direction
direction.bootstrap_direction_getter
direction.closest_peak_direction_getter
direction.peaks
direction.pmf
direction.probabilistic_direction_getter
BootDirectionGetter
ClosestPeakDirectionGetter
DeterministicMaximumDirectionGetter
EuDXDirectionGetter
InTemporaryDirectory
PeaksAndMetrics
ProbabilisticDirectionGetter
Sphere
repeat
BootDirectionGetter
BootPmfGen
BaseDirectionGetter
BasePmfDirectionGetter
ClosestPeakDirectionGetter
PmfGenDirectionGetter
EuDXDirectionGetter
InTemporaryDirectory
PeaksAndMetrics
Sphere
repeat
BootPmfGen
PmfGen
SHCoeffPmfGen
SimplePmfGen
DeterministicMaximumDirectionGetter
ProbabilisticDirectionGetter
direction
Methods 

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

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

Deterministic Direction Getter based on peak directions. 


Create, return, and change directory to a temporary directory 


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


Points on the unit sphere. 

for the specified number of times. 

Returns a process pool object 

Deprecate a renamed or removed function argument. 

Determine the effective number of processes for parallelization. 

The general fractional anisotropy of a function evaluated on the unit sphere 
Local maxima of a function evaluated on a discrete set of points. 


An Ndimensional iterator object to index arrays. 

Get the directions of odf peaks. 

Non Linear Direction Finder. 

Fit the model to data and computes peaks and metrics 
Remove vertices that are less than theta degrees from any other 

Reshape peaks for visualization. 

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


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

Methods 
direction.closest_peak_direction_getter
Methods 

A base class for dynamic direction getters 

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

A base class for direction getter using a pmf 


Get the directions of odf peaks. 
direction.peaks
Deterministic Direction Getter based on peak directions. 


Create, return, and change directory to a temporary directory 



Points on the unit sphere. 

for the specified number of times. 

Returns a process pool object 

Deprecate a renamed or removed function argument. 

Determine the effective number of processes for parallelization. 

The general fractional anisotropy of a function evaluated on the unit sphere 
Local maxima of a function evaluated on a discrete set of points. 


An Ndimensional iterator object to index arrays. 

Get the directions of odf peaks. 

Non Linear Direction Finder. 

Fit the model to data and computes peaks and metrics 
Remove vertices that are less than theta degrees from any other 

Reshape peaks for visualization. 

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


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

Methods 

Methods 

Methods 


Return angles for Cartesian 3D coordinates x, y, and z 
direction.probabilistic_direction_getter
Implementation of a probabilistic direction getter based on sampling from discrete distribution (pmf) at each step of the tracking.
Return direction of a sphere with the highest probability mass function (pmf). 

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


Get the directions of odf peaks. 

BootDirectionGetter
Bases: dipy.direction.closest_peak_direction_getter.BasePmfDirectionGetter
Methods
Create a BootDirectionGetter using HARDI data and an ODF type model 


Returns best directions at seed location to start tracking. 
generate_streamline 

get_direction 
Create a BootDirectionGetter using HARDI data and an ODF type model
Diffusion MRI data with N volumes.
Must provide fit with odf method.
Maximum angle between tract segments. This angle can be more generous (larger) than values typically used with probabilistic direction getters.
The sphere used to sample the diffusion ODF.
The order of the SH “model” used to estimate bootstrap residuals.
Max number of bootstrap samples used to find tracking direction before giving up.
Threshold for ODF functions.
Relative threshold for excluding ODF peaks.
Angular threshold for excluding ODF peaks.
ClosestPeakDirectionGetter
Bases: dipy.direction.closest_peak_direction_getter.PmfGenDirectionGetter
A direction getter that returns the closest odf peak to previous tracking direction.
Methods

Constructor for making a DirectionGetter from an array of Pmfs 

Probabilistic direction getter from a distribution of directions on the sphere 

Returns best directions at seed location to start tracking. 
generate_streamline 

get_direction 
DeterministicMaximumDirectionGetter
Bases: dipy.direction.probabilistic_direction_getter.ProbabilisticDirectionGetter
Return direction of a sphere with the highest probability mass function (pmf).
Methods

