# tracking

Tracking objects

 Streamlines alias of nibabel.streamlines.array_sequence.ArraySequence bench([label, verbose, extra_argv]) Run benchmarks for module using nose. test([label, verbose, extra_argv, doctests, …]) Run tests for module using nose.

## Module: tracking._utils

This is a helper module for dipy.tracking.utils.

 warn(/, message[, category, stacklevel, source]) Issue a warning, or maybe ignore it or raise an exception.

## Module: tracking.benchmarks.bench_streamline

Benchmarks for functions related to streamline

Run all benchmarks with:

import dipy.tracking as dipytracking
dipytracking.bench()

With Pytest, Run this benchmark with:

pytest -svv -c bench.ini /path/to/bench_streamline.py

 Streamlines alias of nibabel.streamlines.array_sequence.ArraySequence assert_array_almost_equal(x, y[, decimal, …]) Raises an AssertionError if two objects are not equal up to desired precision. assert_array_equal(x, y[, err_msg, verbose]) Raises an AssertionError if two array_like objects are not equal. compress_streamlines Compress streamlines by linearization as in [Presseau15]. compress_streamlines_python(streamline[, …]) Python version of the FiberCompression found on https://github.com/scilus/FiberCompression. generate_streamlines(nb_streamlines, …) get_fnames([name]) Provide full paths to example or test datasets. length Euclidean length of streamlines length_python(xyz[, along]) load_tractogram(filename, reference[, …]) Load the stateful tractogram from any format (trk, tck, vtk, fib, dpy) measure(code_str[, times, label]) Return elapsed time for executing code in the namespace of the caller. set_number_of_points Change the number of points of streamlines set_number_of_points_python(xyz[, n_pols]) setup()

## Module: tracking.learning

Learning algorithms for tractography

 detect_corresponding_tracks(indices, …) Detect corresponding tracks from list tracks1 to list tracks2 where tracks1 & tracks2 are lists of tracks detect_corresponding_tracks_plus(indices, …) Detect corresponding tracks from 1 to 2 where tracks1 & tracks2 are sequences of tracks

## Module: tracking.life

This is an implementation of the Linear Fascicle Evaluation (LiFE) algorithm described in:

Pestilli, F., Yeatman, J, Rokem, A. Kay, K. and Wandell B.A. (2014). Validation and statistical inference in living connectomes. Nature Methods 11: 1058-1063. doi:10.1038/nmeth.3098

 FiberFit(fiber_model, life_matrix, …) A fit of the LiFE model to diffusion data FiberModel(gtab) A class for representing and solving predictive models based on tractography solutions. LifeSignalMaker(gtab[, evals, sphere]) A class for generating signals from streamlines in an efficient and speedy manner. ReconstFit(model, data) Abstract class which holds the fit result of ReconstModel ReconstModel(gtab) Abstract class for signal reconstruction models grad_tensor(grad, evals) Calculate the 3 by 3 tensor for a given spatial gradient, given a canonical tensor shape (also as a 3 by 3), pointing at [1,0,0] gradient(f) Return the gradient of an N-dimensional array. streamline_gradients(streamline) Calculate the gradients of the streamline along the spatial dimension streamline_signal(streamline, gtab[, evals]) The signal from a single streamline estimate along each of its nodes. streamline_tensors(streamline[, evals]) The tensors generated by this fiber. transform_streamlines(streamlines, mat[, …]) Apply affine transformation to streamlines unique_rows(in_array[, dtype]) This (quickly) finds the unique rows in an array voxel2streamline(streamline, affine[, …]) Maps voxels to streamlines and streamlines to voxels, for setting up the LiFE equations matrix

## Module: tracking.local_tracking

 AnatomicalStoppingCriterion Abstract class that takes as input included and excluded tissue maps. Iterable LocalTracking(direction_getter, …[, …]) ParticleFilteringTracking(direction_getter, …) StreamlineStatus An enumeration. local_tracker Tracks one direction from a seed. pft_tracker Tracks one direction from a seed using the particle filtering algorithm.

## Module: tracking.metrics

Metrics for tracks, where tracks are arrays of points

 arbitrarypoint(xyz, distance) Select an arbitrary point along distance on the track (curve) bytes(xyz) Size of track in bytes. center_of_mass(xyz) Center of mass of streamline deprecate_with_version(message[, since, …]) Return decorator function function for deprecation warning / error. downsample(xyz[, n_pols]) downsample for a specific number of points along the streamline Uses the length of the curve. endpoint(xyz) Parameters frenet_serret(xyz) Frenet-Serret Space Curve Invariants generate_combinations(items, n) Combine sets of size n from items inside_sphere(xyz, center, radius) If any point of the track is inside a sphere of a specified center and radius return True otherwise False. inside_sphere_points(xyz, center, radius) If a track intersects with a sphere of a specified center and radius return the points that are inside the sphere otherwise False. intersect_sphere(xyz, center, radius) If any segment of the track is intersecting with a sphere of specific center and radius return True otherwise False length(xyz[, along]) Euclidean length of track line longest_track_bundle(bundle[, sort]) Return longest track or length sorted track indices in bundle magn(xyz[, n]) magnitude of vector mean_curvature(xyz) Calculates the mean curvature of a curve mean_orientation(xyz) Calculates the mean orientation of a curve midpoint(xyz) Midpoint of track midpoint2point(xyz, p) Calculate distance from midpoint of a curve to arbitrary point p principal_components(xyz) We use PCA to calculate the 3 principal directions for a track set_number_of_points Change the number of points of streamlines splev(x, tck[, der, ext]) Evaluate a B-spline or its derivatives. spline(xyz[, s, k, nest]) Generate B-splines as documented in http://www.scipy.org/Cookbook/Interpolation splprep(x[, w, u, ub, ue, k, task, s, t, …]) Find the B-spline representation of an N-D curve. startpoint(xyz) First point of the track winding(xyz) Total turning angle projected.

## Module: tracking.streamline

 Streamlines alias of nibabel.streamlines.array_sequence.ArraySequence apply_affine(aff, pts) Apply affine matrix aff to points pts bundles_distances_mdf Calculate distances between list of tracks A and list of tracks B cdist(XA, XB[, metric]) Compute distance between each pair of the two collections of inputs. center_streamlines(streamlines) Move streamlines to the origin cluster_confidence(streamlines[, max_mdf, …]) Computes the cluster confidence index (cci), which is an estimation of the support a set of streamlines gives to a particular pathway. compress_streamlines Compress streamlines by linearization as in [Presseau15]. deepcopy(x[, memo, _nil]) Deep copy operation on arbitrary Python objects. deform_streamlines(streamlines, …) Apply deformation field to streamlines dist_to_corner(affine) Calculate the maximal distance from the center to a corner of a voxel, given an affine interpolate_scalar_3d Trilinear interpolation of a 3D scalar image interpolate_vector_3d Trilinear interpolation of a 3D vector field length Euclidean length of streamlines nbytes(streamlines) orient_by_rois(streamlines, affine, roi1, roi2) Orient a set of streamlines according to a pair of ROIs orient_by_streamline(streamlines, standard) Orient a bundle of streamlines to a standard streamline. relist_streamlines(points, offsets) Given a representation of a set of streamlines as a large array and an offsets array return the streamlines as a list of shorter arrays. select_by_rois(streamlines, affine, rois, …) Select streamlines based on logical relations with several regions of interest (ROIs). select_random_set_of_streamlines(…[, rng]) Select a random set of streamlines set_number_of_points Change the number of points of streamlines 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 values_from_volume(data, streamlines, affine) Extract values of a scalar/vector along each streamline from a volume. warn(/, message[, category, stacklevel, source]) Issue a warning, or maybe ignore it or raise an exception.

## Module: tracking.utils

Various tools related to creating and working with streamlines

This module provides tools for targeting streamlines using ROIs, for making connectivity matrices from whole brain fiber tracking and some other tools that allow streamlines to interact with image data.

### Important Notes

Dipy uses affine matrices to represent the relationship between streamline points, which are defined as points in a continuous 3d space, and image voxels, which are typically arranged in a discrete 3d grid. Dipy uses a convention similar to nifti files to interpret these affine matrices. This convention is that the point at the center of voxel [i, j, k] is represented by the point [x, y, z] where [x, y, z, 1] = affine * [i, j, k, 1]. Also when the phrase “voxel coordinates” is used, it is understood to be the same as affine = eye(4).

As an example, lets take a 2d image where the affine is:

[[1., 0., 0.],
[0., 2., 0.],
[0., 0., 1.]]

The pixels of an image with this affine would look something like:

A------------
|   |   |   |
| C |   |   |
|   |   |   |
----B--------
|   |   |   |
|   |   |   |
|   |   |   |
-------------
|   |   |   |
|   |   |   |
|   |   |   |
------------D

And the letters A-D represent the following points in “real world coordinates”:

A = [-.5, -1.]
B = [ .5,  1.]
C = [ 0.,  0.]
D = [ 2.5,  5.]
 OrderedDict Dictionary that remembers insertion order combinations combinations(iterable, r) –> combinations object defaultdict defaultdict(default_factory[, …]) –> dict with default factory groupby(iterable[, key]) keys and groups from the iterable. apply_affine(aff, pts) Apply affine matrix aff to points pts asarray(a[, dtype, order]) Convert the input to an array. cdist(XA, XB[, metric]) Compute distance between each pair of the two collections of inputs. connectivity_matrix(streamlines, affine, …) Counts the streamlines that start and end at each label pair. density_map(streamlines, affine, vol_dims) Counts the number of unique streamlines that pass through each voxel. dist_to_corner(affine) Calculate the maximal distance from the center to a corner of a voxel, given an affine empty(shape[, dtype, order]) Return a new array of given shape and type, without initializing entries. length(streamlines) Calculate the lengths of many streamlines in a bundle. minimum_at(a, indices[, b]) Performs unbuffered in place operation on operand ‘a’ for elements specified by ‘indices’. ndbincount(x[, weights, shape]) Like bincount, but for nd-indices. near_roi(streamlines, affine, region_of_interest) Provide filtering criteria for a set of streamlines based on whether they fall within a tolerance distance from an ROI path_length(streamlines, affine, aoi[, …]) Computes the shortest path, along any streamline, between aoi and each voxel. random_seeds_from_mask(mask, affine[, …]) Create randomly placed seeds for fiber tracking from a binary mask. ravel_multi_index(multi_index, dims[, mode, …]) Converts a tuple of index arrays into an array of flat indices, applying boundary modes to the multi-index. reduce_labels(label_volume) Reduces an array of labels to the integers from 0 to n with smallest possible n. reduce_rois(rois, include) Reduce multiple ROIs to one inclusion and one exclusion ROI. seeds_from_mask(mask, affine[, density]) Create seeds for fiber tracking from a binary mask. streamline_near_roi(streamline, roi_coords, tol) Is a streamline near an ROI. subsegment(streamlines, max_segment_length) Splits the segments of the streamlines into small segments. target(streamlines, affine, target_mask[, …]) Filters streamlines based on whether or not they pass through an ROI. target_line_based(streamlines, affine, …) Filters streamlines based on whether or not they pass through a ROI, using a line-based algorithm. transform_tracking_output(tracking_output, …) Applies a linear transformation, given by affine, to streamlines. unique_rows(in_array[, dtype]) This (quickly) finds the unique rows in an array warn(/, message[, category, stacklevel, source]) Issue a warning, or maybe ignore it or raise an exception. wraps(wrapped[, assigned, updated]) Decorator factory to apply update_wrapper() to a wrapper function

### Streamlines

dipy.tracking.Streamlines

alias of nibabel.streamlines.array_sequence.ArraySequence

### bench

dipy.tracking.bench(label='fast', verbose=1, extra_argv=None)

Run benchmarks for module using nose.

Parameters
label{‘fast’, ‘full’, ‘’, attribute identifier}, optional

Identifies the benchmarks to run. This can be a string to pass to the nosetests executable with the ‘-A’ option, or one of several special values. Special values are:

• ‘fast’ - the default - which corresponds to the nosetests -A option of ‘not slow’.

• ‘full’ - fast (as above) and slow benchmarks as in the ‘no -A’ option to nosetests - this is the same as ‘’.

• None or ‘’ - run all tests.

• attribute_identifier - string passed directly to nosetests as ‘-A’.

verboseint, optional

Verbosity value for benchmark outputs, in the range 1-10. Default is 1.

extra_argvlist, optional

List with any extra arguments to pass to nosetests.

Returns
successbool

Returns True if running the benchmarks works, False if an error occurred.

Notes

Benchmarks are like tests, but have names starting with “bench” instead of “test”, and can be found under the “benchmarks” sub-directory of the module.

Each NumPy module exposes bench in its namespace to run all benchmarks for it.

Examples

>>> success = np.lib.bench()
Running benchmarks for numpy.lib
...
using 562341 items:
unique:
0.11
unique1d:
0.11
ratio: 1.0
nUnique: 56230 == 56230
...
OK
>>> success
True

### test

dipy.tracking.test(label='fast', verbose=1, extra_argv=None, doctests=False, coverage=False, raise_warnings=None, timer=False)

Run tests for module using nose.

Parameters
label{‘fast’, ‘full’, ‘’, attribute identifier}, optional

Identifies the tests to run. This can be a string to pass to the nosetests executable with the ‘-A’ option, or one of several special values. Special values are:

• ‘fast’ - the default - which corresponds to the nosetests -A option of ‘not slow’.

• ‘full’ - fast (as above) and slow tests as in the ‘no -A’ option to nosetests - this is the same as ‘’.

• None or ‘’ - run all tests.

• attribute_identifier - string passed directly to nosetests as ‘-A’.

verboseint, optional

Verbosity value for test outputs, in the range 1-10. Default is 1.

extra_argvlist, optional

List with any extra arguments to pass to nosetests.

doctestsbool, optional

If True, run doctests in module. Default is False.

coveragebool, optional

If True, report coverage of NumPy code. Default is False. (This requires the coverage module).

raise_warningsNone, str or sequence of warnings, optional

This specifies which warnings to configure as ‘raise’ instead of being shown once during the test execution. Valid strings are:

• “develop” : equals (Warning,)

• “release” : equals (), do not raise on any warnings.

timerbool or int, optional

Timing of individual tests with nose-timer (which needs to be installed). If True, time tests and report on all of them. If an integer (say N), report timing results for N slowest tests.

Returns
resultobject

Returns the result of running the tests as a nose.result.TextTestResult object.

