`direction`¶

`BootDirectionGetter`	Methods
`ClosestPeakDirectionGetter`	A direction getter that returns the closest odf peak to previous tracking direction.
`DeterministicMaximumDirectionGetter`	Return direction of a sphere with the highest probability mass function (pmf).
`EuDXDirectionGetter`	Deterministic Direction Getter based on peak directions.
`InTemporaryDirectory`([suffix, prefix, dir])	Create, return, and change directory to a temporary directory
`PeaksAndMetrics`	Attributes
`ProbabilisticDirectionGetter`	Randomly samples direction of a sphere based on probability mass function (pmf).
`Sphere`([x, y, z, theta, phi, xyz, faces, edges])	Points on the unit sphere.
`repeat`(object [,times])	for the specified number of times.
`Pool`([processes, initializer, initargs, …])	Returns a process pool object
`cpu_count`()	Returns the number of CPUs in the system
`gfa`(samples)	The general fractional anisotropy of a function evaluated on the unit sphere
`local_maxima`	Local maxima of a function evaluated on a discrete set of points.
`ndindex`(shape)	An N-dimensional iterator object to index arrays.
`peak_directions`(odf, sphere[, …])	Get the directions of odf peaks.
`peak_directions_nl`(sphere_eval[, …])	Non Linear Direction Finder.
`peaks_from_model`(model, data, sphere, …[, …])	Fit the model to data and computes peaks and metrics
`remove_similar_vertices`	Remove vertices that are less than theta degrees from any other
`reshape_peaks_for_visualization`(peaks)	Reshape peaks for visualization.
`search_descending`	i in descending array a so a[i] < a[0] * relative_threshold
`sh_to_sf_matrix`(sphere, sh_order[, …])	Matrix that transforms Spherical harmonics (SH) to spherical function (SF).
`warn`	Issue a warning, or maybe ignore it or raise an exception.

Module: `direction.peaks`¶

`EuDXDirectionGetter`	Deterministic Direction Getter based on peak directions.
`InTemporaryDirectory`([suffix, prefix, dir])	Create, return, and change directory to a temporary directory
`PeaksAndMetrics`	Attributes
`Sphere`([x, y, z, theta, phi, xyz, faces, edges])	Points on the unit sphere.
`repeat`(object [,times])	for the specified number of times.
`Pool`([processes, initializer, initargs, …])	Returns a process pool object
`cpu_count`()	Returns the number of CPUs in the system
`gfa`(samples)	The general fractional anisotropy of a function evaluated on the unit sphere
`local_maxima`	Local maxima of a function evaluated on a discrete set of points.
`ndindex`(shape)	An N-dimensional iterator object to index arrays.
`peak_directions`(odf, sphere[, …])	Get the directions of odf peaks.
`peak_directions_nl`(sphere_eval[, …])	Non Linear Direction Finder.
`peaks_from_model`(model, data, sphere, …[, …])	Fit the model to data and computes peaks and metrics
`remove_similar_vertices`	Remove vertices that are less than theta degrees from any other
`reshape_peaks_for_visualization`(peaks)	Reshape peaks for visualization.
`search_descending`	i in descending array a so a[i] < a[0] * relative_threshold
`sh_to_sf_matrix`(sphere, sh_order[, …])	Matrix that transforms Spherical harmonics (SH) to spherical function (SF).
`warn`	Issue a warning, or maybe ignore it or raise an exception.

`BootDirectionGetter`¶

class dipy.direction.BootDirectionGetter¶

Bases: dipy.direction.closest_peak_direction_getter.BaseDirectionGetter

Methods

`from_data`	Create a BootDirectionGetter using HARDI data and an ODF type model
`initial_direction`	Returns best directions at seed location to start tracking.

get_direction

__init__($self, /, *args, **kwargs)¶: Initialize self. See help(type(self)) for accurate signature.

from_data()¶

Create a BootDirectionGetter using HARDI data and an ODF type model

Parameters

datandarray, float, (…, N): Diffusion MRI data with N volumes.
modeldipy diffusion model: Must provide fit with odf method.
max_anglefloat (0, 90): Maximum angle between tract segments. This angle can be more generous (larger) than values typically used with probabilistic direction getters.
sphereSphere: The sphere used to sample the diffusion ODF.
sh_ordereven int: The order of the SH “model” used to estimate bootstrap residuals.
max_attemptsint: Max number of bootstrap samples used to find tracking direction before giving up.
pmf_thresholdfloat: Threshold for ODF functions.
relative_peak_thresholdfloat in [0., 1.]: Relative threshold for excluding ODF peaks.
min_separation_anglefloat in [0, 90]: Angular threshold for excluding ODF peaks.

`ClosestPeakDirectionGetter`¶

class dipy.direction.ClosestPeakDirectionGetter¶

Bases: dipy.direction.closest_peak_direction_getter.PmfGenDirectionGetter

A direction getter that returns the closest odf peak to previous tracking direction.