Constructor for making a DirectionGetter from an array of Pmfs 

Probabilistic direction getter from a distribution of directions on the sphere 

Returns best directions at seed location to start tracking. 
generate_streamline 

get_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.
Methods
The best starting directions for fiber tracking from point 
generate_streamline 

get_direction 
InTemporaryDirectory
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 
PeaksAndMetrics
Bases: dipy.reconst.eudx_direction_getter.EuDXDirectionGetter
Methods

The best starting directions for fiber tracking from point 
generate_streamline 

get_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

Constructor for making a DirectionGetter from an array of Pmfs 

Probabilistic direction getter from a distribution of directions on the sphere 

Returns best directions at seed location to start tracking. 
generate_streamline 

get_direction 
Direction getter from a pmf generator.
Used to get probability mass function for selecting tracking directions.
The maximum allowed angle between incoming direction and new direction.
The set of directions to be used for tracking.
Used to remove direction from the probability mass function for selecting the tracking direction.
Used for extracting initial tracking directions. Passed to peak_directions.
Used for extracting initial tracking directions. Passed to peak_directions.
See also
Sphere
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)
Vertices as xyz coordinates.
Vertices as spherical coordinates. Theta and phi are the inclination and azimuth angles respectively.
Vertices as xyz coordinates.
Indices into vertices that form triangular faces. If unspecified, the faces are computed using a Delaunay triangulation.
Edges between vertices. If unspecified, the edges are derived from the faces.
Methods