Notes

Each NumPy module exposes test in its namespace to run all tests for it. For example, to run all tests for numpy.lib:

>>> np.lib.test()

Examples

>>> result = np.lib.test()
Running unit tests for numpy.lib
...
Ran 976 tests in 3.933s

OK

>>> result.errors
[]
>>> result.knownfail
[]

### warn

dipy.tracking._utils.warn(/, message, category=None, stacklevel=1, source=None)

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

### Streamlines

dipy.tracking.benchmarks.bench_streamline.Streamlines

alias of nibabel.streamlines.array_sequence.ArraySequence

### assert_array_almost_equal

dipy.tracking.benchmarks.bench_streamline.assert_array_almost_equal(x, y, decimal=6, err_msg='', verbose=True)

Raises an AssertionError if two objects are not equal up to desired precision.

Note

It is recommended to use one of assert_allclose, assert_array_almost_equal_nulp or assert_array_max_ulp instead of this function for more consistent floating point comparisons.

The test verifies identical shapes and that the elements of actual and desired satisfy.

abs(desired-actual) < 1.5 * 10**(-decimal)

That is a looser test than originally documented, but agrees with what the actual implementation did up to rounding vagaries. An exception is raised at shape mismatch or conflicting values. In contrast to the standard usage in numpy, NaNs are compared like numbers, no assertion is raised if both objects have NaNs in the same positions.

Parameters
xarray_like

The actual object to check.

yarray_like

The desired, expected object.

decimalint, optional

Desired precision, default is 6.

err_msgstr, optional

The error message to be printed in case of failure.

verbosebool, optional

If True, the conflicting values are appended to the error message.

Raises
AssertionError

If actual and desired are not equal up to specified precision.

assert_allclose

Compare two array_like objects for equality with desired relative and/or absolute precision.

assert_array_almost_equal_nulp, assert_array_max_ulp, assert_equal

Examples

the first assert does not raise an exception

>>> np.testing.assert_array_almost_equal([1.0,2.333,np.nan],
...                                      [1.0,2.333,np.nan])
>>> np.testing.assert_array_almost_equal([1.0,2.33333,np.nan],
...                                      [1.0,2.33339,np.nan], decimal=5)
Traceback (most recent call last):
...
AssertionError:
Arrays are not almost equal to 5 decimals

Mismatched elements: 1 / 3 (33.3%)
Max absolute difference: 6.e-05
Max relative difference: 2.57136612e-05
x: array([1.     , 2.33333,     nan])
y: array([1.     , 2.33339,     nan])
>>> np.testing.assert_array_almost_equal([1.0,2.33333,np.nan],
...                                      [1.0,2.33333, 5], decimal=5)
Traceback (most recent call last):
...
AssertionError:
Arrays are not almost equal to 5 decimals

x and y nan location mismatch:
x: array([1.     , 2.33333,     nan])
y: array([1.     , 2.33333, 5.     ])

### assert_array_equal

dipy.tracking.benchmarks.bench_streamline.assert_array_equal(x, y, err_msg='', verbose=True)

Raises an AssertionError if two array_like objects are not equal.

Given two array_like objects, check that the shape is equal and all elements of these objects are equal (but see the Notes for the special handling of a scalar). An exception is raised at shape mismatch or conflicting values. In contrast to the standard usage in numpy, NaNs are compared like numbers, no assertion is raised if both objects have NaNs in the same positions.

The usual caution for verifying equality with floating point numbers is advised.

Parameters
xarray_like

The actual object to check.

yarray_like

The desired, expected object.

err_msgstr, optional

The error message to be printed in case of failure.

verbosebool, optional

If True, the conflicting values are appended to the error message.

Raises
AssertionError

If actual and desired objects are not equal.

assert_allclose

Compare two array_like objects for equality with desired relative and/or absolute precision.

assert_array_almost_equal_nulp, assert_array_max_ulp, assert_equal

Notes

When one of x and y is a scalar and the other is array_like, the function checks that each element of the array_like object is equal to the scalar.

Examples

The first assert does not raise an exception:

>>> np.testing.assert_array_equal([1.0,2.33333,np.nan],
...                               [np.exp(0),2.33333, np.nan])

Assert fails with numerical imprecision with floats:

>>> np.testing.assert_array_equal([1.0,np.pi,np.nan],
...                               [1, np.sqrt(np.pi)**2, np.nan])
Traceback (most recent call last):
...
AssertionError:
Arrays are not equal

Mismatched elements: 1 / 3 (33.3%)
Max absolute difference: 4.4408921e-16
Max relative difference: 1.41357986e-16
x: array([1.      , 3.141593,      nan])
y: array([1.      , 3.141593,      nan])

Use assert_allclose or one of the nulp (number of floating point values) functions for these cases instead:

>>> np.testing.assert_allclose([1.0,np.pi,np.nan],
...                            [1, np.sqrt(np.pi)**2, np.nan],
...                            rtol=1e-10, atol=0)

As mentioned in the Notes section, assert_array_equal has special handling for scalars. Here the test checks that each value in x is 3:

>>> x = np.full((2, 5), fill_value=3)
>>> np.testing.assert_array_equal(x, 3)

### bench_compress_streamlines

dipy.tracking.benchmarks.bench_streamline.bench_compress_streamlines()

### bench_length

dipy.tracking.benchmarks.bench_streamline.bench_length()

### bench_set_number_of_points

dipy.tracking.benchmarks.bench_streamline.bench_set_number_of_points()

### compress_streamlines

dipy.tracking.benchmarks.bench_streamline.compress_streamlines()

Compress streamlines by linearization as in [Presseau15].

The compression consists in merging consecutive segments that are nearly collinear. The merging is achieved by removing the point the two segments have in common.

The linearization process [Presseau15] ensures that every point being removed are within a certain margin (in mm) of the resulting streamline. Recommendations for setting this margin can be found in [Presseau15] (in which they called it tolerance error).

The compression also ensures that two consecutive points won’t be too far from each other (precisely less or equal than max_segment_lengthmm). This is a tradeoff to speed up the linearization process [Rheault15]. A low value will result in a faster linearization but low compression, whereas a high value will result in a slower linearization but high compression.

Parameters
streamlinesone or a list of array-like of shape (N,3)

Array representing x,y,z of N points in a streamline.

tol_errorfloat (optional)

Tolerance error in mm (default: 0.01). A rule of thumb is to set it to 0.01mm for deterministic streamlines and 0.1mm for probabilitic streamlines.

max_segment_lengthfloat (optional)

Maximum length in mm of any given segment produced by the compression. The default is 10mm. (In [Presseau15], they used a value of np.inf).

Returns
compressed_streamlinesone or a list of array-like

Results of the linearization process.

Notes

Be aware that compressed streamlines have variable step sizes. One needs to be careful when computing streamlines-based metrics [Houde15].

References

Presseau15(1,2,3,4,5)

Presseau C. et al., A new compression format for fiber tracking datasets, NeuroImage, no 109, 73-83, 2015.

Rheault15

Rheault F. et al., Real Time Interaction with Millions of Streamlines, ISMRM, 2015.

Houde15

Houde J.-C. et al. How to Avoid Biased Streamlines-Based Metrics for Streamlines with Variable Step Sizes, ISMRM, 2015.

Examples

>>> from dipy.tracking.streamline import compress_streamlines
>>> import numpy as np
>>> # One streamline: a wiggling line
>>> rng = np.random.RandomState(42)
>>> streamline = np.linspace(0, 10, 100*3).reshape((100, 3))
>>> streamline += 0.2 * rng.rand(100, 3)
>>> c_streamline = compress_streamlines(streamline, tol_error=0.2)
>>> len(streamline)
100
>>> len(c_streamline)
10
>>> # Multiple streamlines
>>> streamlines = [streamline, streamline[::2]]
>>> c_streamlines = compress_streamlines(streamlines, tol_error=0.2)
>>> [len(s) for s in streamlines]
[100, 50]
>>> [len(s) for s in c_streamlines]
[10, 7]

### compress_streamlines_python

dipy.tracking.benchmarks.bench_streamline.compress_streamlines_python(streamline, tol_error=0.01, max_segment_length=10)

Python version of the FiberCompression found on https://github.com/scilus/FiberCompression.

### generate_streamlines

dipy.tracking.benchmarks.bench_streamline.generate_streamlines(nb_streamlines, min_nb_points, max_nb_points, rng)

### get_fnames

dipy.tracking.benchmarks.bench_streamline.get_fnames(name='small_64D')

Provide full paths to example or test datasets.

Parameters
namestr

the filename/s of which dataset to return, one of: - ‘small_64D’ small region of interest nifti,bvecs,bvals 64 directions - ‘small_101D’ small region of interest nifti, bvecs, bvals

101 directions

• ‘aniso_vox’ volume with anisotropic voxel size as Nifti

• ‘fornix’ 300 tracks in Trackvis format (from Pittsburgh Brain Competition)

• ‘gqi_vectors’ the scanner wave vectors needed for a GQI acquisitions of 101 directions tested on Siemens 3T Trio

• ‘small_25’ small ROI (10x8x2) DTI data (b value 2000, 25 directions)

• ‘test_piesno’ slice of N=8, K=14 diffusion data

• ‘reg_c’ small 2D image used for validating registration

• ‘reg_o’ small 2D image used for validation registration

• ‘cb_2’ two vectorized cingulum bundles

Returns
fnamestuple

filenames for dataset

Examples

>>> import numpy as np
>>> from dipy.data import get_fnames
>>> fimg, fbvals, fbvecs = get_fnames('small_101D')
>>> data.shape == (6, 10, 10, 102)
True
>>> bvals.shape == (102,)
True
>>> bvecs.shape == (102, 3)
True

### length

dipy.tracking.benchmarks.bench_streamline.length()

Euclidean length of streamlines

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

Parameters
streamlinesndarray or a list or dipy.tracking.Streamlines

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

Returns
lengthsscalar 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

### length_python

dipy.tracking.benchmarks.bench_streamline.length_python(xyz, along=False)

Load the stateful tractogram from any format (trk, tck, vtk, fib, dpy)

Parameters
filenamestring

Filename with valid extension

referenceNifti or Trk filename, Nifti1Image or TrkFile, Nifti1Header or

trk.header (dict), or ‘same’ if the input is a trk file. Reference that provides the spatial attribute. Typically a nifti-related object from the native diffusion used for streamlines generation

to_spaceEnum (dipy.io.stateful_tractogram.Space)

to_originEnum (dipy.io.stateful_tractogram.Origin)

NIFTI standard, default (center of the voxel) TRACKVIS standard (corner of the voxel)

bbox_valid_checkbool

Verification for negative voxel coordinates or values above the volume dimensions. Default is True, to enforce valid file.

Verification that the reference has the same header as the spatial attributes as the input tractogram when a Trk is loaded

Returns
outputStatefulTractogram

The tractogram to load (must have been saved properly)

### measure

dipy.tracking.benchmarks.bench_streamline.measure(code_str, times=1, label=None)

Return elapsed time for executing code in the namespace of the caller.

The supplied code string is compiled with the Python builtin compile. The precision of the timing is 10 milli-seconds. If the code will execute fast on this timescale, it can be executed many times to get reasonable timing accuracy.

Parameters
code_strstr

The code to be timed.

timesint, optional

The number of times the code is executed. Default is 1. The code is only compiled once.

labelstr, optional

A label to identify code_str with. This is passed into compile as the second argument (for run-time error messages).

Returns
elapsedfloat

Total elapsed time in seconds for executing code_str times times.

Examples

>>> times = 10
>>> etime = np.testing.measure('for i in range(1000): np.sqrt(i**2)', times=times)
>>> print("Time for a single execution : ", etime / times, "s")
Time for a single execution :  0.005 s

### set_number_of_points

dipy.tracking.benchmarks.bench_streamline.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
streamlinesndarray 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_pointsint

integer representing number of points wanted along the curve.

Returns
new_streamlinesndarray 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]

### set_number_of_points_python

dipy.tracking.benchmarks.bench_streamline.set_number_of_points_python(xyz, n_pols=3)

### setup

dipy.tracking.benchmarks.bench_streamline.setup()

### detect_corresponding_tracks

dipy.tracking.learning.detect_corresponding_tracks(indices, tracks1, tracks2)

Detect corresponding tracks from list tracks1 to list tracks2 where tracks1 & tracks2 are lists of tracks

Parameters
indicessequence

of indices of tracks1 that are to be detected in tracks2

tracks1sequence

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

tracks2sequence

of tracks as arrays, shape (M1,3) .. (Mm,3)

Returns
track2trackarray (N,2) where N is len(indices) of int

it shows the correspondance in the following way: the first column is the current index in tracks1 the second column is the corresponding index in tracks2

Notes

To find the corresponding tracks we use mam_distances with ‘avg’ option. Then we calculate the argmin of all the calculated distances and return it for every index. (See 3rd column of arr in the example given below.)

Examples

>>> import numpy as np
>>> import dipy.tracking.learning as tl
>>> A = np.array([[0, 0, 0], [1, 1, 1], [2, 2, 2]])
>>> B = np.array([[1, 0, 0], [2, 0, 0], [3, 0, 0]])
>>> C = np.array([[0, 0, -1], [0, 0, -2], [0, 0, -3]])
>>> bundle1 = [A, B, C]
>>> bundle2 = [B, A]
>>> indices = [0, 1]
>>> arr = tl.detect_corresponding_tracks(indices, bundle1, bundle2)

### detect_corresponding_tracks_plus

dipy.tracking.learning.detect_corresponding_tracks_plus(indices, tracks1, indices2, tracks2)

Detect corresponding tracks from 1 to 2 where tracks1 & tracks2 are sequences of tracks

Parameters
indicessequence

of indices of tracks1 that are to be detected in tracks2

tracks1sequence

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

indices2sequence

of indices of tracks2 in the initial brain

tracks2sequence

of tracks as arrays, shape (M1,3) .. (Mm,3)

Returns
track2trackarray (N,2) where N is len(indices)

of int showing the correspondance in th following way the first colum is the current index of tracks1 the second column is the corresponding index in tracks2

distances.mam_distances

Notes

To find the corresponding tracks we use mam_distances with ‘avg’ option. Then we calculate the argmin of all the calculated distances and return it for every index. (See 3rd column of arr in the example given below.)