Methods

`from_pmf`	Constructor for making a DirectionGetter from an array of Pmfs
`from_shcoeff`	Probabilistic direction getter from a distribution of directions on the sphere
`initial_direction`	Returns best directions at seed location to start tracking.

get_direction

__init__($self, /, *args, **kwargs)¶: Initialize self. See help(type(self)) for accurate signature.

`DeterministicMaximumDirectionGetter`¶

class dipy.direction.DeterministicMaximumDirectionGetter¶

Bases: dipy.direction.probabilistic_direction_getter.ProbabilisticDirectionGetter

Return direction of a sphere with the highest probability mass function (pmf).

Methods

`from_pmf`	Constructor for making a DirectionGetter from an array of Pmfs
`from_shcoeff`	Probabilistic direction getter from a distribution of directions on the sphere
`initial_direction`	Returns best directions at seed location to start tracking.

get_direction

__init__($self, /, *args, **kwargs)¶: Initialize self. See help(type(self)) for accurate signature.

`EuDXDirectionGetter`¶

class dipy.direction.EuDXDirectionGetter¶

Bases: dipy.tracking.direction_getter.DirectionGetter

Deterministic Direction Getter based on peak directions.

This class contains the cython portion of the code for PeaksAndMetrics and is not meant to be used on its own.

Attributes

ang_thr
qa_thr
total_weight

Methods

initial_direction

The best starting directions for fiber tracking from point

get_direction

__init__($self, /, *args, **kwargs)¶: Initialize self. See help(type(self)) for accurate signature.

ang_thr¶

initial_direction()¶

The best starting directions for fiber tracking from point

All the valid peaks in the voxel closest to point are returned as initial directions.

qa_thr¶

total_weight¶

`InTemporaryDirectory`¶

class dipy.direction.InTemporaryDirectory(suffix='', prefix='tmp', dir=None)¶

Bases: nibabel.tmpdirs.TemporaryDirectory

Create, return, and change directory to a temporary directory

Examples

>>> import os
>>> my_cwd = os.getcwd()
>>> with InTemporaryDirectory() as tmpdir:
...     _ = open('test.txt', 'wt').write('some text')
...     assert os.path.isfile('test.txt')
...     assert os.path.isfile(os.path.join(tmpdir, 'test.txt'))
>>> os.path.exists(tmpdir)
False
>>> os.getcwd() == my_cwd
True

Methods

cleanup

__init__(suffix='', prefix='tmp', dir=None)¶: Initialize self. See help(type(self)) for accurate signature.

`PeaksAndMetrics`¶

class dipy.direction.PeaksAndMetrics¶

Bases: dipy.reconst.peak_direction_getter.EuDXDirectionGetter

Attributes

ang_thr
qa_thr
total_weight

Methods

initial_direction

The best starting directions for fiber tracking from point

get_direction

__init__($self, /, *args, **kwargs)¶: Initialize self. See help(type(self)) for accurate signature.

`ProbabilisticDirectionGetter`¶

class dipy.direction.ProbabilisticDirectionGetter¶

Bases: dipy.direction.closest_peak_direction_getter.PmfGenDirectionGetter

Randomly samples direction of a sphere based on probability mass function (pmf).

The main constructors for this class are current from_pmf and from_shcoeff. The pmf gives the probability that each direction on the sphere should be chosen as the next direction. To get the true pmf from the “raw pmf” directions more than max_angle degrees from the incoming direction are set to 0 and the result is normalized.

Methods

`from_pmf`	Constructor for making a DirectionGetter from an array of Pmfs
`from_shcoeff`	Probabilistic direction getter from a distribution of directions on the sphere
`initial_direction`	Returns best directions at seed location to start tracking.

get_direction

__init__()¶

Direction getter from a pmf generator.

Parameters

pmf_genPmfGen: Used to get probability mass function for selecting tracking directions.
max_anglefloat, [0, 90]: The maximum allowed angle between incoming direction and new direction.
sphereSphere: The set of directions to be used for tracking.
pmf_thresholdfloat [0., 1.]: Used to remove direction from the probability mass function for selecting the tracking direction.
relative_peak_thresholdfloat in [0., 1.]: Used for extracting initial tracking directions. Passed to peak_directions.
min_separation_anglefloat in [0, 90]: Used for extracting initial tracking directions. Passed to peak_directions.

`Sphere`¶

class dipy.direction.Sphere(x=None, y=None, z=None, theta=None, phi=None, xyz=None, faces=None, edges=None)¶

Bases: object

Points on the unit sphere.

The sphere can be constructed using one of three conventions:

Sphere(x, y, z)
Sphere(xyz=xyz)
Sphere(theta=theta, phi=phi)

Parameters

x, y, z1-D array_like: Vertices as x-y-z coordinates.
theta, phi1-D array_like: Vertices as spherical coordinates. Theta and phi are the inclination and azimuth angles respectively.
xyz(N, 3) ndarray: Vertices as x-y-z coordinates.
faces(N, 3) ndarray: Indices into vertices that form triangular faces. If unspecified, the faces are computed using a Delaunay triangulation.
edges(N, 2) ndarray: Edges between vertices. If unspecified, the edges are derived from the faces.