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

Subdivides each face of the sphere into four new faces. 
edges 

faces 

vertices 
Find the index of the vertex in the Sphere closest to the input vector
A unit vector
The index into the Sphere.vertices array that gives the closest vertex (in angle).
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/____\b
/\ /\
/ \ / \
/____\/____\
x c z
The number of subdivisions to preform.
The subdivided sphere.
repeat
Bases: object
for the specified number of times. If not specified, returns the object endlessly.
Deprecate a renamed or removed function argument.
The decorator assumes that the argument with the old_name
was removed
from the function signature and the new_name
replaced it at the
same position in the signature. If the old_name
argument is
given when calling the decorated function the decorator will catch it and
issue a deprecation warning and pass it on as new_name
argument.
The old name of the argument.
None
, optionalThe new name of the argument. Set this to None to remove the
argument old_name
instead of renaming it.
The release at which the old argument became deprecated.
Last released version at which this function will still raise a deprecation warning. Versions higher than this will raise an error.
Callable accepting string as argument, and return 1 if string
represents a higher version than encoded in the version_comparator
,
0 if the version is equal, and 1 if the version is lower. For example,
the version_comparator
may compare the input version string to the
current package version string.
If the argument is not a named argument (for example it
was meant to be consumed by **kwargs
) set this to
True
. Otherwise the decorator will throw an Exception
if the new_name
cannot be found in the signature of
the decorated function.
Default is False
.
Warning to be issued.
Error to be issued
An alternative function or class name that the user may use in
place of the deprecated object if new_name
is None. The deprecation
warning will tell the user about this alternative if provided.
If the new argument name cannot be found in the function
signature and arg_in_kwargs was False or if it is used to
deprecate the name of the *args
, **kwargs
like arguments.
At runtime such an Error is raised if both the new_name
and old_name were specified when calling the function and
“relax=False”.
Notes
This function is based on the Astropy (major modification). https://github.com/astropy/astropy. See COPYING file distributed along with the astropy package for the copyright and license terms.
Examples
The deprecation warnings are not shown in the following examples. To deprecate a positional or keyword argument:: >>> from dipy.utils.deprecator import deprecated_params >>> @deprecated_params(‘sig’, ‘sigma’, ‘0.3’) … def test(sigma): … return sigma >>> test(2) 2 >>> test(sigma=2) 2 >>> test(sig=2) # doctest: +SKIP 2
It is also possible to replace multiple arguments. The old_name
,
new_name
and since
have to be tuple or list and contain the
same number of entries::
>>> @deprecated_params([‘a’, ‘b’], [‘alpha’, ‘beta’],
… [‘0.2’, 0.4])
… def test(alpha, beta):
… return alpha, beta
>>> test(a=2, b=3) # doctest: +SKIP
(2, 3)
Determine the effective number of processes for parallelization.
For num_processes = None` return the maximum number of cores retrieved
by cpu_count().
For num_processes > 0
, return this value.
For num_processes < 0
, return the maximal number of cores minus
num_processes + 1
. In particular num_processes = 1
will use as
many cores as possible.
For num_processes = 0
a ValueError is raised.
Desired number of processes to be used.
The general fractional anisotropy of a function evaluated on the unit sphere
Values of data on the unit sphere.
GFA evaluated in each entry of the array, along the last dimension. An np.nan is returned for coordinates that contain allzeros in samples.
Notes
The GFA is defined as [1]
\sqrt{\frac{n \sum_i{(\Psi_i  <\Psi>)^2}}{(n1) \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.
Quality assessment of High Angular Resolution Diffusion Imaging data using bootstrap on Qball reconstruction. J. Cohen Adad, M. Descoteaux, L.L. Wald. JMRI 33: 11941208.
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.
The function evaluated on a set of discrete points.
The set of neighbor relations between the points. Every edge, ie edges[i, :], is a pair of neighboring points.
Value of odf at a maximum point. Peak values is sorted in descending order.
Indices of maximum points. Sorted in the same order as peak_values so odf[peak_indices[i]] == peak_values[i].
See also
Notes
A point is a local maximum if it is > at least one neighbor and >= all neighbors. If no points meet the above criteria, 1 maximum is returned such that odf[maximum] == max(odf).
An Ndimensional iterator object to index arrays.
Given the shape of an array, an ndindex instance iterates over the Ndimensional index of the array. At each iteration a tuple of indices is returned; the last dimension is iterated over first.
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)
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.
The odf function evaluated on the vertices of sphere
The Sphere providing discrete directions for evaluation.
Only peaks greater than min + relative_peak_threshold * scale