Examples

>>> import numpy as np
>>> import dipy.tracking.learning as tl
>>> A = np.array([[0, 0, 0], [1, 1, 1], [2, 2, 2]])
>>> B = np.array([[1, 0, 0], [2, 0, 0], [3, 0, 0]])
>>> C = np.array([[0, 0, -1], [0, 0, -2], [0, 0, -3]])
>>> bundle1 = [A, B, C]
>>> bundle2 = [B, A]
>>> indices = [0, 1]
>>> indices2 = indices
>>> arr = tl.detect_corresponding_tracks_plus(indices, bundle1, indices2, bundle2)

### FiberFit

class dipy.tracking.life.FiberFit(fiber_model, life_matrix, vox_coords, to_fit, beta, weighted_signal, b0_signal, relative_signal, mean_sig, vox_data, streamline, affine, evals)

A fit of the LiFE model to diffusion data

Methods

 predict([gtab, S0]) Predict the signal
__init__(fiber_model, life_matrix, vox_coords, to_fit, beta, weighted_signal, b0_signal, relative_signal, mean_sig, vox_data, streamline, affine, evals)
Parameters
fiber_modelA FiberModel class instance
paramsthe parameters derived from a fit of the model to the data.
predict(gtab=None, S0=None)

Predict the signal

Parameters

Default: use self.gtab

S0float or array

The non-diffusion-weighted signal in the voxels for which a prediction is made. Default: use self.b0_signal

Returns
predictionndarray of shape (voxels, bvecs)

An array with a prediction of the signal in each voxel/direction

### FiberModel

class dipy.tracking.life.FiberModel(gtab)

A class for representing and solving predictive models based on tractography solutions.

Notes

This is an implementation of the LiFE model described in [1]_

[1] Pestilli, F., Yeatman, J, Rokem, A. Kay, K. and Wandell

B.A. (2014). Validation and statistical inference in living connectomes. Nature Methods.

Methods

 fit(data, streamline, affine[, evals, sphere]) Fit the LiFE FiberModel for data and a set of streamlines associated with this data setup(streamline, affine[, evals, sphere]) Set up the necessary components for the LiFE model: the matrix of fiber-contributions to the DWI signal, and the coordinates of voxels for which the equations will be solved
__init__(gtab)
Parameters
fit(data, streamline, affine, evals=[0.001, 0, 0], sphere=None)

Fit the LiFE FiberModel for data and a set of streamlines associated with this data

Parameters
data4D array

Diffusion-weighted data

streamlinelist

A bunch of streamlines

affinearray_like (4, 4)

The mapping from voxel coordinates to streamline points. The voxel_to_rasmm matrix, typically from a NIFTI file.

evalslist (optional)

The eigenvalues of the tensor response function used in constructing the model signal. Default: [0.001, 0, 0]

sphere: dipy.core.Sphere instance, or False

Whether to approximate (and cache) the signal on a discrete sphere. This may confer a significant speed-up in setting up the problem, but is not as accurate. If False, we use the exact gradients along the streamlines to calculate the matrix, instead of an approximation.

Returns
FiberFit class instance
setup(streamline, affine, evals=[0.001, 0, 0], sphere=None)

Set up the necessary components for the LiFE model: the matrix of fiber-contributions to the DWI signal, and the coordinates of voxels for which the equations will be solved

Parameters
streamlinelist

Streamlines, each is an array of shape (n, 3)

affinearray_like (4, 4)

The mapping from voxel coordinates to streamline points. The voxel_to_rasmm matrix, typically from a NIFTI file.

evalslist (3 items, optional)

The eigenvalues of the canonical tensor used as a response function. Default:[0.001, 0, 0].

sphere: dipy.core.Sphere instance.

Whether to approximate (and cache) the signal on a discrete sphere. This may confer a significant speed-up in setting up the problem, but is not as accurate. If False, we use the exact gradients along the streamlines to calculate the matrix, instead of an approximation. Defaults to use the 724-vertex symmetric sphere from dipy.data

### LifeSignalMaker

class dipy.tracking.life.LifeSignalMaker(gtab, evals=[0.001, 0, 0], sphere=None)

Bases: object

A class for generating signals from streamlines in an efficient and speedy manner.

Methods

 streamline_signal(streamline) Approximate the signal for a given streamline
 calc_signal
__init__(gtab, evals=[0.001, 0, 0], sphere=None)

Initialize a signal maker

Parameters

The gradient table on which the signal is calculated.

evalslist of 3 items

The eigenvalues of the canonical tensor to use in calculating the signal.

spheredipy.core.Sphere class instance

The discrete sphere to use as an approximation for the continuous sphere on which the signal is represented. If integer - we will use an instance of one of the symmetric spheres cached in dps.get_sphere. If a ‘dipy.core.Sphere’ class instance is provided, we will use this object. Default: the dipy.data symmetric sphere with 724 vertices

calc_signal(xyz)
streamline_signal(streamline)

Approximate the signal for a given streamline

### ReconstFit

class dipy.tracking.life.ReconstFit(model, data)

Bases: object

Abstract class which holds the fit result of ReconstModel

For example that could be holding FA or GFA etc.

__init__(model, data)

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

### ReconstModel

class dipy.tracking.life.ReconstModel(gtab)

Bases: object

Abstract class for signal reconstruction models

Methods

 fit
__init__(gtab)

Initialization of the abstract class for signal reconstruction models

Parameters

Calculate the 3 by 3 tensor for a given spatial gradient, given a canonical tensor shape (also as a 3 by 3), pointing at [1,0,0]

Parameters

The spatial gradient (e.g between two nodes of a streamline).

evals: 1d array of shape (3,)

The eigenvalues of a canonical tensor to be used as a response function.

Return the gradient of an N-dimensional array.

The gradient is computed using central differences in the interior and first differences at the boundaries. The returned gradient hence has the same shape as the input array.

Parameters
farray_like

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

Returns

N arrays of the same shape as f giving the derivative of f with respect to each dimension.

Notes

This is a simplified implementation of gradient that is part of numpy 1.8. In order to mitigate the effects of changes added to this implementation in version 1.9 of numpy, we include this implementation here.

Examples

>>> x = np.array([1, 2, 4, 7, 11, 16], dtype=np.float)
array([ 1. ,  1.5,  2.5,  3.5,  4.5,  5. ])
>>> gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=np.float))
[array([[ 2.,  2., -1.],
[ 2.,  2., -1.]]), array([[ 1. ,  2.5,  4. ],
[ 1. ,  1. ,  1. ]])]

Calculate the gradients of the streamline along the spatial dimension

Parameters
streamlinearray-like of shape (n, 3)

The 3d coordinates of a single streamline

Returns
Array of shape (3, n): Spatial gradients along the length of the
streamline.

### streamline_signal

dipy.tracking.life.streamline_signal(streamline, gtab, evals=[0.001, 0, 0])

The signal from a single streamline estimate along each of its nodes.

Parameters
streamlinea single streamline
evalslist of length 3 (optional. Default: [0.001, 0, 0])

The eigenvalues of the canonical tensor used as an estimate of the signal generated by each node of the streamline.

### streamline_tensors

dipy.tracking.life.streamline_tensors(streamline, evals=[0.001, 0, 0])

The tensors generated by this fiber.

Parameters
streamlinearray-like of shape (n, 3)

The 3d coordinates of a single streamline

evalsiterable with three entries

The estimated eigenvalues of a single fiber tensor. (default: [0.001, 0, 0]).

Returns
An n_nodes by 3 by 3 array with the tensor for each node in the fiber.

Notes

Estimates of the radial/axial diffusivities may rely on empirical measurements (for example, the AD in the Corpus Callosum), or may be based on a biophysical model of some kind.

### transform_streamlines

dipy.tracking.life.transform_streamlines(streamlines, mat, in_place=False)

Apply affine transformation to streamlines

Parameters
streamlinesStreamlines

Streamlines object

matarray, (4, 4)

transformation matrix

in_placebool

If True then change data in place. Be careful changes input streamlines.

Returns
new_streamlinesStreamlines

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

### unique_rows

dipy.tracking.life.unique_rows(in_array, dtype='f4')

This (quickly) finds the unique rows in an array

Parameters
in_array: ndarray

The array for which the unique rows should be found

dtype: str, optional

This determines the intermediate representation used for the values. Should at least preserve the values of the input array.

Returns
u_return: ndarray

Array with the unique rows of the original array.

### voxel2streamline

dipy.tracking.life.voxel2streamline(streamline, affine, unique_idx=None)

Maps voxels to streamlines and streamlines to voxels, for setting up the LiFE equations matrix

Parameters
streamlinelist

A collection of streamlines, each n by 3, with n being the number of nodes in the fiber.

affinearray_like (4, 4)

The mapping from voxel coordinates to streamline points. The voxel_to_rasmm matrix, typically from a NIFTI file.

unique_idxarray (optional).

The unique indices in the streamlines

Returns
v2f, v2fntuple of dicts
The first dict in the tuple answers the question: Given a voxel (from
the unique indices in this model), which fibers pass through it?
The second answers the question: Given a streamline, for each voxel that
this streamline passes through, which nodes of that streamline are in that
voxel?

### AnatomicalStoppingCriterion

class dipy.tracking.local_tracking.AnatomicalStoppingCriterion

Bases: dipy.tracking.stopping_criterion.StoppingCriterion

Abstract class that takes as input included and excluded tissue maps. The ‘include_map’ defines when the streamline reached a ‘valid’ stopping region (e.g. gray matter partial volume estimation (PVE) map) and the ‘exclude_map’ defines when the streamline reached an ‘invalid’ stopping region (e.g. corticospinal fluid PVE map). The background of the anatomical image should be added to the ‘include_map’ to keep streamlines exiting the brain (e.g. through the brain stem).

cdef:

double interp_out_double[1] double[:] interp_out_view = interp_out_view double[:, :, :] include_map, exclude_map

Methods

 from_pve AnatomicalStoppingCriterion from partial volume fraction (PVE) maps.
 check_point get_exclude get_include
__init__(*args, **kwargs)

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

from_pve()

AnatomicalStoppingCriterion from partial volume fraction (PVE) maps.

Parameters
wm_maparray

The partial volume fraction of white matter at each voxel.

gm_maparray

The partial volume fraction of gray matter at each voxel.

csf_maparray

The partial volume fraction of corticospinal fluid at each voxel.

get_exclude()
get_include()

### Iterable

class dipy.tracking.local_tracking.Iterable

Bases: object

__init__(*args, **kwargs)

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

### LocalTracking

class dipy.tracking.local_tracking.LocalTracking(direction_getter, stopping_criterion, seeds, affine, step_size, max_cross=None, maxlen=500, fixedstep=True, return_all=True, random_seed=None, save_seeds=False)

Bases: object

__init__(direction_getter, stopping_criterion, seeds, affine, step_size, max_cross=None, maxlen=500, fixedstep=True, return_all=True, random_seed=None, save_seeds=False)

Creates streamlines by using local fiber-tracking.

Parameters
direction_getterinstance of DirectionGetter

Used to get directions for fiber tracking.

stopping_criterioninstance of StoppingCriterion

Identifies endpoints and invalid points to inform tracking.

seedsarray (N, 3)

Points to seed the tracking. Seed points should be given in point space of the track (see affine).

affinearray (4, 4)

Coordinate space for the streamline point with respect to voxel indices of input data. This affine can contain scaling, rotational, and translational components but should not contain any shearing. An identity matrix can be used to generate streamlines in “voxel coordinates” as long as isotropic voxels were used to acquire the data.

step_sizefloat

Step size used for tracking.

max_crossint or None

The maximum number of direction to track from each seed in crossing voxels. By default all initial directions are tracked.

maxlenint

Maximum number of steps to track from seed. Used to prevent infinite loops.

fixedstepbool

If true, a fixed stepsize is used, otherwise a variable step size is used.

return_allbool

If true, return all generated streamlines, otherwise only streamlines reaching end points or exiting the image.

random_seedint

The seed for the random seed generator (numpy.random.seed and random.seed).

save_seedsbool

If True, return seeds alongside streamlines

### ParticleFilteringTracking

class dipy.tracking.local_tracking.ParticleFilteringTracking(direction_getter, stopping_criterion, seeds, affine, step_size, max_cross=None, maxlen=500, pft_back_tracking_dist=2, pft_front_tracking_dist=1, pft_max_trial=20, particle_count=15, return_all=True, random_seed=None, save_seeds=False)
__init__(direction_getter, stopping_criterion, seeds, affine, step_size, max_cross=None, maxlen=500, pft_back_tracking_dist=2, pft_front_tracking_dist=1, pft_max_trial=20, particle_count=15, return_all=True, random_seed=None, save_seeds=False)

A streamline generator using the particle filtering tractography method [1].

Parameters
direction_getterinstance of ProbabilisticDirectionGetter

Used to get directions for fiber tracking.

stopping_criterioninstance of AnatomicalStoppingCriterion

Identifies endpoints and invalid points to inform tracking.

seedsarray (N, 3)

Points to seed the tracking. Seed points should be given in point space of the track (see affine).

affinearray (4, 4)

Coordinate space for the streamline point with respect to voxel indices of input data. This affine can contain scaling, rotational, and translational components but should not contain any shearing. An identity matrix can be used to generate streamlines in “voxel coordinates” as long as isotropic voxels were used to acquire the data.

step_sizefloat

Step size used for tracking.

max_crossint or None

The maximum number of direction to track from each seed in crossing voxels. By default all initial directions are tracked.

maxlenint

Maximum number of steps to track from seed. Used to prevent infinite loops.

pft_back_tracking_distfloat

Distance in mm to back track before starting the particle filtering tractography. The total particle filtering tractography distance is equal to back_tracking_dist + front_tracking_dist. By default this is set to 2 mm.

pft_front_tracking_distfloat

Distance in mm to run the particle filtering tractography after the the back track distance. The total particle filtering tractography distance is equal to back_tracking_dist + front_tracking_dist. By default this is set to 1 mm.

pft_max_trialint

Maximum number of trial for the particle filtering tractography (Prevents infinite loops).

particle_countint

Number of particles to use in the particle filter.

return_allbool

If true, return all generated streamlines, otherwise only streamlines reaching end points or exiting the image.

random_seedint

The seed for the random seed generator (numpy.random.seed and random.seed).

save_seedsbool

If True, return seeds alongside streamlines

References

1

Girard, G., Whittingstall, K., Deriche, R., & Descoteaux, M. Towards quantitative connectivity analysis: reducing tractography biases. NeuroImage, 98, 266-278, 2014.

### StreamlineStatus

class dipy.tracking.local_tracking.StreamlineStatus

Bases: enum.IntEnum

An enumeration.

__init__(*args, **kwargs)

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

ENDPOINT = 2
INVALIDPOINT = 0
OUTSIDEIMAGE = -1
PYERROR = -2
TRACKPOINT = 1

### local_tracker

dipy.tracking.local_tracking.local_tracker()

Tracks one direction from a seed.

This function is the main workhorse of the LocalTracking class defined in dipy.tracking.local_tracking.