Attributes

x
y
z

Methods

`find_closest`(xyz)	Find the index of the vertex in the Sphere closest to the input vector
`subdivide`([n])	Subdivides each face of the sphere into four new faces.

edges
faces
vertices

__init__(x=None, y=None, z=None, theta=None, phi=None, xyz=None, faces=None, edges=None)¶: Initialize self. See help(type(self)) for accurate signature.

edges()¶

faces()¶

find_closest(xyz)¶

Find the index of the vertex in the Sphere closest to the input vector

Parameters

xyzarray-like, 3 elements: A unit vector

Returns

idxint: The index into the Sphere.vertices array that gives the closest vertex (in angle).

subdivide(n=1)¶

Subdivides each face of the sphere into four new faces.

New vertices are created at a, b, and c. Then each face [x, y, z] is divided into faces [x, a, c], [y, a, b], [z, b, c], and [a, b, c].

   y
   /               /               a/____
/\    /            /  \  /             /____\/____          x      c     z

Parameters

nint, optional: The number of subdivisions to preform.

Returns

new_sphereSphere: The subdivided sphere.

vertices()¶

property x¶

property y¶

property z¶

`repeat`¶

class dipy.direction.repeat(object[, times]) → create an iterator which returns the object¶

Bases: object

for the specified number of times. If not specified, returns the object endlessly.

__init__($self, /, *args, **kwargs)¶: Initialize self. See help(type(self)) for accurate signature.

Pool¶

dipy.direction.Pool(processes=None, initializer=None, initargs=(), maxtasksperchild=None)¶: Returns a process pool object

cpu_count¶

dipy.direction.cpu_count()¶: Returns the number of CPUs in the system

gfa¶

dipy.direction.gfa(samples)¶

The general fractional anisotropy of a function evaluated on the unit sphere

Parameters

samplesndarray: Values of data on the unit sphere.

Returns

gfandarray: GFA evaluated in each entry of the array, along the last dimension. An np.nan is returned for coordinates that contain all-zeros in samples.

Notes

The GFA is defined as [1]

\sqrt{\frac{n \sum_i{(\Psi_i - <\Psi>)^2}}{(n-1) \sum{\Psi_i ^ 2}}}

Where $\Psi$ is an orientation distribution function sampled discretely on the unit sphere and angle brackets denote average over the samples on the sphere.

1: Quality assessment of High Angular Resolution Diffusion Imaging data using bootstrap on Q-ball reconstruction. J. Cohen Adad, M. Descoteaux, L.L. Wald. JMRI 33: 1194-1208.

local_maxima¶

dipy.direction.local_maxima()¶

Local maxima of a function evaluated on a discrete set of points.

If a function is evaluated on some set of points where each pair of neighboring points is an edge in edges, find the local maxima.

Parameters

odfarray, 1d, dtype=double: The function evaluated on a set of discrete points.
edgesarray (N, 2): The set of neighbor relations between the points. Every edge, ie edges[i, :], is a pair of neighboring points.

Returns

peak_valuesndarray: Value of odf at a maximum point. Peak values is sorted in descending order.
peak_indicesndarray: Indices of maximum points. Sorted in the same order as peak_values so odf[peak_indices[i]] == peak_values[i].

ndindex¶

dipy.direction.ndindex(shape)¶

An N-dimensional iterator object to index arrays.

Given the shape of an array, an ndindex instance iterates over the N-dimensional index of the array. At each iteration a tuple of indices is returned; the last dimension is iterated over first.

Parameters

shapetuple of ints: The dimensions of the array.

Examples

>>> from dipy.core.ndindex import ndindex
>>> shape = (3, 2, 1)
>>> for index in ndindex(shape):
...     print(index)
(0, 0, 0)
(0, 1, 0)
(1, 0, 0)
(1, 1, 0)
(2, 0, 0)
(2, 1, 0)

peak_directions¶

dipy.direction.peak_directions(odf, sphere, relative_peak_threshold=0.5, min_separation_angle=25)¶

Get the directions of odf peaks.

Peaks are defined as points on the odf that are greater than at least one neighbor and greater than or equal to all neighbors. Peaks are sorted in descending order by their values then filtered based on their relative size and spacing on the sphere. An odf may have 0 peaks, for example if the odf is perfectly isotropic.

Parameters

odf1d ndarray: The odf function evaluated on the vertices of sphere
sphereSphere: The Sphere providing discrete directions for evaluation.
relative_peak_thresholdfloat in [0., 1.]: Only peaks greater than min + relative_peak_threshold * scale are kept, where min = max(0, odf.min()) and scale = odf.max() - min.
min_separation_anglefloat in [0, 90]: The minimum distance between directions. If two peaks are too close only the larger of the two is returned.