are
kept, where min = max(0, odf.min())
and
scale = odf.max()  min
.
The minimum distance between directions. If two peaks are too close only the larger of the two is returned.
N vertices for sphere, one for each peak
peak values
peak indices of the directions on the sphere
Notes
If the odf has any negative values, they will be clipped to zeros.
Non Linear Direction Finder.
A function which can be evaluated on a sphere.
Only return peaks greater than relative_peak_threshold * m
where m
is the largest peak.
The minimum distance between directions. If two peaks are too close only the larger of the two is returned.
A discrete Sphere. The points on the sphere will be used for initial estimate of maximums.
Relative tolerance for optimization.
Points on the sphere corresponding to N local maxima on the sphere.
Value of sphere_eval at each point on directions.
Fit the model to data and computes peaks and metrics
model will be used to fit the data.
Diffusion data.
The Sphere providing discrete directions for evaluation.
Only return peaks greater than relative_peak_threshold * m
where m
is the largest peak.
directions. If two peaks are too close only the larger of the two is returned.
If mask is provided, voxels that are False in mask are skipped and no peaks are returned.
If True, the odfs are returned.
If True, the odf as spherical harmonics coefficients is returned
Voxels with gfa less than gfa_thr are skipped, no peaks are returned.
If true, all peak values are calculated relative to max(odf).
Maximum SH order in the SH fit. For sh_order, there will be
(sh_order + 1) * (sh_order + 2) / 2
SH coefficients (default 8).
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
).
Maximum number of peaks found (default 5 peaks).
Matrix that transforms spherical harmonics to spherical function
sf = np.dot(sh, B)
.
Inverse of B.
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'
.
If parallel is True, the number of subprocesses to use
(default multiprocessing.cpu_count()). If < 0 the maximal number of
cores minus num_processes + 1
is used (enter 1 to use as many
cores as possible). 0 raises an error.
An object with gfa
, peak_directions
, peak_values
,
peak_indices
, odf
, shm_coeffs
as attributes
References
Descoteaux, M., Angelino, E., Fitzgibbons, S. and Deriche, R. Regularized, Fast, and Robust Analytical Qball Imaging. Magn. Reson. Med. 2007;58:497510.
Tournier J.D., Calamante F. and Connelly A. Robust determination of the fibre orientation distribution in diffusion MRI: Nonnegativity constrained superresolved spherical deconvolution. NeuroImage. 2007;35(4):14591472.
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.
N unit vectors.
The minimum separation between vertices in degrees.
If True, return mapping as well as vertices and maybe indices (see below).
If True, return indices as well as vertices and maybe mapping (see below).
Vertices sufficiently separated from one another.
For each element vertices[i]
(\(i \in 0..N1\)), 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 gives the reverse of mapping. For each element
unique_vertices[j]
(\(j \in 0..M1\)), 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.
Reshape and convert to float32 a set of peaks for visualisation with mrtrix or the fibernavigator.
The peaks to be reshaped and converted to float32.
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.
Array to be searched. We assume a is in descending order.
Applied threshold will be T
with T = a[0] * relative_threshold
.
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
Matrix that transforms Spherical harmonics (SH) to spherical function (SF).
The points on which to sample the spherical function.
Maximum SH order in the SH fit. For sh_order
, there will be
(sh_order + 1) * (sh_order + 2) / 2
SH coefficients for a symmetric
basis and (sh_order + 1) * (sh_order + 1)
coefficients for a full
SH basis.
None
for the default DIPY basis,
tournier07
for the Tournier 2007 [R0296267dba6e2]_[R0296267dba6e3]_ basis,
descoteaux07
for the Descoteaux 2007 [1] basis,
(None
defaults to descoteaux07
).
If True, uses a SH basis containing even and odd order SH functions. Else, uses a SH basis consisting only of even order SH functions.
True to use a legacy basis definition for backward compatibility
with previous tournier07
and descoteaux07
implementations.
If True then the inverse of the matrix is also returned.
Lambdaregularization in the SH fit.
Matrix that transforms spherical harmonics to spherical function
sf = np.dot(sh, B)
.
Inverse of B.
References
Descoteaux, M., Angelino, E., Fitzgibbons, S. and Deriche, R. Regularized, Fast, and Robust Analytical Qball Imaging. Magn. Reson. Med. 2007;58:497510.
Tournier J.D., Calamante F. and Connelly A. Robust determination of the fibre orientation distribution in diffusion MRI: Nonnegativity constrained superresolved spherical deconvolution. NeuroImage. 2007;35(4):14591472.
Tournier JD, Smith R, Raffelt D, Tabbara R, Dhollander T, Pietsch M, et al. MRtrix3: A fast, flexible and open software framework for medical image processing and visualisation. NeuroImage. 2019 Nov 15;202:116137.
BootDirectionGetter
Bases: dipy.direction.closest_peak_direction_getter.BasePmfDirectionGetter
Methods
Create a BootDirectionGetter using HARDI data and an ODF type model 