Parameters
dgDirectionGetter

Used to choosing tracking directions.

scStoppingCriterion

Used to check the streamline status (e.g. endpoint) along path.

seed_posarray, float, 1d, (3,)

First point of the (partial) streamline.

first_steparray, float, 1d, (3,)

Initial seeding direction. Used as prev_dir for selecting the step direction from the seed point.

voxel_sizearray, float, 1d, (3,)

Size of voxels in the data set.

streamlinearray, float, 2d, (N, 3)

Output of tracking will be put into this array. The length of this array, N, will set the maximum allowable length of the streamline.

step_sizefloat

Size of tracking steps in mm if fixed_step.

fixedstepbool

If true, a fixed step_size is used, otherwise a variable step size is used.

Returns
endint

Length of the tracked streamline

stream_statusStreamlineStatus

Ending state of the streamlines as determined by the StoppingCriterion.

### pft_tracker

dipy.tracking.local_tracking.pft_tracker()

Tracks one direction from a seed using the particle filtering algorithm.

This function is the main workhorse of the ParticleFilteringTracking class defined in dipy.tracking.local_tracking.

Parameters
dgDirectionGetter

Used to choosing tracking directions.

scAnatomicalStoppingCriterion

Used to check the streamline status (e.g. endpoint) along path.

seed_posarray, float, 1d, (3,)

First point of the (partial) streamline.

first_steparray, float, 1d, (3,)

Initial seeding direction. Used as prev_dir for selecting the step direction from the seed point.

voxel_sizearray, float, 1d, (3,)

Size of voxels in the data set.

streamlinearray, float, 2d, (N, 3)

Output of tracking will be put into this array. The length of this array, N, will set the maximum allowable length of the streamline.

directionsarray, float, 2d, (N, 3)

Output of tracking directions will be put into this array. The length of this array, N, will set the maximum allowable length of the streamline.

step_sizefloat

Size of tracking steps in mm if fixed_step.

pft_max_nbr_back_stepsint

Number of tracking steps to back track before starting the particle filtering tractography.

pft_max_nbr_front_stepsint

Number of additional tracking steps to track.

pft_max_trialsint

Maximum number of trials for the particle filtering tractography (Prevents infinite loops).

particle_countint

Number of particles to use in the particle filter.

particle_pathsarray, float, 4d, (2, particle_count, pft_max_steps, 3)

Temporary array for paths followed by all particles.

particle_dirsarray, float, 4d, (2, particle_count, pft_max_steps, 3)

Temporary array for directions followed by particles.

particle_weightsarray, float, 1d (particle_count)

Temporary array for the weights of particles.

particle_stepsarray, float, (2, particle_count)

Temporary array for the number of steps of particles.

particle_stream_statusesarray, float, (2, particle_count)

Temporary array for the stream status of particles.

Returns
endint

Length of the tracked streamline

stream_statusStreamlineStatus

Ending state of the streamlines as determined by the StoppingCriterion.

### arbitrarypoint

dipy.tracking.metrics.arbitrarypoint(xyz, distance)

Select an arbitrary point along distance on the track (curve)

Parameters
xyzarray-like shape (N,3)

array representing x,y,z of N points in a track

distancefloat

float representing distance travelled from the xyz[0] point of the curve along the curve.

Returns
aparray shape (3,)

Arbitrary point of line, such that, if the arbitrary point is not a point in xyz, then we take the interpolation between the two nearest xyz points. If xyz is empty, return a ValueError

Examples

>>> import numpy as np
>>> from dipy.tracking.metrics import arbitrarypoint, length
>>> theta=np.pi*np.linspace(0,1,100)
>>> x=np.cos(theta)
>>> y=np.sin(theta)
>>> z=0*x
>>> xyz=np.vstack((x,y,z)).T
>>> ap=arbitrarypoint(xyz,length(xyz)/3)

### bytes

dipy.tracking.metrics.bytes(xyz)

Size of track in bytes.

Parameters
xyzarray-like shape (N,3)

Array representing x,y,z of N points in a track.

Returns
bint

Number of bytes.

### center_of_mass

dipy.tracking.metrics.center_of_mass(xyz)

Center of mass of streamline

Parameters
xyzarray-like shape (N,3)

array representing x,y,z of N points in a track

Returns
comarray shape (3,)

center of mass of streamline

Examples

>>> from dipy.tracking.metrics import center_of_mass
>>> center_of_mass([])
Traceback (most recent call last):
...
ValueError: xyz array cannot be empty
>>> center_of_mass([[1,1,1]])
array([ 1.,  1.,  1.])
>>> xyz = np.array([[0,0,0],[1,1,1],[2,2,2]])
>>> center_of_mass(xyz)
array([ 1.,  1.,  1.])

### deprecate_with_version

dipy.tracking.metrics.deprecate_with_version(message, since='', until='', version_comparator=<function cmp_pkg_version>, warn_class=<class 'DeprecationWarning'>, error_class=<class 'dipy.utils.deprecator.ExpiredDeprecationError'>)

Return decorator function function for deprecation warning / error.

The decorated function / method will:

• Raise the given warning_class warning when the function / method gets called, up to (and including) version until (if specified);

• Raise the given error_class error when the function / method gets called, when the package version is greater than version until (if specified).

Parameters
messagestr

Message explaining deprecation, giving possible alternatives.

sincestr, optional

Released version at which object was first deprecated.

untilstr, optional

Last released version at which this function will still raise a deprecation warning. Versions higher than this will raise an error.

version_comparatorcallable

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.

warn_classclass, optional

Class of warning to generate for deprecation.

error_classclass, optional

Class of error to generate when version_comparator returns 1 for a given argument of until.

Returns
deprecatorfunc

Function returning a decorator.

### downsample

dipy.tracking.metrics.downsample(xyz, n_pols=3)

downsample for a specific number of points along the streamline Uses the length of the curve. It works in a similar fashion to midpoint and arbitrarypoint but it also reduces the number of segments of a streamline.

• deprecated from version: 1.2

• Will raise <class ‘dipy.utils.deprecator.ExpiredDeprecationError’> as of version: 1.4

Parameters
xyzarray-like shape (N,3)

array representing x,y,z of N points in a streamlines

n_polint

integer representing number of points (poles) we need along the curve.

Returns
xyz2array shape (M,3)

array representing x,y,z of M points that where extrapolated. M should be equal to n_pols

### endpoint

dipy.tracking.metrics.endpoint(xyz)
Parameters
xyzarray, shape(N,3)

Track.

Returns
eparray, shape(3,)

First track point.

Examples

>>> from dipy.tracking.metrics import endpoint
>>> import numpy as np
>>> theta=np.pi*np.linspace(0,1,100)
>>> x=np.cos(theta)
>>> y=np.sin(theta)
>>> z=0*x
>>> xyz=np.vstack((x,y,z)).T
>>> ep=endpoint(xyz)
>>> ep.any()==xyz[-1].any()
True

### frenet_serret

dipy.tracking.metrics.frenet_serret(xyz)

Frenet-Serret Space Curve Invariants

Calculates the 3 vector and 2 scalar invariants of a space curve defined by vectors r = (x,y,z). If z is omitted (i.e. the array xyz has shape (N,2)), then the curve is only 2D (planar), but the equations are still valid.

In the following equations the prime ($$'$$) indicates differentiation with respect to the parameter $$s$$ of a parametrised curve $$\mathbf{r}(s)$$.

• $$\mathbf{T}=\mathbf{r'}/|\mathbf{r'}|\qquad$$ (Tangent vector)}

• $$\mathbf{N}=\mathbf{T'}/|\mathbf{T'}|\qquad$$ (Normal vector)

• $$\mathbf{B}=\mathbf{T}\times\mathbf{N}\qquad$$ (Binormal vector)

• $$\kappa=|\mathbf{T'}|\qquad$$ (Curvature)

• $$\mathrm{\tau}=-\mathbf{B'}\cdot\mathbf{N}$$ (Torsion)

Parameters
xyzarray-like shape (N,3)

array representing x,y,z of N points in a track

Returns
Tarray shape (N,3)

array representing the tangent of the curve xyz

Narray shape (N,3)

array representing the normal of the curve xyz

Barray shape (N,3)

array representing the binormal of the curve xyz

karray shape (N,1)

array representing the curvature of the curve xyz

tarray shape (N,1)

array representing the torsion of the curve xyz

Examples

Create a helix and calculate its tangent, normal, binormal, curvature and torsion

>>> from dipy.tracking import metrics as tm
>>> import numpy as np
>>> theta = 2*np.pi*np.linspace(0,2,100)
>>> x=np.cos(theta)
>>> y=np.sin(theta)
>>> z=theta/(2*np.pi)
>>> xyz=np.vstack((x,y,z)).T
>>> T,N,B,k,t=tm.frenet_serret(xyz)

### generate_combinations

dipy.tracking.metrics.generate_combinations(items, n)

Combine sets of size n from items

Parameters
itemssequence
nint
Returns
iciterator

Examples

>>> from dipy.tracking.metrics import generate_combinations
>>> ic=generate_combinations(range(3),2)
>>> for i in ic: print(i)
[0, 1]
[0, 2]
[1, 2]

### inside_sphere

If any point of the track is inside a sphere of a specified center and radius return True otherwise False. Mathematicaly this can be simply described by $$|x-c|\le r$$ where $$x$$ a point $$c$$ the center of the sphere and $$r$$ the radius of the sphere.

Parameters
xyzarray, shape (N,3)

representing x,y,z of the N points of the track

centerarray, shape (3,)

center of the sphere

Returns
tf{True,False}

Whether point is inside sphere.

Examples

>>> from dipy.tracking.metrics import inside_sphere
>>> line=np.array(([0,0,0],[1,1,1],[2,2,2]))
>>> sph_cent=np.array([1,1,1])
True

### inside_sphere_points

If a track intersects with a sphere of a specified center and radius return the points that are inside the sphere otherwise False. Mathematicaly this can be simply described by $$|x-c| \le r$$ where $$x$$ a point $$c$$ the center of the sphere and $$r$$ the radius of the sphere.

Parameters
xyzarray, shape (N,3)

representing x,y,z of the N points of the track

centerarray, shape (3,)

center of the sphere

Returns
xyznarray, shape(M,3)

array representing x,y,z of the M points inside the sphere

Examples

>>> from dipy.tracking.metrics import inside_sphere_points
>>> line=np.array(([0,0,0],[1,1,1],[2,2,2]))
>>> sph_cent=np.array([1,1,1])
array([[1, 1, 1]])

### intersect_sphere

If any segment of the track is intersecting with a sphere of specific center and radius return True otherwise False

Parameters
xyzarray, shape (N,3)

representing x,y,z of the N points of the track

centerarray, shape (3,)

center of the sphere

Returns
tf{True, False}

True if track xyz intersects sphere

>>> from dipy.tracking.metrics import intersect_sphere
..
>>> line=np.array(([0,0,0],[1,1,1],[2,2,2]))
..
>>> sph_cent=np.array([1,1,1])
..
..
..
True

Notes

The ray to sphere intersection method used here is similar with http://local.wasp.uwa.edu.au/~pbourke/geometry/sphereline/ http://local.wasp.uwa.edu.au/~pbourke/geometry/sphereline/source.cpp we just applied it for every segment neglecting the intersections where the intersecting points are not inside the segment

### length

dipy.tracking.metrics.length(xyz, along=False)

Euclidean length of track line

This will give length in mm if tracks are expressed in world coordinates.

Parameters
xyzarray-like shape (N,3)

array representing x,y,z of N points in a track

alongbool, optional

If True, return array giving cumulative length along track, otherwise (default) return scalar giving total length.

Returns
Lscalar or array shape (N-1,)

scalar in case of along == False, giving total length, array if along == True, giving cumulative lengths.

Examples

>>> from dipy.tracking.metrics import length
>>> xyz = np.array([[1,1,1],[2,3,4],[0,0,0]])
>>> expected_lens = np.sqrt([1+2**2+3**2, 2**2+3**2+4**2])
>>> length(xyz) == expected_lens.sum()
True
>>> len_along = length(xyz, along=True)
>>> np.allclose(len_along, expected_lens.cumsum())
True
>>> length([])
0
>>> length([[1, 2, 3]])
0
>>> length([], along=True)
array([0])

### longest_track_bundle

dipy.tracking.metrics.longest_track_bundle(bundle, sort=False)

Return longest track or length sorted track indices in bundle

If sort == True, return the indices of the sorted tracks in the bundle, otherwise return the longest track.

Parameters
bundlesequence

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

sortbool, optional

If False (default) return longest track. If True, return length sorted indices for tracks in bundle

Returns
longest_or_indicesarray

longest track - shape (N,3) - (if sort is False), or indices of length sorted tracks (if sort is True)

Examples

>>> from dipy.tracking.metrics import longest_track_bundle
>>> import numpy as np
>>> bundle = [np.array([[0,0,0],[2,2,2]]),np.array([[0,0,0],[4,4,4]])]
>>> longest_track_bundle(bundle)
array([[0, 0, 0],
[4, 4, 4]])
>>> longest_track_bundle(bundle, True)
array([0, 1]...)

### magn

dipy.tracking.metrics.magn(xyz, n=1)

magnitude of vector

### mean_curvature

dipy.tracking.metrics.mean_curvature(xyz)

Calculates the mean curvature of a curve

Parameters
xyzarray-like shape (N,3)

array representing x,y,z of N points in a curve

Returns
mfloat

Mean curvature.

Examples

Create a straight line and a semi-circle and print their mean curvatures

>>> from dipy.tracking import metrics as tm
>>> import numpy as np
>>> x=np.linspace(0,1,100)
>>> y=0*x
>>> z=0*x
>>> xyz=np.vstack((x,y,z)).T
>>> m=tm.mean_curvature(xyz) #mean curvature straight line
>>> theta=np.pi*np.linspace(0,1,100)
>>> x=np.cos(theta)
>>> y=np.sin(theta)
>>> z=0*x
>>> xyz=np.vstack((x,y,z)).T
>>> _= tm.mean_curvature(xyz) #mean curvature for semi-circle

### mean_orientation

dipy.tracking.metrics.mean_orientation(xyz)

Calculates the mean orientation of a curve

Parameters
xyzarray-like shape (N,3)

array representing x,y,z of N points in a curve

Returns
mfloat

Mean orientation.