Returns

directions(N, 3) ndarray: N vertices for sphere, one for each peak
values(N,) ndarray: peak values
indices(N,) ndarray: peak indices of the directions on the sphere

Notes

If the odf has any negative values, they will be clipped to zeros.

peak_directions_nl¶

dipy.direction.peak_directions_nl(sphere_eval, relative_peak_threshold=0.25, min_separation_angle=25, sphere=<dipy.core.sphere.HemiSphere object>, xtol=1e-07)¶

Non Linear Direction Finder.

Parameters

sphere_evalcallable: A function which can be evaluated on a sphere.
relative_peak_thresholdfloat: Only return peaks greater than relative_peak_threshold * m where m is the largest peak.
min_separation_anglefloat in [0, 90]: The minimum distance between directions. If two peaks are too close only the larger of the two is returned.
sphereSphere: A discrete Sphere. The points on the sphere will be used for initial estimate of maximums.
xtolfloat: Relative tolerance for optimization.

Returns

directionsarray (N, 3): Points on the sphere corresponding to N local maxima on the sphere.
valuesarray (N,): Value of sphere_eval at each point on directions.

peaks_from_model¶

dipy.direction.peaks_from_model(model, data, sphere, relative_peak_threshold, min_separation_angle, mask=None, return_odf=False, return_sh=True, gfa_thr=0, normalize_peaks=False, sh_order=8, sh_basis_type=None, npeaks=5, B=None, invB=None, parallel=False, nbr_processes=None)¶

Fit the model to data and computes peaks and metrics

Parameters

modela model instance: model will be used to fit the data.
sphereSphere: The Sphere providing discrete directions for evaluation.
relative_peak_thresholdfloat: Only return peaks greater than relative_peak_threshold * m where m is the largest peak.
min_separation_anglefloat in [0, 90] The minimum distance between: directions. If two peaks are too close only the larger of the two is returned.
maskarray, optional: If mask is provided, voxels that are False in mask are skipped and no peaks are returned.
return_odfbool: If True, the odfs are returned.
return_shbool: If True, the odf as spherical harmonics coefficients is returned
gfa_thrfloat: Voxels with gfa less than gfa_thr are skipped, no peaks are returned.
normalize_peaksbool: If true, all peak values are calculated relative to max(odf).
sh_orderint, optional: Maximum SH order in the SH fit. For sh_order, there will be (sh_order + 1) * (sh_order + 2) / 2 SH coefficients (default 8).
sh_basis_type{None, ‘tournier07’, ‘descoteaux07’}: None for the default DIPY basis, tournier07 for the Tournier 2007 [2] basis, and descoteaux07 for the Descoteaux 2007 [1] basis (None defaults to descoteaux07).
sh_smoothfloat, optional: Lambda-regularization in the SH fit (default 0.0).
npeaksint: Maximum number of peaks found (default 5 peaks).
Bndarray, optional: Matrix that transforms spherical harmonics to spherical function sf = np.dot(sh, B).
invBndarray, optional: Inverse of B.
parallel: bool: If True, use multiprocessing to compute peaks and metric (default False). Temporary files are saved in the default temporary directory of the system. It can be changed using import tempfile and tempfile.tempdir = '/path/to/tempdir'.
nbr_processes: int: If parallel is True, the number of subprocesses to use (default multiprocessing.cpu_count()).

Returns

pamPeaksAndMetrics: An object with gfa, peak_directions, peak_values, peak_indices, odf, shm_coeffs as attributes

References

1(1,2): Descoteaux, M., Angelino, E., Fitzgibbons, S. and Deriche, R. Regularized, Fast, and Robust Analytical Q-ball Imaging. Magn. Reson. Med. 2007;58:497-510.
2(1,2): Tournier J.D., Calamante F. and Connelly A. Robust determination of the fibre orientation distribution in diffusion MRI: Non-negativity constrained super-resolved spherical deconvolution. NeuroImage. 2007;35(4):1459-1472.

remove_similar_vertices¶

dipy.direction.remove_similar_vertices()¶

Remove vertices that are less than theta degrees from any other

Returns vertices that are at least theta degrees from any other vertex. Vertex v and -v are considered the same so if v and -v are both in vertices only one is kept. Also if v and w are both in vertices, w must be separated by theta degrees from both v and -v to be unique.

Parameters

vertices(N, 3) ndarray: N unit vectors.
thetafloat: The minimum separation between vertices in degrees.
return_mapping{False, True}, optional: If True, return mapping as well as vertices and maybe indices (see below).
return_indices{False, True}, optional: If True, return indices as well as vertices and maybe mapping (see below).