Returns best directions at seed location to start tracking. 
generate_streamline 

get_direction 
Create a BootDirectionGetter using HARDI data and an ODF type model
Diffusion MRI data with N volumes.
Must provide fit with odf method.
Maximum angle between tract segments. This angle can be more generous (larger) than values typically used with probabilistic direction getters.
The sphere used to sample the diffusion ODF.
The order of the SH “model” used to estimate bootstrap residuals.
Max number of bootstrap samples used to find tracking direction before giving up.
Threshold for ODF functions.
Relative threshold for excluding ODF peaks.
Angular threshold for excluding ODF peaks.
BootPmfGen
Bases: dipy.direction.pmf.PmfGen
Methods
Produces an ODF from a SH bootstrap sample 


Return the pmf value corresponding to the closest vertex to the direction xyz. 
get_pmf_no_boot 
BaseDirectionGetter
Bases: dipy.direction.closest_peak_direction_getter.BasePmfDirectionGetter
Methods

Returns best directions at seed location to start tracking. 
generate_streamline 

get_direction 
BasePmfDirectionGetter
Bases: dipy.tracking.direction_getter.DirectionGetter
A base class for dynamic direction getters
Methods
Returns best directions at seed location to start tracking. 
generate_streamline 

get_direction 
Returns best directions at seed location to start tracking.
The point in an image at which to lookup tracking directions.
Possible tracking directions from point. N
may be 0, all
directions should be unique.
ClosestPeakDirectionGetter
Bases: dipy.direction.closest_peak_direction_getter.PmfGenDirectionGetter
A direction getter that returns the closest odf peak to previous tracking direction.
Methods

Constructor for making a DirectionGetter from an array of Pmfs 

Probabilistic direction getter from a distribution of directions on the sphere 

Returns best directions at seed location to start tracking. 
generate_streamline 

get_direction 
PmfGenDirectionGetter
Bases: dipy.direction.closest_peak_direction_getter.BasePmfDirectionGetter
A base class for direction getter using a pmf
Methods
Constructor for making a DirectionGetter from an array of Pmfs 

Probabilistic direction getter from a distribution of directions on the sphere 


Returns best directions at seed location to start tracking. 
generate_streamline 

get_direction 
Constructor for making a DirectionGetter from an array of Pmfs
The pmf to be used for tracking at each voxel.
The maximum allowed angle between incoming direction and new direction.
The set of directions on which the pmf is sampled and to be used for tracking.
Used to remove direction from the probability mass function for selecting the tracking direction.
Used for extracting initial tracking directions. Passed to peak_directions.
Used for extracting initial tracking directions. Passed to peak_directions.
See also
Probabilistic direction getter from a distribution of directions on the sphere
The distribution of tracking directions at each voxel represented
as a function on the sphere using the real spherical harmonic
basis. For example the FOD of the Constrained Spherical
Deconvolution model can be used this way. This distribution will
be discretized using sphere
and tracking directions will be
chosen from the vertices of sphere
based on the distribution.
The maximum allowed angle between incoming direction and new direction.
The set of directions to be used for tracking.
Used to remove direction from the probability mass function for selecting the tracking direction.
The basis that shcoeff
are associated with.
dipy.reconst.shm.real_sh_descoteaux
is used by default.
Used for extracting initial tracking directions. Passed to peak_directions.
Used for extracting initial tracking directions. Passed to peak_directions.
See also
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.
The odf function evaluated on the vertices of sphere
The Sphere providing discrete directions for evaluation.
Only peaks greater than min + relative_peak_threshold * scale
are
kept, where min = max(0, odf.min())
and
scale = odf.max()  min
.
The minimum distance between directions. If two peaks are too close only the larger of the two is returned.
N vertices for sphere, one for each peak
peak values
peak indices of the directions on the sphere
Notes
If the odf has any negative values, they will be clipped to zeros.
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.
Methods
The best starting directions for fiber tracking from point 
generate_streamline 

get_direction 
InTemporaryDirectory
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 
PeaksAndMetrics
Bases: dipy.reconst.eudx_direction_getter.EuDXDirectionGetter
Methods

The best starting directions for fiber tracking from point 
generate_streamline 

get_direction 
Sphere
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)
Vertices as xyz coordinates.
Vertices as spherical coordinates. Theta and phi are the inclination and azimuth angles respectively.
Vertices as xyz coordinates.
Indices into vertices that form triangular faces. If unspecified, the faces are computed using a Delaunay triangulation.
Edges between vertices. If unspecified, the edges are derived from the faces.
Methods