### midpoint

dipy.tracking.metrics.midpoint(xyz)

Midpoint of track

Parameters
xyzarray-like shape (N,3)

array representing x,y,z of N points in a track

Returns
mparray shape (3,)

Middle point of line, such that, if L is the line length then np is the point such that the length xyz[0] to mp and from mp to xyz[-1] is L/2. If the middle point is not a point in xyz, then we take the interpolation between the two nearest xyz points. If xyz is empty, return a ValueError

Examples

>>> from dipy.tracking.metrics import midpoint
>>> midpoint([])
Traceback (most recent call last):
...
ValueError: xyz array cannot be empty
>>> midpoint([[1, 2, 3]])
array([1, 2, 3])
>>> xyz = np.array([[1,1,1],[2,3,4]])
>>> midpoint(xyz)
array([ 1.5,  2. ,  2.5])
>>> xyz = np.array([[0,0,0],[1,1,1],[2,2,2]])
>>> midpoint(xyz)
array([ 1.,  1.,  1.])
>>> xyz = np.array([[0,0,0],[1,0,0],[3,0,0]])
>>> midpoint(xyz)
array([ 1.5,  0. ,  0. ])
>>> xyz = np.array([[0,9,7],[1,9,7],[3,9,7]])
>>> midpoint(xyz)
array([ 1.5,  9. ,  7. ])

### midpoint2point

dipy.tracking.metrics.midpoint2point(xyz, p)

Calculate distance from midpoint of a curve to arbitrary point p

Parameters
xyzarray-like shape (N,3)

array representing x,y,z of N points in a track

parray shape (3,)

array representing an arbitrary point with x,y,z coordinates in space.

Returns
dfloat

a float number representing Euclidean distance

Examples

>>> import numpy as np
>>> from dipy.tracking.metrics import midpoint2point, midpoint
>>> theta=np.pi*np.linspace(0,1,100)
>>> x=np.cos(theta)
>>> y=np.sin(theta)
>>> z=0*x
>>> xyz=np.vstack((x,y,z)).T
>>> dist=midpoint2point(xyz,np.array([0,0,0]))

### principal_components

dipy.tracking.metrics.principal_components(xyz)

We use PCA to calculate the 3 principal directions for a track

Parameters
xyzarray-like shape (N,3)

array representing x,y,z of N points in a track

Returns
vaarray_like

eigenvalues

vearray_like

eigenvectors

Examples

>>> import numpy as np
>>> from dipy.tracking.metrics import principal_components
>>> theta=np.pi*np.linspace(0,1,100)
>>> x=np.cos(theta)
>>> y=np.sin(theta)
>>> z=0*x
>>> xyz=np.vstack((x,y,z)).T
>>> va, ve = principal_components(xyz)
>>> np.allclose(va, [0.51010101, 0.09883545, 0])
True

### set_number_of_points

dipy.tracking.metrics.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
streamlinesndarray 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_pointsint

integer representing number of points wanted along the curve.

Returns
new_streamlinesndarray 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]

### splev

dipy.tracking.metrics.splev(x, tck, der=0, ext=0)

Evaluate a B-spline or its derivatives.

Given the knots and coefficients of a B-spline representation, evaluate the value of the smoothing polynomial and its derivatives. This is a wrapper around the FORTRAN routines splev and splder of FITPACK.

Parameters
xarray_like

An array of points at which to return the value of the smoothed spline or its derivatives. If tck was returned from splprep, then the parameter values, u should be given.

tck3-tuple or a BSpline object

If a tuple, then it should be a sequence of length 3 returned by splrep or splprep containing the knots, coefficients, and degree of the spline. (Also see Notes.)

derint, optional

The order of derivative of the spline to compute (must be less than or equal to k, the degree of the spline).

extint, optional

Controls the value returned for elements of x not in the interval defined by the knot sequence.

• if ext=0, return the extrapolated value.

• if ext=1, return 0

• if ext=2, raise a ValueError

• if ext=3, return the boundary value.

The default value is 0.

Returns
yndarray or list of ndarrays

An array of values representing the spline function evaluated at the points in x. If tck was returned from splprep, then this is a list of arrays representing the curve in an N-D space.

splprep, splrep, sproot, spalde, splint
bisplrep, bisplev
BSpline

Notes

Manipulating the tck-tuples directly is not recommended. In new code, prefer using BSpline objects.

References

1

C. de Boor, “On calculating with b-splines”, J. Approximation Theory, 6, p.50-62, 1972.

2

M. G. Cox, “The numerical evaluation of b-splines”, J. Inst. Maths Applics, 10, p.134-149, 1972.

3

P. Dierckx, “Curve and surface fitting with splines”, Monographs on Numerical Analysis, Oxford University Press, 1993.

### spline

dipy.tracking.metrics.spline(xyz, s=3, k=2, nest=-1)

Generate B-splines as documented in http://www.scipy.org/Cookbook/Interpolation

The scipy.interpolate packages wraps the netlib FITPACK routines (Dierckx) for calculating smoothing splines for various kinds of data and geometries. Although the data is evenly spaced in this example, it need not be so to use this routine.

Parameters
xyzarray, shape (N,3)

array representing x,y,z of N points in 3d space

sfloat, optional

A smoothing condition. The amount of smoothness is determined by satisfying the conditions: sum((w * (y - g))**2,axis=0) <= s where g(x) is the smoothed interpolation of (x,y). The user can use s to control the tradeoff between closeness and smoothness of fit. Larger satisfying the conditions: sum((w * (y - g))**2,axis=0) <= s where g(x) is the smoothed interpolation of (x,y). The user can use s to control the tradeoff between closeness and smoothness of fit. Larger s means more smoothing while smaller values of s indicate less smoothing. Recommended values of s depend on the weights, w. If the weights represent the inverse of the standard-deviation of y, then a: good s value should be found in the range (m-sqrt(2*m),m+sqrt(2*m)) where m is the number of datapoints in x, y, and w.

kint, optional

Degree of the spline. Cubic splines are recommended. Even values of k should be avoided especially with a small s-value. for the same set of data. If task=-1 find the weighted least square spline for a given set of knots, t.

nestNone or int, optional

An over-estimate of the total number of knots of the spline to help in determining the storage space. None results in value m+2*k. -1 results in m+k+1. Always large enough is nest=m+k+1. Default is -1.

Returns
xyznarray, shape (M,3)

array representing x,y,z of the M points inside the sphere

scipy.interpolate.splprep
scipy.interpolate.splev

Examples

>>> import numpy as np
>>> t=np.linspace(0,1.75*2*np.pi,100)# make ascending spiral in 3-space
>>> x = np.sin(t)
>>> y = np.cos(t)
>>> z = t
>>> x+= np.random.normal(scale=0.1, size=x.shape) # add noise
>>> y+= np.random.normal(scale=0.1, size=y.shape)
>>> z+= np.random.normal(scale=0.1, size=z.shape)
>>> xyz=np.vstack((x,y,z)).T
>>> xyzn=spline(xyz,3,2,-1)
>>> len(xyzn) > len(xyz)
True

### splprep

dipy.tracking.metrics.splprep(x, w=None, u=None, ub=None, ue=None, k=3, task=0, s=None, t=None, full_output=0, nest=None, per=0, quiet=1)

Find the B-spline representation of an N-D curve.

Given a list of N rank-1 arrays, x, which represent a curve in N-D space parametrized by u, find a smooth approximating spline curve g(u). Uses the FORTRAN routine parcur from FITPACK.

Parameters
xarray_like

A list of sample vector arrays representing the curve.

warray_like, optional

Strictly positive rank-1 array of weights the same length as x[0]. The weights are used in computing the weighted least-squares spline fit. If the errors in the x values have standard-deviation given by the vector d, then w should be 1/d. Default is ones(len(x[0])).

uarray_like, optional

An array of parameter values. If not given, these values are calculated automatically as M = len(x[0]), where

v[0] = 0

v[i] = v[i-1] + distance(x[i], x[i-1])

u[i] = v[i] / v[M-1]

ub, ueint, optional

The end-points of the parameters interval. Defaults to u[0] and u[-1].

kint, optional

Degree of the spline. Cubic splines are recommended. Even values of k should be avoided especially with a small s-value. 1 <= k <= 5, default is 3.

If task==0 (default), find t and c for a given smoothing factor, s. If task==1, find t and c for another value of the smoothing factor, s. There must have been a previous call with task=0 or task=1 for the same set of data. If task=-1 find the weighted least square spline for a given set of knots, t.

sfloat, optional

A smoothing condition. The amount of smoothness is determined by satisfying the conditions: sum((w * (y - g))**2,axis=0) <= s, where g(x) is the smoothed interpolation of (x,y). The user can use s to control the trade-off between closeness and smoothness of fit. Larger s means more smoothing while smaller values of s indicate less smoothing. Recommended values of s depend on the weights, w. If the weights represent the inverse of the standard-deviation of y, then a good s value should be found in the range (m-sqrt(2*m),m+sqrt(2*m)), where m is the number of data points in x, y, and w.

tint, optional

full_outputint, optional

If non-zero, then return optional outputs.

nestint, optional

An over-estimate of the total number of knots of the spline to help in determining the storage space. By default nest=m/2. Always large enough is nest=m+k+1.

perint, optional

If non-zero, data points are considered periodic with period x[m-1] - x[0] and a smooth periodic spline approximation is returned. Values of y[m-1] and w[m-1] are not used.

quietint, optional

Non-zero to suppress messages. This parameter is deprecated; use standard Python warning filters instead.

Returns
tcktuple

(t,c,k) a tuple containing the vector of knots, the B-spline coefficients, and the degree of the spline.

uarray

An array of the values of the parameter.

fpfloat

The weighted sum of squared residuals of the spline approximation.

ierint

An integer flag about splrep success. Success is indicated if ier<=0. If ier in [1,2,3] an error occurred but was not raised. Otherwise an error is raised.

msgstr

A message corresponding to the integer flag, ier.

splrep, splev, sproot, spalde, splint
bisplrep, bisplev
UnivariateSpline, BivariateSpline
BSpline
make_interp_spline

Notes

See splev for evaluation of the spline and its derivatives. The number of dimensions N must be smaller than 11.

The number of coefficients in the c array is k+1 less then the number of knots, len(t). This is in contrast with splrep, which zero-pads the array of coefficients to have the same length as the array of knots. These additional coefficients are ignored by evaluation routines, splev and BSpline.

References

1

P. Dierckx, “Algorithms for smoothing data with periodic and parametric splines, Computer Graphics and Image Processing”, 20 (1982) 171-184.

2

P. Dierckx, “Algorithms for smoothing data with periodic and parametric splines”, report tw55, Dept. Computer Science, K.U.Leuven, 1981.

3

P. Dierckx, “Curve and surface fitting with splines”, Monographs on Numerical Analysis, Oxford University Press, 1993.

Examples

Generate a discretization of a limacon curve in the polar coordinates:

>>> phi = np.linspace(0, 2.*np.pi, 40)
>>> r = 0.5 + np.cos(phi)         # polar coords
>>> x, y = r * np.cos(phi), r * np.sin(phi)    # convert to cartesian

And interpolate:

>>> from scipy.interpolate import splprep, splev
>>> tck, u = splprep([x, y], s=0)
>>> new_points = splev(u, tck)

Notice that (i) we force interpolation by using s=0, (ii) the parameterization, u, is generated automatically. Now plot the result:

>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots()
>>> ax.plot(x, y, 'ro')
>>> ax.plot(new_points[0], new_points[1], 'r-')
>>> plt.show()

### startpoint

dipy.tracking.metrics.startpoint(xyz)

First point of the track

Parameters
xyzarray, shape(N,3)

Track.

Returns
sparray, shape(3,)

First track point.

Examples

>>> from dipy.tracking.metrics import startpoint
>>> import numpy as np
>>> theta=np.pi*np.linspace(0,1,100)
>>> x=np.cos(theta)
>>> y=np.sin(theta)
>>> z=0*x
>>> xyz=np.vstack((x,y,z)).T
>>> sp=startpoint(xyz)
>>> sp.any()==xyz[0].any()
True

### winding

dipy.tracking.metrics.winding(xyz)

Total turning angle projected.

Project space curve to best fitting plane. Calculate the cumulative signed angle between each line segment and the previous one.

Parameters
xyzarray-like shape (N,3)

Array representing x,y,z of N points in a track.

Returns
ascalar

Total turning angle in degrees.

### Streamlines

dipy.tracking.streamline.Streamlines

alias of nibabel.streamlines.array_sequence.ArraySequence

### apply_affine

dipy.tracking.streamline.apply_affine(aff, pts)

Apply affine matrix aff to points pts

Returns result of application of aff to the right of pts. The coordinate dimension of pts should be the last.

For the 3D case, aff will be shape (4,4) and pts will have final axis length 3 - maybe it will just be N by 3. The return value is the transformed points, in this case:

res = np.dot(aff[:3,:3], pts.T) + aff[:3,3:4]
transformed_pts = res.T

This routine is more general than 3D, in that aff can have any shape (N,N), and pts can have any shape, as long as the last dimension is for the coordinates, and is therefore length N-1.

Parameters
aff(N, N) array-like

Homogenous affine, for 3D points, will be 4 by 4. Contrary to first appearance, the affine will be applied on the left of pts.

pts(…, N-1) array-like

Points, where the last dimension contains the coordinates of each point. For 3D, the last dimension will be length 3.

Returns
transformed_pts(…, N-1) array

transformed points

Examples

>>> aff = np.array([[0,2,0,10],[3,0,0,11],[0,0,4,12],[0,0,0,1]])
>>> pts = np.array([[1,2,3],[2,3,4],[4,5,6],[6,7,8]])
>>> apply_affine(aff, pts)
array([[14, 14, 24],
[16, 17, 28],
[20, 23, 36],
[24, 29, 44]]...)

Just to show that in the simple 3D case, it is equivalent to:

>>> (np.dot(aff[:3,:3], pts.T) + aff[:3,3:4]).T
array([[14, 14, 24],
[16, 17, 28],
[20, 23, 36],
[24, 29, 44]]...)

But pts can be a more complicated shape:

>>> pts = pts.reshape((2,2,3))
>>> apply_affine(aff, pts)
array([[[14, 14, 24],
[16, 17, 28]],

[[20, 23, 36],
[24, 29, 44]]]...)

### bundles_distances_mdf

dipy.tracking.streamline.bundles_distances_mdf()

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

All tracks need to have the same number of points

Parameters
tracksAsequence

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

tracksBsequence

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

Returns
DMarray, shape (len(tracksA), len(tracksB))

distances between tracksA and tracksB according to metric

### cdist

dipy.tracking.streamline.cdist(XA, XB, metric='euclidean', *args, **kwargs)

Compute distance between each pair of the two collections of inputs.

See Notes for common calling conventions.

Parameters
XAndarray

An $$m_A$$ by $$n$$ array of $$m_A$$ original observations in an $$n$$-dimensional space. Inputs are converted to float type.