Returns

unique_vertices(M, 3) ndarray: Vertices sufficiently separated from one another.
mapping(N,) ndarray: For each element vertices[i] ($i \in 0..N-1$), the index $j$ to a vertex in unique_vertices that is less than theta degrees from vertices[i]. Only returned if return_mapping is True.
indices(N,) ndarray: indices gives the reverse of mapping. For each element unique_vertices[j] ($j \in 0..M-1$), the index $i$ to a vertex in vertices that is less than theta degrees from unique_vertices[j]. If there is more than one element of vertices that is less than theta degrees from unique_vertices[j], return the first (lowest index) matching value. Only return if return_indices is True.

reshape_peaks_for_visualization¶

dipy.direction.reshape_peaks_for_visualization(peaks)¶

Reshape peaks for visualization.

Reshape and convert to float32 a set of peaks for visualisation with mrtrix or the fibernavigator.

Parameters

peaks: nd array (…, N, 3) or PeaksAndMetrics object: The peaks to be reshaped and converted to float32.

Returns

peaksnd array (…, 3*N)

search_descending¶

dipy.direction.search_descending()¶

i in descending array a so a[i] < a[0] * relative_threshold

Call T = a[0] * relative_threshold. Return value i will be the smallest index in the descending array a such that a[i] < T. Equivalently, i will be the largest index such that all(a[:i] >= T). If all values in a are >= T, return the length of array a.

Parameters

andarray, ndim=1, c-contiguous: Array to be searched. We assume a is in descending order.
relative_thresholdfloat: Applied threshold will be T with T = a[0] * relative_threshold.

Returns

inp.intp: If T = a[0] * relative_threshold then i will be the largest index such that all(a[:i] >= T). If all values in a are >= T then i will be len(a).

Examples

>>> a = np.arange(10, 0, -1, dtype=float)
>>> a
array([ 10.,   9.,   8.,   7.,   6.,   5.,   4.,   3.,   2.,   1.])
>>> search_descending(a, 0.5)
6
>>> a < 10 * 0.5
array([False, False, False, False, False, False,  True,  True,  True,  True], dtype=bool)
>>> search_descending(a, 1)
1
>>> search_descending(a, 2)
0
>>> search_descending(a, 0)
10

sh_to_sf_matrix¶

dipy.direction.sh_to_sf_matrix(sphere, sh_order, basis_type=None, return_inv=True, smooth=0)¶

Matrix that transforms Spherical harmonics (SH) to spherical function (SF).

Parameters

sphereSphere: The points on which to sample the spherical function.
sh_orderint, optional: Maximum SH order in the SH fit. For sh_order, there will be (sh_order + 1) * (sh_order_2) / 2 SH coefficients (default 4).
basis_type{None, ‘tournier07’, ‘descoteaux07’}: None for the default DIPY basis, tournier07 for the Tournier 2007 [2] basis, and descoteaux07 for the Descoteaux 2007 [1] basis (None defaults to descoteaux07).
return_invbool: If True then the inverse of the matrix is also returned
smoothfloat, optional: Lambda-regularization in the SH fit (default 0.0).

Returns

Bndarray: Matrix that transforms spherical harmonics to spherical function sf = np.dot(sh, B).
invBndarray: Inverse of B.

References

1(1,2): Descoteaux, M., Angelino, E., Fitzgibbons, S. and Deriche, R. Regularized, Fast, and Robust Analytical Q-ball Imaging. Magn. Reson. Med. 2007;58:497-510.
2(1,2): Tournier J.D., Calamante F. and Connelly A. Robust determination of the fibre orientation distribution in diffusion MRI: Non-negativity constrained super-resolved spherical deconvolution. NeuroImage. 2007;35(4):1459-1472.

warn¶

dipy.direction.warn()¶: Issue a warning, or maybe ignore it or raise an exception.

`EuDXDirectionGetter`¶

class dipy.direction.peaks.EuDXDirectionGetter¶

Bases: dipy.tracking.direction_getter.DirectionGetter

Deterministic Direction Getter based on peak directions.

This class contains the cython portion of the code for PeaksAndMetrics and is not meant to be used on its own.

Attributes

ang_thr
qa_thr
total_weight

Methods

initial_direction

The best starting directions for fiber tracking from point

get_direction

__init__($self, /, *args, **kwargs)¶: Initialize self. See help(type(self)) for accurate signature.

ang_thr¶

initial_direction()¶

The best starting directions for fiber tracking from point

All the valid peaks in the voxel closest to point are returned as initial directions.

qa_thr¶

total_weight¶

`InTemporaryDirectory`¶

class dipy.direction.peaks.InTemporaryDirectory(suffix='', prefix='tmp', dir=None)¶

Bases: nibabel.tmpdirs.TemporaryDirectory

Create, return, and change directory to a temporary directory

Examples

>>> import os
>>> my_cwd = os.getcwd()
>>> with InTemporaryDirectory() as tmpdir:
...     _ = open('test.txt', 'wt').write('some text')
...     assert os.path.isfile('test.txt')
...     assert os.path.isfile(os.path.join(tmpdir, 'test.txt'))
>>> os.path.exists(tmpdir)
False
>>> os.getcwd() == my_cwd
True

