu/~gohlke/code/transformations.py.html

Parameters:

matrix : array_like

Non-degenerative homogeneous transformation matrix

Returns:

scale : (3,) ndarray

Three scaling factors.

shear : (3,) ndarray

Shear factors for x-y, x-z, y-z axes.

angles : (3,) ndarray

Euler angles about static x, y, z axes.

translate : (3,) ndarray

Translation vector along x, y, z axes.

perspective : ndarray

Perspective partition of matrix.

Raises:

ValueError

If matrix is of wrong type or degenerative.

Examples

>>> import numpy as np
>>> T0=np.diag([2,1,1,1])
>>> scale, shear, angles, trans, persp = decompose_matrix(T0)

decompose_matrix44

dipy.align.streamlinear.decompose_matrix44(mat, size=12)

Given a 4x4 homogeneous matrix return the parameter vector

Parameters:

mat : array

Homogeneous 4x4 transformation matrix

size : int

Size of output vector. 3, for translation, 6 for rigid, 7 for similarity, 9 for scaling and 12 for affine. Default is 12.

Returns:

t : ndarray

One dimensional ndarray of 3, 6, 7, 9 or 12 affine parameters.

distance_matrix_mdf

dipy.align.streamlinear.distance_matrix_mdf()

Minimum direct flipped distance matrix between two streamline sets

All streamlines need to have the same number of points

Parameters:

streamlines_a : sequence

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

streamlines_b : sequence

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

Returns:

DM : array, shape (len(streamlines_a), len(streamlines_b))

distance matrix

length

dipy.align.streamlinear.length()

Euclidean length of streamlines

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

Parameters:

streamlines : ndarray or a list or dipy.tracking.Streamlines

If ndarray, must have shape (N,3) where N is the number of points of the streamline. If list, each item must be ndarray shape (Ni,3) where Ni is the number of points of streamline i. If dipy.tracking.Streamlines, its common_shape must be 3.

Returns:

lengths : scalar or ndarray shape (N,)

If there is only one streamline, a scalar representing the length of the streamline. If there are several streamlines, ndarray containing the length of every streamline.

Examples

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

progressive_slr

dipy.align.streamlinear.progressive_slr(static, moving, metric, x0, bounds, method='L-BFGS-B', verbose=True, num_threads=None)

Progressive SLR

This is an utility function that allows for example to do affine registration using Streamline-based Linear Registration (SLR) [Garyfallidis15] by starting with translation first, then rigid, then similarity, scaling and finally affine.

Similarly, if for example you want to perform rigid then you start with translation first. This progressive strategy can helps with finding the optimal parameters of the final transformation.

Parameters:

static : Streamlines

moving : Streamlines

metric : StreamlineDistanceMetric

x0 : string

Could be any of ‘translation’, ‘rigid’, ‘similarity’, ‘scaling’, ‘affine’

bounds : array

Boundaries of registration parameters. See variable DEFAULT_BOUNDS for example.

method : string

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

verbose : bool

If True show messages in stdout (default True).

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]Garyfallidis et al. “Robust and efficient linear registration of white-matter fascicles in the space of streamlines”, NeuroImage, 117, 124–140, 2015

remove_clusters_by_size

dipy.align.streamlinear.remove_clusters_by_size(clusters, min_size=0)

select_random_set_of_streamlines

dipy.align.streamlinear.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.align.streamlinear.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]

slr_with_qb

dipy.align.streamlinear.slr_with_qb(static, moving, x0='affine', rm_small_clusters=50, maxiter=100, select_random=None, verbose=False, greater_than=50, less_than=250, qb_thr=15, nb_pts=20, progressive=True, num_threads=None)

Utility function for registering large tractograms.

For efficiency we apply the registration on cluster centroids and remove small clusters.

Parameters:

static : Streamlines

moving : Streamlines

x0 : str

rigid, similarity or affine transformation model (default affine)

rm_small_clusters : int

Remove clusters that have less than rm_small_clusters (default 50)

verbose : bool,

If True then information about the optimization is shown.

select_random : int

If not None select a random number of streamlines to apply clustering Default None.

options : None or dict,

Extra options to be used with the selected method.

num_threads : int

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

Notes

The order of operations is the following. First short or long streamlines are removed. Second the tractogram or a random selection of the tractogram is clustered with QuickBundles. Then SLR [Garyfallidis15] is applied.

References

[Garyfallidis15]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.

time

dipy.align.streamlinear.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.

transform_streamlines

dipy.align.streamlinear.transform_streamlines(streamlines, mat)

Apply affine transformation to streamlines

Parameters:

streamlines : list

List of 2D ndarrays of shape[-1]==3

mat : array, (4, 4)

transformation matrix

Returns:

new_streamlines : list

List of the transformed 2D ndarrays of shape[-1]==3

unlist_streamlines

dipy.align.streamlinear.unlist_streamlines(streamlines)

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

Parameters:

streamlines: sequence

Returns:

points : array

offsets : array

whole_brain_slr

dipy.align.streamlinear.whole_brain_slr(static, moving, x0='affine', rm_small_clusters=50, maxiter=100, select_random=None, verbose=False, greater_than=50, less_than=250, qb_thr=15, nb_pts=20, progressive=True, num_threads=None)

Utility function for registering large tractograms.

For efficiency we apply the registration on cluster centroids and remove small clusters.

Parameters:

static : Streamlines

moving : Streamlines

x0 : str

rigid, similarity or affine transformation model (default affine)

rm_small_clusters : int

Remove clusters that have less than rm_small_clusters (default 50)

verbose : bool,

If True then information about the optimization is shown.

select_random : int

If not None select a random number of streamlines to apply clustering Default None.

options : None or dict,

Extra options to be used with the selected method.

num_threads : int

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

Notes

The order of operations is the following. First short or long streamlines are removed. Second the tractogram or a random selection of the tractogram is clustered with QuickBundles. Then SLR [Garyfallidis15] is applied.

References

[Garyfallidis15]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.

with_metaclass

dipy.align.streamlinear.with_metaclass(meta, *bases)

Create a base class with a metaclass.