XBndarray

An $$m_B$$ by $$n$$ array of $$m_B$$ original observations in an $$n$$-dimensional space. Inputs are converted to float type.

metricstr or callable, optional

The distance metric to use. If a string, the distance function can be ‘braycurtis’, ‘canberra’, ‘chebyshev’, ‘cityblock’, ‘correlation’, ‘cosine’, ‘dice’, ‘euclidean’, ‘hamming’, ‘jaccard’, ‘jensenshannon’, ‘kulsinski’, ‘mahalanobis’, ‘matching’, ‘minkowski’, ‘rogerstanimoto’, ‘russellrao’, ‘seuclidean’, ‘sokalmichener’, ‘sokalsneath’, ‘sqeuclidean’, ‘wminkowski’, ‘yule’.

*argstuple. Deprecated.

Additional arguments should be passed as keyword arguments

**kwargsdict, optional

Extra arguments to metric: refer to each metric documentation for a list of all possible arguments.

Some possible arguments:

p : scalar The p-norm to apply for Minkowski, weighted and unweighted. Default: 2.

w : ndarray The weight vector for metrics that support weights (e.g., Minkowski).

V : ndarray The variance vector for standardized Euclidean. Default: var(vstack([XA, XB]), axis=0, ddof=1)

VI : ndarray The inverse of the covariance matrix for Mahalanobis. Default: inv(cov(vstack([XA, XB].T))).T

out : ndarray The output array If not None, the distance matrix Y is stored in this array. Note: metric independent, it will become a regular keyword arg in a future scipy version

Returns
Yndarray

A $$m_A$$ by $$m_B$$ distance matrix is returned. For each $$i$$ and $$j$$, the metric dist(u=XA[i], v=XB[j]) is computed and stored in the $$ij$$ th entry.

Raises
ValueError

An exception is thrown if XA and XB do not have the same number of columns.

Notes

The following are common calling conventions:

1. Y = cdist(XA, XB, 'euclidean')

Computes the distance between $$m$$ points using Euclidean distance (2-norm) as the distance metric between the points. The points are arranged as $$m$$ $$n$$-dimensional row vectors in the matrix X.

2. Y = cdist(XA, XB, 'minkowski', p=2.)

Computes the distances using the Minkowski distance $$||u-v||_p$$ ($$p$$-norm) where $$p \geq 1$$.

3. Y = cdist(XA, XB, 'cityblock')

Computes the city block or Manhattan distance between the points.

4. Y = cdist(XA, XB, 'seuclidean', V=None)

Computes the standardized Euclidean distance. The standardized Euclidean distance between two n-vectors u and v is

$\sqrt{\sum {(u_i-v_i)^2 / V[x_i]}}.$

V is the variance vector; V[i] is the variance computed over all the i’th components of the points. If not passed, it is automatically computed.

5. Y = cdist(XA, XB, 'sqeuclidean')

Computes the squared Euclidean distance $$||u-v||_2^2$$ between the vectors.

6. Y = cdist(XA, XB, 'cosine')

Computes the cosine distance between vectors u and v,

$1 - \frac{u \cdot v} {{||u||}_2 {||v||}_2}$

where $$||*||_2$$ is the 2-norm of its argument *, and $$u \cdot v$$ is the dot product of $$u$$ and $$v$$.

7. Y = cdist(XA, XB, 'correlation')

Computes the correlation distance between vectors u and v. This is

$1 - \frac{(u - \bar{u}) \cdot (v - \bar{v})} {{||(u - \bar{u})||}_2 {||(v - \bar{v})||}_2}$

where $$\bar{v}$$ is the mean of the elements of vector v, and $$x \cdot y$$ is the dot product of $$x$$ and $$y$$.

8. Y = cdist(XA, XB, 'hamming')

Computes the normalized Hamming distance, or the proportion of those vector elements between two n-vectors u and v which disagree. To save memory, the matrix X can be of type boolean.

9. Y = cdist(XA, XB, 'jaccard')

Computes the Jaccard distance between the points. Given two vectors, u and v, the Jaccard distance is the proportion of those elements u[i] and v[i] that disagree where at least one of them is non-zero.

10. Y = cdist(XA, XB, 'chebyshev')

Computes the Chebyshev distance between the points. The Chebyshev distance between two n-vectors u and v is the maximum norm-1 distance between their respective elements. More precisely, the distance is given by

$d(u,v) = \max_i {|u_i-v_i|}.$
1. Y = cdist(XA, XB, 'canberra')

Computes the Canberra distance between the points. The Canberra distance between two points u and v is

$d(u,v) = \sum_i \frac{|u_i-v_i|} {|u_i|+|v_i|}.$
1. Y = cdist(XA, XB, 'braycurtis')

Computes the Bray-Curtis distance between the points. The Bray-Curtis distance between two points u and v is

$d(u,v) = \frac{\sum_i (|u_i-v_i|)} {\sum_i (|u_i+v_i|)}$
1. Y = cdist(XA, XB, 'mahalanobis', VI=None)

Computes the Mahalanobis distance between the points. The Mahalanobis distance between two points u and v is $$\sqrt{(u-v)(1/V)(u-v)^T}$$ where $$(1/V)$$ (the VI variable) is the inverse covariance. If VI is not None, VI will be used as the inverse covariance matrix.

1. Y = cdist(XA, XB, 'yule')

Computes the Yule distance between the boolean vectors. (see yule function documentation)

1. Y = cdist(XA, XB, 'matching')

Synonym for ‘hamming’.

1. Y = cdist(XA, XB, 'dice')

Computes the Dice distance between the boolean vectors. (see dice function documentation)

1. Y = cdist(XA, XB, 'kulsinski')

Computes the Kulsinski distance between the boolean vectors. (see kulsinski function documentation)

1. Y = cdist(XA, XB, 'rogerstanimoto')

Computes the Rogers-Tanimoto distance between the boolean vectors. (see rogerstanimoto function documentation)

1. Y = cdist(XA, XB, 'russellrao')

Computes the Russell-Rao distance between the boolean vectors. (see russellrao function documentation)

1. Y = cdist(XA, XB, 'sokalmichener')

Computes the Sokal-Michener distance between the boolean vectors. (see sokalmichener function documentation)

1. Y = cdist(XA, XB, 'sokalsneath')

Computes the Sokal-Sneath distance between the vectors. (see sokalsneath function documentation)

1. Y = cdist(XA, XB, 'wminkowski', p=2., w=w)

Computes the weighted Minkowski distance between the vectors. (see wminkowski function documentation)

1. Y = cdist(XA, XB, f)

Computes the distance between all pairs of vectors in X using the user supplied 2-arity function f. For example, Euclidean distance between the vectors could be computed as follows:

dm = cdist(XA, XB, lambda u, v: np.sqrt(((u-v)**2).sum()))

Note that you should avoid passing a reference to one of the distance functions defined in this library. For example,:

dm = cdist(XA, XB, sokalsneath)

would calculate the pair-wise distances between the vectors in X using the Python function sokalsneath. This would result in sokalsneath being called $${n \choose 2}$$ times, which is inefficient. Instead, the optimized C version is more efficient, and we call it using the following syntax:

dm = cdist(XA, XB, 'sokalsneath')

Examples

Find the Euclidean distances between four 2-D coordinates:

>>> from scipy.spatial import distance
>>> coords = [(35.0456, -85.2672),
...           (35.1174, -89.9711),
...           (35.9728, -83.9422),
...           (36.1667, -86.7833)]
>>> distance.cdist(coords, coords, 'euclidean')
array([[ 0.    ,  4.7044,  1.6172,  1.8856],
[ 4.7044,  0.    ,  6.0893,  3.3561],
[ 1.6172,  6.0893,  0.    ,  2.8477],
[ 1.8856,  3.3561,  2.8477,  0.    ]])

Find the Manhattan distance from a 3-D point to the corners of the unit cube:

>>> a = np.array([[0, 0, 0],
...               [0, 0, 1],
...               [0, 1, 0],
...               [0, 1, 1],
...               [1, 0, 0],
...               [1, 0, 1],
...               [1, 1, 0],
...               [1, 1, 1]])
>>> b = np.array([[ 0.1,  0.2,  0.4]])
>>> distance.cdist(a, b, 'cityblock')
array([[ 0.7],
[ 0.9],
[ 1.3],
[ 1.5],
[ 1.5],
[ 1.7],
[ 2.1],
[ 2.3]])

### center_streamlines

dipy.tracking.streamline.center_streamlines(streamlines)

Move streamlines to the origin

Parameters
streamlineslist

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

Returns
new_streamlineslist

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

inv_shiftndarray

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

### cluster_confidence

dipy.tracking.streamline.cluster_confidence(streamlines, max_mdf=5, subsample=12, power=1, override=False)

Computes the cluster confidence index (cci), which is an estimation of the support a set of streamlines gives to a particular pathway.

Ex: A single streamline with no others in the dataset following a similar pathway has a low cci. A streamline in a bundle of 100 streamlines that follow similar pathways has a high cci.

See: Jordan et al. 2017 (Based on streamline MDF distance from Garyfallidis et al. 2012)

Parameters
streamlineslist of 2D (N, 3) arrays

A sequence of streamlines of length N (# streamlines)

max_mdfint

The maximum MDF distance (mm) that will be considered a “supporting” streamline and included in cci calculation

subsample: int

The number of points that are considered for each streamline in the calculation. To save on calculation time, each streamline is subsampled to subsampleN points.

power: int

The power to which the MDF distance for each streamline will be raised to determine how much it contributes to the cci. High values of power make the contribution value degrade much faster. E.g., a streamline with 5mm MDF similarity contributes 1/5 to the cci if power is 1, but only contributes 1/5^2 = 1/25 if power is 2.

override: bool, False by default

override means that the cci calculation will still occur even though there are short streamlines in the dataset that may alter expected behaviour.

Returns
Returns an array of CCI scores

References

[Jordan17] Jordan K. Et al., Cluster Confidence Index: A Streamline-Wise Pathway Reproducibility Metric for Diffusion-Weighted MRI Tractography, Journal of Neuroimaging, vol 28, no 1, 2017.

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

### compress_streamlines

dipy.tracking.streamline.compress_streamlines()

Compress streamlines by linearization as in [Presseau15].

The compression consists in merging consecutive segments that are nearly collinear. The merging is achieved by removing the point the two segments have in common.

The linearization process [Presseau15] ensures that every point being removed are within a certain margin (in mm) of the resulting streamline. Recommendations for setting this margin can be found in [Presseau15] (in which they called it tolerance error).

The compression also ensures that two consecutive points won’t be too far from each other (precisely less or equal than max_segment_lengthmm). This is a tradeoff to speed up the linearization process [Rheault15]. A low value will result in a faster linearization but low compression, whereas a high value will result in a slower linearization but high compression.

Parameters
streamlinesone or a list of array-like of shape (N,3)

Array representing x,y,z of N points in a streamline.

tol_errorfloat (optional)

Tolerance error in mm (default: 0.01). A rule of thumb is to set it to 0.01mm for deterministic streamlines and 0.1mm for probabilitic streamlines.

max_segment_lengthfloat (optional)

Maximum length in mm of any given segment produced by the compression. The default is 10mm. (In [Presseau15], they used a value of np.inf).

Returns
compressed_streamlinesone or a list of array-like

Results of the linearization process.

Notes

Be aware that compressed streamlines have variable step sizes. One needs to be careful when computing streamlines-based metrics [Houde15].

References

Presseau15(1,2,3,4,5)

Presseau C. et al., A new compression format for fiber tracking datasets, NeuroImage, no 109, 73-83, 2015.

Rheault15

Rheault F. et al., Real Time Interaction with Millions of Streamlines, ISMRM, 2015.

Houde15

Houde J.-C. et al. How to Avoid Biased Streamlines-Based Metrics for Streamlines with Variable Step Sizes, ISMRM, 2015.

Examples

>>> from dipy.tracking.streamline import compress_streamlines
>>> import numpy as np
>>> # One streamline: a wiggling line
>>> rng = np.random.RandomState(42)
>>> streamline = np.linspace(0, 10, 100*3).reshape((100, 3))
>>> streamline += 0.2 * rng.rand(100, 3)
>>> c_streamline = compress_streamlines(streamline, tol_error=0.2)
>>> len(streamline)
100
>>> len(c_streamline)
10
>>> # Multiple streamlines
>>> streamlines = [streamline, streamline[::2]]
>>> c_streamlines = compress_streamlines(streamlines, tol_error=0.2)
>>> [len(s) for s in streamlines]
[100, 50]
>>> [len(s) for s in c_streamlines]
[10, 7]

### deepcopy

dipy.tracking.streamline.deepcopy(x, memo=None, _nil=[])

Deep copy operation on arbitrary Python objects.

### deform_streamlines

dipy.tracking.streamline.deform_streamlines(streamlines, deform_field, stream_to_current_grid, current_grid_to_world, stream_to_ref_grid, ref_grid_to_world)

Apply deformation field to streamlines

Parameters
streamlineslist

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

deform_field4D numpy array

x,y,z displacements stored in volume, shape[-1]==3

stream_to_current_gridarray, (4, 4)

transform matrix voxmm space to original grid space

current_grid_to_worldarray (4, 4)

transform matrix original grid space to world coordinates

stream_to_ref_gridarray (4, 4)

transform matrix voxmm space to new grid space

ref_grid_to_worldarray(4, 4)

transform matrix new grid space to world coordinates

Returns
new_streamlineslist

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

### dist_to_corner

dipy.tracking.streamline.dist_to_corner(affine)

Calculate the maximal distance from the center to a corner of a voxel, given an affine

Parameters
affine4 by 4 array.

The spatial transformation from the measurement to the scanner space.

Returns
dist: float

The maximal distance to the corner of a voxel, given voxel size encoded in the affine.

