# align

 Bunch(**kwds) floating alias of numpy.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, …])
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 numpy.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 numpy.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 numpy.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, …])
StreamlineDistanceMetric([num_threads])

Methods

StreamlineLinearRegistration([metric, x0, …])

Methods

StreamlineRegistrationMap(matopt, xopt, …)

Methods

Streamlines alias of nibabel.streamlines.array_sequence.ArraySequence
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
qbx_and_merge(streamlines, thresholds[, …]) Run QuickBundlesX and then run again on the centroids of the last layer
remove_clusters_by_size(clusters[, min_size])
select_random_set_of_streamlines(…[, rng]) Select a random set of streamlines
set_number_of_points Change the number of points of streamlines
slr_with_qbx(static, moving[, x0, …]) Utility function for registering large tractograms.
time() 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 numpy.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__(self, /, *args, **kwargs) 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__(self, /, *args, **kwargs)

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 : 2D or 3D array 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 : 2D or 3D array 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, ret_metric=False)

Starts the optimization process

Parameters: static : 2D or 3D array the image to be used as reference during optimization. moving : 2D or 3D array 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. ret_metric : boolean, optional if True, it returns the parameters for measuring the similarity between the images (default ‘False’). The metric containing optimal parameters and the distance between the images. affine_map : instance of AffineMap the affine resulting affine transformation xopt : optimal parameters the optimal parameters (translation, rotation shear etc.) fopt : Similarity metric the value of the function at the optimal parameters.

### IsotropicScaleSpace

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

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 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 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 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.

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 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 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 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.

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 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.

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 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 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 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 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 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 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 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 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. 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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)

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 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. 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 numpy.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. 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) 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)

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')

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) 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) 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')

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) 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) 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 numpy.float32

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 points and either first 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 : list of scalar or array, optional Spacing between f values. Default unitary spacing for all dimensions. Spacing can be specified using: single scalar to specify a sample distance for all dimensions. N scalars to specify a constant sample distance for each dimension. i.e. dx, dy, dz, … N arrays to specify the coordinates of the values along each dimension of F. The length of the array must match the size of the corresponding dimension Any combination of N scalars/arrays with the meaning of 2. and 3. If axis is given, the number of varargs must equal the number of axes. Default: 1. 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. gradient : ndarray or list of ndarray A set of ndarrays (or a single ndarray if there is only one dimension) corresponding to the derivatives of f with respect to each dimension. Each derivative has the same shape as f.

Notes

Assuming that $$f\in C^{3}$$ (i.e., $$f$$ has at least 3 continuous derivatives) and let $$h_{*}$$ be a non-homogeneous stepsize, we minimize the “consistency error” $$\eta_{i}$$ between the true gradient and its estimate from a linear combination of the neighboring grid-points:

$\eta_{i} = f_{i}^{\left(1\right)} - \left[ \alpha f\left(x_{i}\right) + \beta f\left(x_{i} + h_{d}\right) + \gamma f\left(x_{i}-h_{s}\right) \right]$

By substituting $$f(x_{i} + h_{d})$$ and $$f(x_{i} - h_{s})$$ with their Taylor series expansion, this translates into solving the following the linear system:

$\begin{split}\left\{ \begin{array}{r} \alpha+\beta+\gamma=0 \\ \beta h_{d}-\gamma h_{s}=1 \\ \beta h_{d}^{2}+\gamma h_{s}^{2}=0 \end{array} \right.\end{split}$

The resulting approximation of $$f_{i}^{(1)}$$ is the following:

$\hat f_{i}^{(1)} = \frac{ h_{s}^{2}f\left(x_{i} + h_{d}\right) + \left(h_{d}^{2} - h_{s}^{2}\right)f\left(x_{i}\right) - h_{d}^{2}f\left(x_{i}-h_{s}\right)} { h_{s}h_{d}\left(h_{d} + h_{s}\right)} + \mathcal{O}\left(\frac{h_{d}h_{s}^{2} + h_{s}h_{d}^{2}}{h_{d} + h_{s}}\right)$

It is worth noting that if $$h_{s}=h_{d}$$ (i.e., data are evenly spaced) we find the standard second order approximation:

$\hat f_{i}^{(1)}= \frac{f\left(x_{i+1}\right) - f\left(x_{i-1}\right)}{2h} + \mathcal{O}\left(h^{2}\right)$

With a similar procedure the forward/backward approximations used for boundaries can be derived.