Methods

cleanup

__init__(suffix='', prefix='tmp', dir=None)¶: Initialize self. See help(type(self)) for accurate signature.

`PeaksAndMetrics`¶

class dipy.direction.peaks.PeaksAndMetrics¶

Bases: dipy.reconst.peak_direction_getter.EuDXDirectionGetter

Attributes

ang_thr
qa_thr
total_weight

Methods

initial_direction

The best starting directions for fiber tracking from point

get_direction

__init__($self, /, *args, **kwargs)¶: Initialize self. See help(type(self)) for accurate signature.

`Sphere`¶

class dipy.direction.peaks.Sphere(x=None, y=None, z=None, theta=None, phi=None, xyz=None, faces=None, edges=None)¶

Bases: object

Points on the unit sphere.

The sphere can be constructed using one of three conventions:

Sphere(x, y, z)
Sphere(xyz=xyz)
Sphere(theta=theta, phi=phi)

Parameters

x, y, z1-D array_like: Vertices as x-y-z coordinates.
theta, phi1-D array_like: Vertices as spherical coordinates. Theta and phi are the inclination and azimuth angles respectively.
xyz(N, 3) ndarray: Vertices as x-y-z coordinates.
faces(N, 3) ndarray: Indices into vertices that form triangular faces. If unspecified, the faces are computed using a Delaunay triangulation.
edges(N, 2) ndarray: Edges between vertices. If unspecified, the edges are derived from the faces.

Attributes

x
y
z

Methods

`find_closest`(xyz)	Find the index of the vertex in the Sphere closest to the input vector
`subdivide`([n])	Subdivides each face of the sphere into four new faces.

edges
faces
vertices

__init__(x=None, y=None, z=None, theta=None, phi=None, xyz=None, faces=None, edges=None)¶: Initialize self. See help(type(self)) for accurate signature.

edges()¶

faces()¶

find_closest(xyz)¶

Find the index of the vertex in the Sphere closest to the input vector

Parameters

xyzarray-like, 3 elements: A unit vector

Returns

idxint: The index into the Sphere.vertices array that gives the closest vertex (in angle).

subdivide(n=1)¶

Subdivides each face of the sphere into four new faces.

New vertices are created at a, b, and c. Then each face [x, y, z] is divided into faces [x, a, c], [y, a, b], [z, b, c], and [a, b, c].

   y
   /               /               a/____
/\    /            /  \  /             /____\/____          x      c     z

Parameters

nint, optional: The number of subdivisions to preform.

Returns

new_sphereSphere: The subdivided sphere.

vertices()¶

property x¶

property y¶

property z¶

`repeat`¶

class dipy.direction.peaks.repeat(object[, times]) → create an iterator which returns the object¶

Bases: object

for the specified number of times. If not specified, returns the object endlessly.

__init__($self, /, *args, **kwargs)¶: Initialize self. See help(type(self)) for accurate signature.

Pool¶

dipy.direction.peaks.Pool(processes=None, initializer=None, initargs=(), maxtasksperchild=None)¶: Returns a process pool object

cpu_count¶

dipy.direction.peaks.cpu_count()¶: Returns the number of CPUs in the system

gfa¶

dipy.direction.peaks.gfa(samples)¶

The general fractional anisotropy of a function evaluated on the unit sphere

Parameters

samplesndarray: Values of data on the unit sphere.

Returns

gfandarray: GFA evaluated in each entry of the array, along the last dimension. An np.nan is returned for coordinates that contain all-zeros in samples.

Notes

The GFA is defined as [1]

\sqrt{\frac{n \sum_i{(\Psi_i - <\Psi>)^2}}{(n-1) \sum{\Psi_i ^ 2}}}

Where $\Psi$ is an orientation distribution function sampled discretely on the unit sphere and angle brackets denote average over the samples on the sphere.

1: Quality assessment of High Angular Resolution Diffusion Imaging data using bootstrap on Q-ball reconstruction. J. Cohen Adad, M. Descoteaux, L.L. Wald. JMRI 33: 1194-1208.

local_maxima¶

dipy.direction.peaks.local_maxima()¶

Local maxima of a function evaluated on a discrete set of points.

If a function is evaluated on some set of points where each pair of neighboring points is an edge in edges, find the local maxima.

Parameters

odfarray, 1d, dtype=double: The function evaluated on a set of discrete points.
edgesarray (N, 2): The set of neighbor relations between the points. Every edge, ie edges[i, :], is a pair of neighboring points.

Returns

peak_valuesndarray: Value of odf at a maximum point. Peak values is sorted in descending order.
peak_indicesndarray: Indices of maximum points. Sorted in the same order as peak_values so odf[peak_indices[i]] == peak_values[i].

ndindex¶

dipy.direction.peaks.ndindex(shape)¶

An N-dimensional iterator object to index arrays.