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

Subdivides each face of the sphere into four new faces. 
edges 

faces 

vertices 
Find the index of the vertex in the Sphere closest to the input vector
A unit vector
The index into the Sphere.vertices array that gives the closest vertex (in angle).
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/____\b
/\ /\
/ \ / \
/____\/____\
x c z
The number of subdivisions to preform.
The subdivided sphere.
repeat
Bases: object
for the specified number of times. If not specified, returns the object endlessly.
Deprecate a renamed or removed function argument.
The decorator assumes that the argument with the old_name
was removed
from the function signature and the new_name
replaced it at the
same position in the signature. If the old_name
argument is
given when calling the decorated function the decorator will catch it and
issue a deprecation warning and pass it on as new_name
argument.
The old name of the argument.
None
, optionalThe new name of the argument. Set this to None to remove the
argument old_name
instead of renaming it.
The release at which the old argument became deprecated.
Last released version at which this function will still raise a deprecation warning. Versions higher than this will raise an error.
Callable accepting string as argument, and return 1 if string
represents a higher version than encoded in the version_comparator
,
0 if the version is equal, and 1 if the version is lower. For example,
the version_comparator
may compare the input version string to the
current package version string.
If the argument is not a named argument (for example it
was meant to be consumed by **kwargs
) set this to
True
. Otherwise the decorator will throw an Exception
if the new_name
cannot be found in the signature of
the decorated function.
Default is False
.
Warning to be issued.
Error to be issued
An alternative function or class name that the user may use in
place of the deprecated object if new_name
is None. The deprecation
warning will tell the user about this alternative if provided.
If the new argument name cannot be found in the function
signature and arg_in_kwargs was False or if it is used to
deprecate the name of the *args
, **kwargs
like arguments.
At runtime such an Error is raised if both the new_name
and old_name were specified when calling the function and
“relax=False”.
Notes
This function is based on the Astropy (major modification). https://github.com/astropy/astropy. See COPYING file distributed along with the astropy package for the copyright and license terms.
Examples
The deprecation warnings are not shown in the following examples. To deprecate a positional or keyword argument:: >>> from dipy.utils.deprecator import deprecated_params >>> @deprecated_params(‘sig’, ‘sigma’, ‘0.3’) … def test(sigma): … return sigma >>> test(2) 2 >>> test(sigma=2) 2 >>> test(sig=2) # doctest: +SKIP 2
It is also possible to replace multiple arguments. The old_name
,
new_name
and since
have to be tuple or list and contain the
same number of entries::
>>> @deprecated_params([‘a’, ‘b’], [‘alpha’, ‘beta’],
… [‘0.2’, 0.4])
… def test(alpha, beta):
… return alpha, beta
>>> test(a=2, b=3) # doctest: +SKIP
(2, 3)
Determine the effective number of processes for parallelization.
For num_processes = None` return the maximum number of cores retrieved
by cpu_count().
For num_processes > 0
, return this value.
For num_processes < 0
, return the maximal number of cores minus
num_processes + 1
. In particular num_processes = 1
will use as
many cores as possible.
For num_processes = 0
a ValueError is raised.
Desired number of processes to be used.
The general fractional anisotropy of a function evaluated on the unit sphere
Values of data on the unit sphere.
GFA evaluated in each entry of the array, along the last dimension. An np.nan is returned for coordinates that contain allzeros in samples.
Notes
The GFA is defined as [1]
\sqrt{\frac{n \sum_i{(\Psi_i  <\Psi>)^2}}{(n1) \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.
Quality assessment of High Angular Resolution Diffusion Imaging data using bootstrap on Qball reconstruction. J. Cohen Adad, M. Descoteaux, L.L. Wald. JMRI 33: 11941208.
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.
The function evaluated on a set of discrete points.
The set of neighbor relations between the points. Every edge, ie edges[i, :], is a pair of neighboring points.
Value of odf at a maximum point. Peak values is sorted in descending order.
Indices of maximum points. Sorted in the same order as peak_values so odf[peak_indices[i]] == peak_values[i].
See also
Notes
A point is a local maximum if it is > at least one neighbor and >= all neighbors. If no points meet the above criteria, 1 maximum is returned such that odf[maximum] == max(odf).
An Ndimensional iterator object to index arrays.
Given the shape of an array, an ndindex instance iterates over the Ndimensional index of the array. At each iteration a tuple of indices is returned; the last dimension is iterated over first.
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)
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.
The odf function evaluated on the vertices of sphere
The Sphere providing discrete directions for evaluation.