References

 [1] Quarteroni A., Sacco R., Saleri F. (2007) Numerical Mathematics (Texts in Applied Mathematics). New York: Springer.
 [2] Durran D. R. (1999) Numerical Methods for Wave Equations in Geophysical Fluid Dynamics. New York: Springer.
 [3] Fornberg B. (1988) Generation of Finite Difference Formulas on Arbitrarily Spaced Grids, Mathematics of Computation 51, no. 184 : 699-706. PDF.

Examples

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


Spacing can be also specified with an array that represents the coordinates of the values F along the dimensions. For instance a uniform spacing:

>>> x = np.arange(f.size)
array([ 1. ,  1.5,  2.5,  3.5,  4.5,  5. ])


Or a non uniform one:

>>> x = np.array([0., 1., 1.5, 3.5, 4., 6.], dtype=float)
array([ 1. ,  3. ,  3.5,  6.7,  6.9,  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=float))
[array([[ 2.,  2., -1.],
[ 2.,  2., -1.]]), array([[ 1. ,  2.5,  4. ],
[ 1. ,  1. ,  1. ]])]


In this example the spacing is also specified: uniform for axis=0 and non uniform for axis=1

>>> dx = 2.
>>> y = [1., 1.5, 3.5]
>>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=float), dx, y)
[array([[ 1. ,  1. , -0.5],
[ 1. ,  1. , -0.5]]), array([[ 2. ,  2. ,  2. ],
[ 2. ,  1.7,  0.5]])]


It is possible to specify how boundaries are treated using edge_order

>>> x = np.array([0, 1, 2, 3, 4])
>>> f = x**2
array([ 1.,  2.,  4.,  6.,  7.])
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=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 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 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(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.

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

Parameters: input : array_like The input array. matrix : ndarray The inverse coordinate transformation matrix, mapping output coordinates to input coordinates. If ndim is the number of dimensions of input, the given matrix must have one of the following shapes: (ndim, ndim): the linear transformation matrix for each output coordinate. (ndim,): assume that the 2D transformation matrix is diagonal, with the diagonal specified by the given value. A more efficient algorithm is then used that exploits the separability of the problem. (ndim + 1, ndim + 1): assume that the transformation is specified using homogeneous coordinates [1]. In this case, any value passed to offset is ignored. (ndim, ndim + 1): as above, but the bottom row of a homogeneous transformation matrix is always [0, 0, ..., 1], and may be omitted. 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 : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. order : int, optional The order of the spline interpolation, default is 3. The order has to be in the range 0-5. mode : {‘reflect’, ‘constant’, ‘nearest’, ‘mirror’, ‘wrap’}, optional The mode parameter determines how the input array is extended when the filter overlaps a border. Default is ‘reflect’. Behavior for each valid value is as follows: ‘reflect’ (d c b a | a b c d | d c b a) The input is extended by reflecting about the edge of the last pixel. ‘constant’ (k k k k | a b c d | k k k k) The input is extended by filling all values beyond the edge with the same constant value, defined by the cval parameter. ‘nearest’ (a a a a | a b c d | d d d d) The input is extended by replicating the last pixel. ‘mirror’ (d c b | a b c d | c b a) The input is extended by reflecting about the center of the last pixel. ‘wrap’ (a b c d | a b c d | a b c d) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if mode is ‘constant’. Default is 0.0. prefilter : bool, optional Determines if the input array is prefiltered with spline_filter before interpolation. The default is True, which will create a temporary float64 array of filtered values if order > 1. If setting this to False, the output will be slightly blurred if order > 1, unless the input is prefiltered, i.e. it is the result of calling spline_filter on the original input. affine_transform : ndarray The transformed input.

Notes

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.

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).

References

### cpu_count

dipy.align.reslice.cpu_count()

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. 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_fnames
>>> fimg = get_fnames('aniso_vox')
>>> data = img.get_data()
>>> data.shape == (58, 58, 24)
True
>>> affine = img.affine
>>> 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)

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 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 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 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 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 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 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 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 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 numpy.float32

### BundleMinDistanceAsymmetricMetric

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

Asymmetric Bundle-based Minimum distance

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

Methods

 distance(xopt) Distance calculated from this Metric 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)

Distance calculated from this Metric

Parameters: xopt : sequence List of affine parameters as an 1D vector

### BundleMinDistanceMatrixMetric

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

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)

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)

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.