Given the shape of an array, an ndindex instance iterates over the N-dimensional index of the array. At each iteration a tuple of indices is returned; the last dimension is iterated over first.

Parameters

shapetuple of ints: The dimensions of the array.

Examples

>>> from dipy.core.ndindex import ndindex
>>> shape = (3, 2, 1)
>>> for index in ndindex(shape):
...     print(index)
(0, 0, 0)
(0, 1, 0)
(1, 0, 0)
(1, 1, 0)
(2, 0, 0)
(2, 1, 0)

peak_directions¶

dipy.direction.peaks.peak_directions(odf, sphere, relative_peak_threshold=0.5, min_separation_angle=25)¶

Get the directions of odf peaks.

Parameters

odf1d ndarray: The odf function evaluated on the vertices of sphere
sphereSphere: The Sphere providing discrete directions for evaluation.
relative_peak_thresholdfloat in [0., 1.]: Only peaks greater than min + relative_peak_threshold * scale are kept, where min = max(0, odf.min()) and scale = odf.max() - min.
min_separation_anglefloat in [0, 90]: The minimum distance between directions. If two peaks are too close only the larger of the two is returned.

Returns

directions(N, 3) ndarray: N vertices for sphere, one for each peak
values(N,) ndarray: peak values
indices(N,) ndarray: peak indices of the directions on the sphere

Notes

If the odf has any negative values, they will be clipped to zeros.

peak_directions_nl¶

dipy.direction.peaks.peak_directions_nl(sphere_eval, relative_peak_threshold=0.25, min_separation_angle=25, sphere=<dipy.core.sphere.HemiSphere object>, xtol=1e-07)¶

Non Linear Direction Finder.

Parameters

sphere_evalcallable: A function which can be evaluated on a sphere.
relative_peak_thresholdfloat: Only return peaks greater than relative_peak_threshold * m where m is the largest peak.
min_separation_anglefloat in [0, 90]: The minimum distance between directions. If two peaks are too close only the larger of the two is returned.
sphereSphere: A discrete Sphere. The points on the sphere will be used for initial estimate of maximums.
xtolfloat: Relative tolerance for optimization.

Returns

directionsarray (N, 3): Points on the sphere corresponding to N local maxima on the sphere.
valuesarray (N,): Value of sphere_eval at each point on directions.

peaks_from_model¶

dipy.direction.peaks.peaks_from_model(model, data, sphere, relative_peak_threshold, min_separation_angle, mask=None, return_odf=False, return_sh=True, gfa_thr=0, normalize_peaks=False, sh_order=8, sh_basis_type=None, npeaks=5, B=None, invB=None, parallel=False, nbr_processes=None)¶

Fit the model to data and computes peaks and metrics

Parameters

modela model instance: model will be used to fit the data.
sphereSphere: The Sphere providing discrete directions for evaluation.
relative_peak_thresholdfloat: Only return peaks greater than relative_peak_threshold * m where m is the largest peak.
min_separation_anglefloat in [0, 90] The minimum distance between: directions. If two peaks are too close only the larger of the two is returned.
maskarray, optional: If mask is provided, voxels that are False in mask are skipped and no peaks are returned.
return_odfbool: If True, the odfs are returned.
return_shbool: If True, the odf as spherical harmonics coefficients is returned
gfa_thrfloat: Voxels with gfa less than gfa_thr are skipped, no peaks are returned.
normalize_peaksbool: If true, all peak values are calculated relative to max(odf).
sh_orderint, optional: Maximum SH order in the SH fit. For sh_order, there will be (sh_order + 1) * (sh_order + 2) / 2 SH coefficients (default 8).
sh_basis_type{None, ‘tournier07’, ‘descoteaux07’}: None for the default DIPY basis, tournier07 for the Tournier 2007 [2] basis, and descoteaux07 for the Descoteaux 2007 [1] basis (None defaults to descoteaux07).
sh_smoothfloat, optional: Lambda-regularization in the SH fit (default 0.0).
npeaksint: Maximum number of peaks found (default 5 peaks).
Bndarray, optional: Matrix that transforms spherical harmonics to spherical function sf = np.dot(sh, B).
invBndarray, optional: Inverse of B.
parallel: bool: If True, use multiprocessing to compute peaks and metric (default False). Temporary files are saved in the default temporary directory of the system. It can be changed using import tempfile and tempfile.tempdir = '/path/to/tempdir'.
nbr_processes: int: If parallel is True, the number of subprocesses to use (default multiprocessing.cpu_count()).