Only peaks greater than min + relative_peak_threshold * scale
are
kept, where min = max(0, odf.min())
and
scale = odf.max()  min
.
The minimum distance between directions. If two peaks are too close only the larger of the two is returned.
N vertices for sphere, one for each peak
peak values
peak indices of the directions on the sphere
Notes
If the odf has any negative values, they will be clipped to zeros.
Non Linear Direction Finder.
A function which can be evaluated on a sphere.
Only return peaks greater than relative_peak_threshold * m
where m
is the largest peak.
The minimum distance between directions. If two peaks are too close only the larger of the two is returned.
A discrete Sphere. The points on the sphere will be used for initial estimate of maximums.
Relative tolerance for optimization.
Points on the sphere corresponding to N local maxima on the sphere.
Value of sphere_eval at each point on directions.
Fit the model to data and computes peaks and metrics
model will be used to fit the data.
Diffusion data.
The Sphere providing discrete directions for evaluation.
Only return peaks greater than relative_peak_threshold * m
where m
is the largest peak.
directions. If two peaks are too close only the larger of the two is returned.
If mask is provided, voxels that are False in mask are skipped and no peaks are returned.
If True, the odfs are returned.
If True, the odf as spherical harmonics coefficients is returned
Voxels with gfa less than gfa_thr are skipped, no peaks are returned.
If true, all peak values are calculated relative to max(odf).
Maximum SH order in the SH fit. For sh_order, there will be
(sh_order + 1) * (sh_order + 2) / 2
SH coefficients (default 8).
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
).
Maximum number of peaks found (default 5 peaks).
Matrix that transforms spherical harmonics to spherical function
sf = np.dot(sh, B)
.
Inverse of B.
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'
.
If parallel is True, the number of subprocesses to use
(default multiprocessing.cpu_count()). If < 0 the maximal number of
cores minus num_processes + 1
is used (enter 1 to use as many
cores as possible). 0 raises an error.
An object with gfa
, peak_directions
, peak_values
,
peak_indices
, odf
, shm_coeffs
as attributes
References
Descoteaux, M., Angelino, E., Fitzgibbons, S. and Deriche, R. Regularized, Fast, and Robust Analytical Qball Imaging. Magn. Reson. Med. 2007;58:497510.
Tournier J.D., Calamante F. and Connelly A. Robust determination of the fibre orientation distribution in diffusion MRI: Nonnegativity constrained superresolved spherical deconvolution. NeuroImage. 2007;35(4):14591472.
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.
N unit vectors.
The minimum separation between vertices in degrees.
If True, return mapping as well as vertices and maybe indices (see below).
If True, return indices as well as vertices and maybe mapping (see below).
Vertices sufficiently separated from one another.
For each element vertices[i]
(\(i \in 0..N1\)), 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 gives the reverse of mapping. For each element
unique_vertices[j]
(\(j \in 0..M1\)), 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.
Reshape and convert to float32 a set of peaks for visualisation with mrtrix or the fibernavigator.
The peaks to be reshaped and converted to float32.
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.
Array to be searched. We assume a is in descending order.
Applied threshold will be T
with T = a[0] * relative_threshold
.
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
Matrix that transforms Spherical harmonics (SH) to spherical function (SF).
The points on which to sample the spherical function.
Maximum SH order in the SH fit. For sh_order
, there will be
(sh_order + 1) * (sh_order + 2) / 2
SH coefficients for a symmetric
basis and (sh_order + 1) * (sh_order + 1)
coefficients for a full
SH basis.
None
for the default DIPY basis,
tournier07
for the Tournier 2007 [Rc855ec8258482]_[Rc855ec8258483]_ basis,
descoteaux07
for the Descoteaux 2007 [1] basis,
(None
defaults to descoteaux07
).
If True, uses a SH basis containing even and odd order SH functions. Else, uses a SH basis consisting only of even order SH functions.
True to use a legacy basis definition for backward compatibility
with previous tournier07
and descoteaux07
implementations.
If True then the inverse of the matrix is also returned.
Lambdaregularization in the SH fit.
Matrix that transforms spherical harmonics to spherical function
sf = np.dot(sh, B)
.
Inverse of B.
References
Descoteaux, M., Angelino, E., Fitzgibbons, S. and Deriche, R. Regularized, Fast, and Robust Analytical Qball Imaging. Magn. Reson. Med. 2007;58:497510.
Tournier J.D., Calamante F. and Connelly A. Robust determination of the fibre orientation distribution in diffusion MRI: Nonnegativity constrained superresolved spherical deconvolution. NeuroImage. 2007;35(4):14591472.
Tournier JD, Smith R, Raffelt D, Tabbara R, Dhollander T, Pietsch M, et al. MRtrix3: A fast, flexible and open software framework for medical image processing and visualisation. NeuroImage. 2019 Nov 15;202:116137.
BootPmfGen
Bases: dipy.direction.pmf.PmfGen
Methods
Produces an ODF from a SH bootstrap sample 