scipy.optimize.minimize

evolution
fopt
message
nfev
nit
print_summary()
xopt

### StreamlineDistanceMetric

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

Bases: abc.NewBase

Methods

 distance(xopt) calculate distance for current set of parameters
 setup
__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: 6 x0 = np.array([0, 0, 0, 0, 0, 0]) 7 x0 = np.array([0, 0, 0, 0, 0, 0, 1.]) 12 x0 = np.array([0, 0, 0, 0, 0, 0, 1., 1., 1, 0, 0, 0]) If str: “rigid” x0 = np.array([0, 0, 0, 0, 0, 0]) “similarity” x0 = np.array([0, 0, 0, 0, 0, 0, 1.]) “affine” x0 = np.array([0, 0, 0, 0, 0, 0, 1., 1., 1, 0, 0, 0]) method : str, ‘L_BFGS_B’ or ‘Powell’ optimizers can be used. Default is ‘L_BFGS_B’. bounds : list of tuples or None, If method == ‘L_BFGS_B’ then we can use bounded optimization. For example for the six parameters of rigid rotation we can set the bounds = [(-30, 30), (-30, 30), (-30, 30), (-45, 45), (-45, 45), (-45, 45)] That means that we have set the bounds for the three translations and three rotation axes (in degrees). verbose : bool, If True then information about the optimization is shown. options : None or dict, Extra options to be used with the selected method. evolution : boolean If True save the transformation for each iteration of the optimizer. Default is False. Supported only with Scipy >= 0.11. num_threads : int Number of threads. If None (default) then all available threads will be used. Only metrics using OpenMP will use this variable.

References

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

Find the minimum of the provided metric.

Parameters: static : streamlines Reference or fixed set of streamlines. moving : streamlines Moving set of streamlines. mat : array Transformation (4, 4) matrix to start the registration. mat is applied to moving. Default value None which means that initial transformation will be generated by shifting the centers of moving and static sets of streamlines to the origin. 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 moved : streamlines

Notes

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

### Streamlines

dipy.align.streamlinear.Streamlines

alias of nibabel.streamlines.array_sequence.ArraySequence

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

### qbx_and_merge

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

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

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

Parameters: streamlines : Streamlines thresholds : sequence List of distance thresholds for QuickBundlesX. nb_pts : int Number of points for discretizing each streamline select_randomly : int Randomly select a specific number of streamlines. If None all the streamlines are used. rng : RandomState If None then RandomState is initialized internally. verbose : bool If True print information in stdout. clusters : obj Contains the clusters of the last layer of QuickBundlesX after merging.

References

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

### 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, rng=None)

Select a random set of streamlines

Parameters: streamlines : Steamlines Object 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). rng : RandomState Default None. 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. 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_qbx

dipy.align.streamlinear.slr_with_qbx(static, moving, x0='affine', rm_small_clusters=50, maxiter=100, select_random=None, verbose=False, greater_than=50, less_than=250, qbx_thr=[40, 30, 20, 15], nb_pts=20, progressive=True, rng=None, 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) select_random : int If not None select a random number of streamlines to apply clustering Default None. verbose : bool, If True then information about the optimization is shown. greater_than : int, optional Keep streamlines that have length greater than this value (default 50) less_than : int, optional Keep streamlines have length less than this value (default 250) qbx_thr : variable int Thresholds for QuickBundlesX (default [40, 30, 20, 15]) np_pts : int, optional Number of points for discretizing each streamline (default 20) progressive : boolean, optional (default True) rng : RandomState If None creates RandomState in function. 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] (1, 2) Garyfallidis et al. “Robust and efficient linear

registration of white-matter fascicles in the space of streamlines”, NeuroImage, 117, 124–140, 2015 .. [R778a6c20f622-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, in_place=False)

Apply affine transformation to streamlines

Parameters: streamlines : Streamlines Streamlines object mat : array, (4, 4) transformation matrix in_place : bool If True then change data in place. Be careful changes input streamlines. new_streamlines : Streamlines Sequence 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 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, qbx_thr=[40, 30, 20, 15], nb_pts=20, progressive=True, rng=None, 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) select_random : int If not None select a random number of streamlines to apply clustering Default None. verbose : bool, If True then information about the optimization is shown. greater_than : int, optional Keep streamlines that have length greater than this value (default 50) less_than : int, optional Keep streamlines have length less than this value (default 250) qbx_thr : variable int Thresholds for QuickBundlesX (default [40, 30, 20, 15]) np_pts : int, optional Number of points for discretizing each streamline (default 20) progressive : boolean, optional (default True) rng : RandomState If None creates RandomState in function. 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] (1, 2) Garyfallidis et al. “Robust and efficient linear

registration of white-matter fascicles in the space of streamlines”, NeuroImage, 117, 124–140, 2015 .. [R9eb8c2315518-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.