Returns

pamPeaksAndMetrics: An object with gfa, peak_directions, peak_values, peak_indices, odf, shm_coeffs as attributes

References

1(1,2): Descoteaux, M., Angelino, E., Fitzgibbons, S. and Deriche, R. Regularized, Fast, and Robust Analytical Q-ball Imaging. Magn. Reson. Med. 2007;58:497-510.
2(1,2): Tournier J.D., Calamante F. and Connelly A. Robust determination of the fibre orientation distribution in diffusion MRI: Non-negativity constrained super-resolved spherical deconvolution. NeuroImage. 2007;35(4):1459-1472.

remove_similar_vertices¶

dipy.direction.peaks.remove_similar_vertices()¶

Remove vertices that are less than theta degrees from any other

Parameters

vertices(N, 3) ndarray: N unit vectors.
thetafloat: The minimum separation between vertices in degrees.
return_mapping{False, True}, optional: If True, return mapping as well as vertices and maybe indices (see below).
return_indices{False, True}, optional: If True, return indices as well as vertices and maybe mapping (see below).

Returns

unique_vertices(M, 3) ndarray: Vertices sufficiently separated from one another.
mapping(N,) ndarray: For each element vertices[i] ($i \in 0..N-1$), the index $j$ to a vertex in unique_vertices that is less than theta degrees from vertices[i]. Only returned if return_mapping is True.
indices(N,) ndarray: indices gives the reverse of mapping. For each element unique_vertices[j] ($j \in 0..M-1$), the index $i$ to a vertex in vertices that is less than theta degrees from unique_vertices[j]. If there is more than one element of vertices that is less than theta degrees from unique_vertices[j], return the first (lowest index) matching value. Only return if return_indices is True.

reshape_peaks_for_visualization¶

dipy.direction.peaks.reshape_peaks_for_visualization(peaks)¶

Reshape peaks for visualization.

Reshape and convert to float32 a set of peaks for visualisation with mrtrix or the fibernavigator.

Parameters

peaks: nd array (…, N, 3) or PeaksAndMetrics object: The peaks to be reshaped and converted to float32.

Returns

peaksnd array (…, 3*N)

search_descending¶

dipy.direction.peaks.search_descending()¶

i in descending array a so a[i] < a[0] * relative_threshold

Parameters

andarray, ndim=1, c-contiguous: Array to be searched. We assume a is in descending order.
relative_thresholdfloat: Applied threshold will be T with T = a[0] * relative_threshold.

Returns

inp.intp: If T = a[0] * relative_threshold then i will be the largest index such that all(a[:i] >= T). If all values in a are >= T then i will be len(a).

Examples

>>> a = np.arange(10, 0, -1, dtype=float)
>>> a
array([ 10.,   9.,   8.,   7.,   6.,   5.,   4.,   3.,   2.,   1.])
>>> search_descending(a, 0.5)
6
>>> a < 10 * 0.5
array([False, False, False, False, False, False,  True,  True,  True,  True], dtype=bool)
>>> search_descending(a, 1)
1
>>> search_descending(a, 2)
0
>>> search_descending(a, 0)
10

sh_to_sf_matrix¶

dipy.direction.peaks.sh_to_sf_matrix(sphere, sh_order, basis_type=None, return_inv=True, smooth=0)¶

Matrix that transforms Spherical harmonics (SH) to spherical function (SF).

Parameters

sphereSphere: The points on which to sample the spherical function.
sh_orderint, optional: Maximum SH order in the SH fit. For sh_order, there will be (sh_order + 1) * (sh_order_2) / 2 SH coefficients (default 4).
basis_type{None, ‘tournier07’, ‘descoteaux07’}: None for the default DIPY basis, tournier07 for the Tournier 2007 [2] basis, and descoteaux07 for the Descoteaux 2007 [1] basis (None defaults to descoteaux07).
return_invbool: If True then the inverse of the matrix is also returned
smoothfloat, optional: Lambda-regularization in the SH fit (default 0.0).

Returns

Bndarray: Matrix that transforms spherical harmonics to spherical function sf = np.dot(sh, B).
invBndarray: Inverse of B.

References

1(1,2): Descoteaux, M., Angelino, E., Fitzgibbons, S. and Deriche, R. Regularized, Fast, and Robust Analytical Q-ball Imaging. Magn. Reson. Med. 2007;58:497-510.
2(1,2): Tournier J.D., Calamante F. and Connelly A. Robust determination of the fibre orientation distribution in diffusion MRI: Non-negativity constrained super-resolved spherical deconvolution. NeuroImage. 2007;35(4):1459-1472.

warn¶

dipy.direction.peaks.warn()¶: Issue a warning, or maybe ignore it or raise an exception.

direction¶

Module: direction.peaks¶

Pool¶

cpu_count¶

gfa¶

local_maxima¶

ndindex¶

peak_directions¶

peak_directions_nl¶

peaks_from_model¶

remove_similar_vertices¶

reshape_peaks_for_visualization¶

search_descending¶

sh_to_sf_matrix¶

warn¶

Pool¶

cpu_count¶

gfa¶

local_maxima¶

ndindex¶

peak_directions¶

peak_directions_nl¶

peaks_from_model¶

remove_similar_vertices¶

reshape_peaks_for_visualization¶

search_descending¶

sh_to_sf_matrix¶

warn¶

`direction`¶

Module: `direction.peaks`¶