Return the pmf value corresponding to the closest vertex to the direction xyz. 
get_pmf_no_boot 
PmfGen
Bases: object
Methods
Return the pmf value corresponding to the closest vertex to the direction xyz. 
get_pmf 
SHCoeffPmfGen
Bases: dipy.direction.pmf.PmfGen
Methods

Return the pmf value corresponding to the closest vertex to the direction xyz. 
get_pmf 
SimplePmfGen
Bases: dipy.direction.pmf.PmfGen
Methods

Return the pmf value corresponding to the closest vertex to the direction xyz. 
get_pmf 
Return angles for Cartesian 3D coordinates x, y, and z
See doc for sphere2cart
for angle conventions and derivation
of the formulae.
\(0\le\theta\mathrm{(theta)}\le\pi\) and \(\pi\le\phi\mathrm{(phi)}\le\pi\)
x coordinate in Cartesian space
y coordinate in Cartesian space
z coordinate
radius
inclination (polar) angle
azimuth angle
DeterministicMaximumDirectionGetter
Bases: dipy.direction.probabilistic_direction_getter.ProbabilisticDirectionGetter
Return direction of a sphere with the highest probability mass function (pmf).
Methods

Constructor for making a DirectionGetter from an array of Pmfs 

Probabilistic direction getter from a distribution of directions on the sphere 

Returns best directions at seed location to start tracking. 
generate_streamline 

get_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

Constructor for making a DirectionGetter from an array of Pmfs 

Probabilistic direction getter from a distribution of directions on the sphere 

Returns best directions at seed location to start tracking. 
generate_streamline 

get_direction 
Direction getter from a pmf generator.
Used to get probability mass function for selecting tracking directions.
The maximum allowed angle between incoming direction and new direction.
The set of directions to be used for tracking.
Used to remove direction from the probability mass function for selecting the tracking direction.
Used for extracting initial tracking directions. Passed to peak_directions.
Used for extracting initial tracking directions. Passed to peak_directions.
See also
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.
The odf function evaluated on the vertices of sphere
The Sphere providing discrete directions for evaluation.
Only peaks greater than min + relative_peak_threshold * scale
are
kept, where min = max(0, odf.min())
and
scale = odf.max()  min
.
The minimum distance between directions. If two peaks are too close only the larger of the two is returned.
N vertices for sphere, one for each peak
peak values
peak indices of the directions on the sphere
Notes
If the odf has any negative values, they will be clipped to zeros.