### interpolate_scalar_3d

dipy.tracking.streamline.interpolate_scalar_3d()

Trilinear interpolation of a 3D scalar image

Interpolates the 3D image at the given locations. This function is a wrapper for _interpolate_scalar_3d for testing purposes, it is equivalent to scipy.ndimage.interpolation.map_coordinates with trilinear interpolation

Parameters
fieldarray, shape (S, R, C)

the 3D image to be interpolated

locationsarray, shape (n, 3)

(locations[i,0], locations[i,1], locations[i,2), 0<=i<n must contain the coordinates to interpolate the image at

Returns
outarray, shape (n,)

out[i], 0<=i<n will be the interpolated scalar at coordinates locations[i,:], or 0 if locations[i,:] is outside the image

insidearray, (n,)

if locations[i,:] is inside the image then inside[i]=1, else inside[i]=0

### interpolate_vector_3d

dipy.tracking.streamline.interpolate_vector_3d()

Trilinear interpolation of a 3D vector field

Interpolates the 3D vector field at the given locations. This function is a wrapper for _interpolate_vector_3d for testing purposes, it is equivalent to using scipy.ndimage.interpolation.map_coordinates with trilinear interpolation at each vector component

Parameters
fieldarray, shape (S, R, C, 3)

the 3D vector field to be interpolated

locationsarray, shape (n, 3)

(locations[i,0], locations[i,1], locations[i,2), 0<=i<n must contain the coordinates to interpolate the vector field at

Returns
outarray, shape (n, 3)

out[i,:], 0<=i<n will be the interpolated vector at coordinates locations[i,:], or (0,0,0) if locations[i,:] is outside the field

insidearray, (n,)

if locations[i,:] is inside the vector field then inside[i]=1, else inside[i]=0

### length

dipy.tracking.streamline.length()

Euclidean length of streamlines

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

Parameters
streamlinesndarray or a list or dipy.tracking.Streamlines

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

Returns
lengthsscalar 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

### nbytes

dipy.tracking.streamline.nbytes(streamlines)

### orient_by_rois

dipy.tracking.streamline.orient_by_rois(streamlines, affine, roi1, roi2, in_place=False, as_generator=False)

Orient a set of streamlines according to a pair of ROIs

Parameters
streamlineslist or generator

List or generator of 2d arrays of 3d coordinates. Each array contains the xyz coordinates of a single streamline.

affinearray_like (4, 4)

The mapping from voxel coordinates to streamline points. The voxel_to_rasmm matrix, typically from a NIFTI file.

roi1, roi2ndarray

Binary masks designating the location of the regions of interest, or coordinate arrays (n-by-3 array with ROI coordinate in each row).

in_placebool

Whether to make the change in-place in the original list (and return a reference to the list), or to make a copy of the list and return this copy, with the relevant streamlines reoriented. Default: False.

as_generatorbool

Whether to return a generator as output. Default: False

Returns
streamlineslist or generator

The same 3D arrays as a list or generator, but reoriented with respect to the ROIs

Examples

>>> streamlines = [np.array([[0, 0., 0],
...                          [1, 0., 0.],
...                          [2, 0., 0.]]),
...                np.array([[2, 0., 0.],
...                          [1, 0., 0],
...                          [0, 0,  0.]])]
>>> roi1 = np.zeros((4, 4, 4), dtype=bool)
>>> roi2 = np.zeros_like(roi1)
>>> roi1[0, 0, 0] = True
>>> roi2[1, 0, 0] = True
>>> orient_by_rois(streamlines, np.eye(4), roi1, roi2)
[array([[ 0.,  0.,  0.],
[ 1.,  0.,  0.],
[ 2.,  0.,  0.]]), array([[ 0.,  0.,  0.],
[ 1.,  0.,  0.],
[ 2.,  0.,  0.]])]

### orient_by_streamline

dipy.tracking.streamline.orient_by_streamline(streamlines, standard, n_points=12, in_place=False, as_generator=False)

Orient a bundle of streamlines to a standard streamline.

Parameters
streamlinesStreamlines, list

The input streamlines to orient.

standardStreamlines, list, or ndarrray

This provides the standard orientation according to which the streamlines in the provided bundle should be reoriented.

n_points: int, optional

The number of samples to apply to each of the streamlines.

in_placebool

Whether to make the change in-place in the original input (and return a reference), or to make a copy of the list and return this copy, with the relevant streamlines reoriented. Default: False.

as_generatorbool

Whether to return a generator as output. Default: False

Returns
Streamlineswith each individual array oriented to be as similar as

possible to the standard.

### relist_streamlines

dipy.tracking.streamline.relist_streamlines(points, offsets)

Given a representation of a set of streamlines as a large array and an offsets array return the streamlines as a list of shorter arrays.

Parameters
pointsarray
offsetsarray
Returns
streamlines: sequence

### select_by_rois

dipy.tracking.streamline.select_by_rois(streamlines, affine, rois, include, mode=None, tol=None)

Select streamlines based on logical relations with several regions of interest (ROIs). For example, select streamlines that pass near ROI1, but only if they do not pass near ROI2.

Parameters
streamlineslist

A list of candidate streamlines for selection

affinearray_like (4, 4)

The mapping from voxel coordinates to streamline points. The voxel_to_rasmm matrix, typically from a NIFTI file.

roislist or ndarray

A list of 3D arrays, each with shape (x, y, z) corresponding to the shape of the brain volume, or a 4D array with shape (n_rois, x, y, z). Non-zeros in each volume are considered to be within the region

includearray or list

A list or 1D array of boolean values marking inclusion or exclusion criteria. If a streamline is near any of the inclusion ROIs, it should evaluate to True, unless it is also near any of the exclusion ROIs.

modestring, optional

One of {“any”, “all”, “either_end”, “both_end”}, where a streamline is associated with an ROI if:

“any” : any point is within tol from ROI. Default.

“all” : all points are within tol from ROI.

“either_end” : either of the end-points is within tol from ROI

“both_end” : both end points are within tol from ROI.

tolfloat

Distance (in the units of the streamlines, usually mm). If any coordinate in the streamline is within this distance from the center of any voxel in the ROI, the filtering criterion is set to True for this streamline, otherwise False. Defaults to the distance between the center of each voxel and the corner of the voxel.

Returns
generator

Generates the streamlines to be included based on these criteria.

Notes

The only operation currently possible is “(A or B or …) and not (X or Y or …)”, where A, B are inclusion regions and X, Y are exclusion regions.

Examples

>>> streamlines = [np.array([[0, 0., 0.9],
...                          [1.9, 0., 0.]]),
...                np.array([[0., 0., 0],
...                          [0, 1., 1.],
...                          [0, 2., 2.]]),
...                np.array([[2, 2, 2],
...                          [3, 3, 3]])]
>>> mask1 = np.zeros((4, 4, 4), dtype=bool)
>>> mask1[0, 0, 0] = True
>>> mask2[1, 0, 0] = True
...                            [True, True],
...                            tol=1)
>>> list(selection) # The result is a generator
[array([[ 0. ,  0. ,  0.9],
[ 1.9,  0. ,  0. ]]), array([[ 0.,  0.,  0.],
[ 0.,  1.,  1.],
[ 0.,  2.,  2.]])]
...                            [True, False],
...                            tol=0.87)
>>> list(selection)
[array([[ 0.,  0.,  0.],
[ 0.,  1.,  1.],
[ 0.,  2.,  2.]])]
...                            [True, True],
...                            mode="both_end",
...                            tol=1.0)
>>> list(selection)
[array([[ 0. ,  0. ,  0.9],
[ 1.9,  0. ,  0. ]])]
>>> mask2[0, 2, 2] = True
...                            [True, True],
...                            mode="both_end",
...                            tol=1.0)
>>> list(selection)
[array([[ 0. ,  0. ,  0.9],
[ 1.9,  0. ,  0. ]]), array([[ 0.,  0.,  0.],
[ 0.,  1.,  1.],
[ 0.,  2.,  2.]])]

### select_random_set_of_streamlines

dipy.tracking.streamline.select_random_set_of_streamlines(streamlines, select, rng=None)

Select a random set of streamlines

Parameters
streamlinesSteamlines

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

selectint

Number of streamlines to select. If there are less streamlines than select then select=len(streamlines).

rngRandomState

Default None.

Returns
selected_streamlineslist

Notes

The same streamline will not be selected twice.

### set_number_of_points

dipy.tracking.streamline.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
streamlinesndarray 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_pointsint

integer representing number of points wanted along the curve.

Returns
new_streamlinesndarray 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]

### transform_streamlines

dipy.tracking.streamline.transform_streamlines(streamlines, mat, in_place=False)

Apply affine transformation to streamlines

Parameters
streamlinesStreamlines

Streamlines object

matarray, (4, 4)

transformation matrix

in_placebool

If True then change data in place. Be careful changes input streamlines.

Returns
new_streamlinesStreamlines

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

### unlist_streamlines

dipy.tracking.streamline.unlist_streamlines(streamlines)

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

Parameters
streamlines: sequence
Returns
pointsarray
offsetsarray

### values_from_volume

dipy.tracking.streamline.values_from_volume(data, streamlines, affine)

Extract values of a scalar/vector along each streamline from a volume.

Parameters
data3D or 4D array

Scalar (for 3D) and vector (for 4D) values to be extracted. For 4D data, interpolation will be done on the 3 spatial dimensions in each volume.

streamlinesndarray or list

If array, of shape (n_streamlines, n_nodes, 3) If list, len(n_streamlines) with (n_nodes, 3) array in each element of the list.

affinearray_like (4, 4)

The mapping from voxel coordinates to streamline points. The voxel_to_rasmm matrix, typically from a NIFTI file.

Returns
array or list (depending on the input)values interpolate to each

coordinate along the length of each streamline.

Notes

Values are extracted from the image based on the 3D coordinates of the nodes that comprise the points in the streamline, without any interpolation into segments between the nodes. Using this function with streamlines that have been resampled into a very small number of nodes will result in very few values.

### warn

dipy.tracking.streamline.warn(/, message, category=None, stacklevel=1, source=None)

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

### OrderedDict

class dipy.tracking.utils.OrderedDict

Bases: dict

Dictionary that remembers insertion order

Methods

 clear() copy() fromkeys(/, iterable[, value]) Create a new ordered dictionary with keys from iterable and values set to value. get(key[, default]) Return the value for key if key is in the dictionary, else default. items() keys() move_to_end(/, key[, last]) Move an existing element to the end (or beginning if last is false). pop(k[,d]) value. popitem(/[, last]) Remove and return a (key, value) pair from the dictionary. setdefault(/, key[, default]) Insert key with a value of default if key is not in the dictionary. update([E, ]**F) If E is present and has a .keys() method, then does: for k in E: D[k] = E[k] If E is present and lacks a .keys() method, then does: for k, v in E: D[k] = v In either case, this is followed by: for k in F: D[k] = F[k] values()
__init__(*args, **kwargs)

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

clear() → None. Remove all items from od.
copy() → a shallow copy of od
fromkeys(/, iterable, value=None)

Create a new ordered dictionary with keys from iterable and values set to value.

items() → a set-like object providing a view on D's items
keys() → a set-like object providing a view on D's keys
move_to_end(/, key, last=True)

Move an existing element to the end (or beginning if last is false).

Raise KeyError if the element does not exist.

pop(k[, d]) → v, remove specified key and return the corresponding

value. If key is not found, d is returned if given, otherwise KeyError is raised.

popitem(/, last=True)

Remove and return a (key, value) pair from the dictionary.

Pairs are returned in LIFO order if last is true or FIFO order if false.

setdefault(/, key, default=None)

Insert key with a value of default if key is not in the dictionary.

Return the value for key if key is in the dictionary, else default.

update([E, ]**F) → None. Update D from dict/iterable E and F.

If E is present and has a .keys() method, then does: for k in E: D[k] = E[k] If E is present and lacks a .keys() method, then does: for k, v in E: D[k] = v In either case, this is followed by: for k in F: D[k] = F[k]

values() → an object providing a view on D's values

### combinations

class dipy.tracking.utils.combinations

Bases: object

combinations(iterable, r) –> combinations object

Return successive r-length combinations of elements in the iterable.

combinations(range(4), 3) –> (0,1,2), (0,1,3), (0,2,3), (1,2,3)

__init__(*args, **kwargs)

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

### defaultdict

class dipy.tracking.utils.defaultdict

Bases: dict

defaultdict(default_factory[, …]) –> dict with default factory

The default factory is called without arguments to produce a new value when a key is not present, in __getitem__ only. A defaultdict compares equal to a dict with the same items. All remaining arguments are treated the same as if they were passed to the dict constructor, including keyword arguments.

Attributes
default_factory

Factory for default value called by __missing__().

Methods

 clear() copy() fromkeys(iterable[, value]) Create a new dictionary with keys from iterable and values set to value. get(key[, default]) Return the value for key if key is in the dictionary, else default. items() keys() pop(k[,d]) If key is not found, d is returned if given, otherwise KeyError is raised popitem() 2-tuple; but raise KeyError if D is empty. setdefault(key[, default]) Insert key with a value of default if key is not in the dictionary. update([E, ]**F) If E is present and has a .keys() method, then does: for k in E: D[k] = E[k] If E is present and lacks a .keys() method, then does: for k, v in E: D[k] = v In either case, this is followed by: for k in F: D[k] = F[k] values()
__init__(*args, **kwargs)

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

copy() → a shallow copy of D.
default_factory

Factory for default value called by __missing__().

### groupby

class dipy.tracking.utils.groupby(iterable, key=None) → make an iterator that returns consecutive

Bases: object

keys and groups from the iterable. If the key function is not specified or is None, the element itself is used for grouping.

__init__(*args, **kwargs)

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

### apply_affine

dipy.tracking.utils.apply_affine(aff, pts)

Apply affine matrix aff to points pts

Returns result of application of aff to the right of pts. The coordinate dimension of pts should be the last.

For the 3D case, aff will be shape (4,4) and pts will have final axis length 3 - maybe it will just be N by 3. The return value is the transformed points, in this case:

res = np.dot(aff[:3,:3], pts.T) + aff[:3,3:4]
transformed_pts = res.T

This routine is more general than 3D, in that aff can have any shape (N,N), and pts can have any shape, as long as the last dimension is for the coordinates, and is therefore length N-1.

Parameters
aff(N, N) array-like

Homogenous affine, for 3D points, will be 4 by 4. Contrary to first appearance, the affine will be applied on the left of pts.

pts(…, N-1) array-like

Points, where the last dimension contains the coordinates of each point. For 3D, the last dimension will be length 3.

Returns
transformed_pts(…, N-1) array

transformed points

Examples

>>> aff = np.array([[0,2,0,10],[3,0,0,11],[0,0,4,12],[0,0,0,1]])
>>> pts = np.array([[1,2,3],[2,3,4],[4,5,6],[6,7,8]])
>>> apply_affine(aff, pts)
array([[14, 14, 24],
[16, 17, 28],
[20, 23, 36],
[24, 29, 44]]...)

Just to show that in the simple 3D case, it is equivalent to:

>>> (np.dot(aff[:3,:3], pts.T) + aff[:3,3:4]).T
array([[14, 14, 24],
[16, 17, 28],
[20, 23, 36],
[24, 29, 44]]...)

But pts can be a more complicated shape:

>>> pts = pts.reshape((2,2,3))
>>> apply_affine(aff, pts)
array([[[14, 14, 24],
[16, 17, 28]],

[[20, 23, 36],
[24, 29, 44]]]...)

### asarray

dipy.tracking.utils.asarray(a, dtype=None, order=None)

Convert the input to an array.

Parameters
aarray_like

Input data, in any form that can be converted to an array. This includes lists, lists of tuples, tuples, tuples of tuples, tuples of lists and ndarrays.

dtypedata-type, optional

By default, the data-type is inferred from the input data.

order{‘C’, ‘F’}, optional

Whether to use row-major (C-style) or column-major (Fortran-style) memory representation. Defaults to ‘C’.

Returns
outndarray

Array interpretation of a. No copy is performed if the input is already an ndarray with matching dtype and order. If a is a subclass of ndarray, a base class ndarray is returned.

asanyarray

Similar function which passes through subclasses.

ascontiguousarray

Convert input to a contiguous array.

asfarray

Convert input to a floating point ndarray.

asfortranarray

Convert input to an ndarray with column-major memory order.

asarray_chkfinite

Similar function which checks input for NaNs and Infs.

fromiter

Create an array from an iterator.

fromfunction

Construct an array by executing a function on grid positions.

Examples

Convert a list into an array:

>>> a = [1, 2]
>>> np.asarray(a)
array([1, 2])

Existing arrays are not copied:

>>> a = np.array([1, 2])
>>> np.asarray(a) is a
True

If dtype is set, array is copied only if dtype does not match:

>>> a = np.array([1, 2], dtype=np.float32)
>>> np.asarray(a, dtype=np.float32) is a
True
>>> np.asarray(a, dtype=np.float64) is a
False

Contrary to asanyarray, ndarray subclasses are not passed through:

>>> issubclass(np.recarray, np.ndarray)
True
>>> a = np.array([(1.0, 2), (3.0, 4)], dtype='f4,i4').view(np.recarray)
>>> np.asarray(a) is a
False
>>> np.asanyarray(a) is a
True

### cdist

dipy.tracking.utils.cdist(XA, XB, metric='euclidean', *args, **kwargs)

Compute distance between each pair of the two collections of inputs.

See Notes for common calling conventions.

Parameters
XAndarray

An $$m_A$$ by $$n$$ array of $$m_A$$ original observations in an $$n$$-dimensional space. Inputs are converted to float type.

XBndarray

An $$m_B$$ by $$n$$ array of $$m_B$$ original observations in an $$n$$-dimensional space. Inputs are converted to float type.

metricstr or callable, optional

The distance metric to use. If a string, the distance function can be ‘braycurtis’, ‘canberra’, ‘chebyshev’, ‘cityblock’, ‘correlation’, ‘cosine’, ‘dice’, ‘euclidean’, ‘hamming’, ‘jaccard’, ‘jensenshannon’, ‘kulsinski’, ‘mahalanobis’, ‘matching’, ‘minkowski’, ‘rogerstanimoto’, ‘russellrao’, ‘seuclidean’, ‘sokalmichener’, ‘sokalsneath’, ‘sqeuclidean’, ‘wminkowski’, ‘yule’.

*argstuple. Deprecated.

Additional arguments should be passed as keyword arguments

**kwargsdict, optional

Extra arguments to metric: refer to each metric documentation for a list of all possible arguments.

Some possible arguments:

p : scalar The p-norm to apply for Minkowski, weighted and unweighted. Default: 2.

w : ndarray The weight vector for metrics that support weights (e.g., Minkowski).

V : ndarray The variance vector for standardized Euclidean. Default: var(vstack([XA, XB]), axis=0, ddof=1)

VI : ndarray The inverse of the covariance matrix for Mahalanobis. Default: inv(cov(vstack([XA, XB].T))).T

out : ndarray The output array If not None, the distance matrix Y is stored in this array. Note: metric independent, it will become a regular keyword arg in a future scipy version

Returns
Yndarray

A $$m_A$$ by $$m_B$$ distance matrix is returned. For each $$i$$ and $$j$$, the metric dist(u=XA[i], v=XB[j]) is computed and stored in the $$ij$$ th entry.

Raises
ValueError

An exception is thrown if XA and XB do not have the same number of columns.

Notes

The following are common calling conventions:

1. Y = cdist(XA, XB, 'euclidean')

Computes the distance between $$m$$ points using Euclidean distance (2-norm) as the distance metric between the points. The points are arranged as $$m$$ $$n$$-dimensional row vectors in the matrix X.

2. Y = cdist(XA, XB, 'minkowski', p=2.)

Computes the distances using the Minkowski distance $$||u-v||_p$$ ($$p$$-norm) where $$p \geq 1$$.

3. Y = cdist(XA, XB, 'cityblock')

Computes the city block or Manhattan distance between the points.

4. Y = cdist(XA, XB, 'seuclidean', V=None)

Computes the standardized Euclidean distance. The standardized Euclidean distance between two n-vectors u and v is

$\sqrt{\sum {(u_i-v_i)^2 / V[x_i]}}.$

V is the variance vector; V[i] is the variance computed over all the i’th components of the points. If not passed, it is automatically computed.

5. Y = cdist(XA, XB, 'sqeuclidean')

Computes the squared Euclidean distance $$||u-v||_2^2$$ between the vectors.

6. Y = cdist(XA, XB, 'cosine')

Computes the cosine distance between vectors u and v,

$1 - \frac{u \cdot v} {{||u||}_2 {||v||}_2}$

where $$||*||_2$$ is the 2-norm of its argument *, and $$u \cdot v$$ is the dot product of $$u$$ and $$v$$.

7. Y = cdist(XA, XB, 'correlation')

Computes the correlation distance between vectors u and v. This is

$1 - \frac{(u - \bar{u}) \cdot (v - \bar{v})} {{||(u - \bar{u})||}_2 {||(v - \bar{v})||}_2}$

where $$\bar{v}$$ is the mean of the elements of vector v, and $$x \cdot y$$ is the dot product of $$x$$ and $$y$$.

8. Y = cdist(XA, XB, 'hamming')

Computes the normalized Hamming distance, or the proportion of those vector elements between two n-vectors u and v which disagree. To save memory, the matrix X can be of type boolean.

9. Y = cdist(XA, XB, 'jaccard')

Computes the Jaccard distance between the points. Given two vectors, u and v, the Jaccard distance is the proportion of those elements u[i] and v[i] that disagree where at least one of them is non-zero.

10. Y = cdist(XA, XB, 'chebyshev')

Computes the Chebyshev distance between the points. The Chebyshev distance between two n-vectors u and v is the maximum norm-1 distance between their respective elements. More precisely, the distance is given by

$d(u,v) = \max_i {|u_i-v_i|}.$
1. Y = cdist(XA, XB, 'canberra')

Computes the Canberra distance between the points. The Canberra distance between two points u and v is

$d(u,v) = \sum_i \frac{|u_i-v_i|} {|u_i|+|v_i|}.$
1. Y = cdist(XA, XB, 'braycurtis')

Computes the Bray-Curtis distance between the points. The Bray-Curtis distance between two points u and v is

$d(u,v) = \frac{\sum_i (|u_i-v_i|)} {\sum_i (|u_i+v_i|)}$
1. Y = cdist(XA, XB, 'mahalanobis', VI=None)

Computes the Mahalanobis distance between the points. The Mahalanobis distance between two points u and v is $$\sqrt{(u-v)(1/V)(u-v)^T}$$ where $$(1/V)$$ (the VI variable) is the inverse covariance. If VI is not None, VI will be used as the inverse covariance matrix.

1. Y = cdist(XA, XB, 'yule')

Computes the Yule distance between the boolean vectors. (see yule function documentation)

1. Y = cdist(XA, XB, 'matching')

Synonym for ‘hamming’.

1. Y = cdist(XA, XB, 'dice')

Computes the Dice distance between the boolean vectors. (see dice function documentation)

1. Y = cdist(XA, XB, 'kulsinski')

Computes the Kulsinski distance between the boolean vectors. (see kulsinski function documentation)

1. Y = cdist(XA, XB, 'rogerstanimoto')

Computes the Rogers-Tanimoto distance between the boolean vectors. (see rogerstanimoto function documentation)

1. Y = cdist(XA, XB, 'russellrao')

Computes the Russell-Rao distance between the boolean vectors. (see russellrao function documentation)

1. Y = cdist(XA, XB, 'sokalmichener')

Computes the Sokal-Michener distance between the boolean vectors. (see sokalmichener function documentation)

1. Y = cdist(XA, XB, 'sokalsneath')

Computes the Sokal-Sneath distance between the vectors. (see sokalsneath function documentation)

1. Y = cdist(XA, XB, 'wminkowski', p=2., w=w)

Computes the weighted Minkowski distance between the vectors. (see wminkowski function documentation)

1. Y = cdist(XA, XB, f)

Computes the distance between all pairs of vectors in X using the user supplied 2-arity function f. For example, Euclidean distance between the vectors could be computed as follows:

dm = cdist(XA, XB, lambda u, v: np.sqrt(((u-v)**2).sum()))

Note that you should avoid passing a reference to one of the distance functions defined in this library. For example,:

dm = cdist(XA, XB, sokalsneath)

would calculate the pair-wise distances between the vectors in X using the Python function sokalsneath. This would result in sokalsneath being called $${n \choose 2}$$ times, which is inefficient. Instead, the optimized C version is more efficient, and we call it using the following syntax:

dm = cdist(XA, XB, 'sokalsneath')

Examples

Find the Euclidean distances between four 2-D coordinates:

>>> from scipy.spatial import distance
>>> coords = [(35.0456, -85.2672),
...           (35.1174, -89.9711),
...           (35.9728, -83.9422),
...           (36.1667, -86.7833)]
>>> distance.cdist(coords, coords, 'euclidean')
array([[ 0.    ,  4.7044,  1.6172,  1.8856],
[ 4.7044,  0.    ,  6.0893,  3.3561],
[ 1.6172,  6.0893,  0.    ,  2.8477],
[ 1.8856,  3.3561,  2.8477,  0.    ]])

Find the Manhattan distance from a 3-D point to the corners of the unit cube:

>>> a = np.array([[0, 0, 0],
...               [0, 0, 1],
...               [0, 1, 0],
...               [0, 1, 1],
...               [1, 0, 0],
...               [1, 0, 1],
...               [1, 1, 0],
...               [1, 1, 1]])
>>> b = np.array([[ 0.1,  0.2,  0.4]])
>>> distance.cdist(a, b, 'cityblock')
array([[ 0.7],
[ 0.9],
[ 1.3],
[ 1.5],
[ 1.5],
[ 1.7],
[ 2.1],
[ 2.3]])

### connectivity_matrix

dipy.tracking.utils.connectivity_matrix(streamlines, affine, label_volume, inclusive=False, symmetric=True, return_mapping=False, mapping_as_streamlines=False)

Counts the streamlines that start and end at each label pair.

Parameters
streamlinessequence

A sequence of streamlines.

affinearray_like (4, 4)

The mapping from voxel coordinates to streamline coordinates. The voxel_to_rasmm matrix, typically from a NIFTI file.

label_volumendarray

An image volume with an integer data type, where the intensities in the volume map to anatomical structures.

inclusive: bool

Whether to analyze the entire streamline, as opposed to just the endpoints. Allowing this will increase calculation time and mapping size, especially if mapping_as_streamlines is True. False by default.

symmetricbool, True by default

Symmetric means we don’t distinguish between start and end points. If symmetric is True, matrix[i, j] == matrix[j, i].

return_mappingbool, False by default

If True, a mapping is returned which maps matrix indices to streamlines.

mapping_as_streamlinesbool, False by default

If True voxel indices map to lists of streamline objects. Otherwise voxel indices map to lists of integers.

Returns
matrixndarray

The number of connection between each pair of regions in label_volume.

mappingdefaultdict(list)

mapping[i, j] returns all the streamlines that connect region i to region j. If symmetric is True mapping will only have one key for each start end pair such that if i < j mapping will have key (i, j) but not key (j, i).

### density_map

dipy.tracking.utils.density_map(streamlines, affine, vol_dims)

Counts the number of unique streamlines that pass through each voxel.

Parameters
streamlinesiterable

A sequence of streamlines.

affinearray_like (4, 4)

The mapping from voxel coordinates to streamline points. The voxel_to_rasmm matrix, typically from a NIFTI file.

vol_dims3 ints

The shape of the volume to be returned containing the streamlines counts

Returns
image_volumendarray, shape=vol_dims

The number of streamline points in each voxel of volume.

Raises
IndexError

When the points of the streamlines lie outside of the return volume.

Notes

A streamline can pass through a voxel even if one of the points of the streamline does not lie in the voxel. For example a step from [0,0,0] to [0,0,2] passes through [0,0,1]. Consider subsegmenting the streamlines when the edges of the voxels are smaller than the steps of the streamlines.

### dist_to_corner

dipy.tracking.utils.dist_to_corner(affine)

Calculate the maximal distance from the center to a corner of a voxel, given an affine

Parameters
affine4 by 4 array.

The spatial transformation from the measurement to the scanner space.

Returns
dist: float

The maximal distance to the corner of a voxel, given voxel size encoded in the affine.

### empty

dipy.tracking.utils.empty(shape, dtype=float, order='C')

Return a new array of given shape and type, without initializing entries.

Parameters
shapeint or tuple of int

Shape of the empty array, e.g., (2, 3) or 2.

dtypedata-type, optional

Desired output data-type for the array, e.g, numpy.int8. Default is numpy.float64.

order{‘C’, ‘F’}, optional, default: ‘C’

Whether to store multi-dimensional data in row-major (C-style) or column-major (Fortran-style) order in memory.

Returns
outndarray

Array of uninitialized (arbitrary) data of the given shape, dtype, and order. Object arrays will be initialized to None.

empty_like

Return an empty array with shape and type of input.

ones

Return a new array setting values to one.

zeros

Return a new array setting values to zero.

full

Return a new array of given shape filled with value.

Notes

empty, unlike zeros, does not set the array values to zero, and may therefore be marginally faster. On the other hand, it requires the user to manually set all the values in the array, and should be used with caution.

Examples

>>> np.empty([2, 2])
array([[ -9.74499359e+001,   6.69583040e-309],
[  2.13182611e-314,   3.06959433e-309]])         #uninitialized
>>> np.empty([2, 2], dtype=int)
array([[-1073741821, -1067949133],
[  496041986,    19249760]])                     #uninitialized

### length

dipy.tracking.utils.length(streamlines)

Calculate the lengths of many streamlines in a bundle.

Parameters
streamlineslist

Each item in the list is an array with 3D coordinates of a streamline.

Returns
Iterator object which then computes the length of each
streamline in the bundle, upon iteration.

### minimum_at

dipy.tracking.utils.minimum_at(a, indices, b=None)

Performs unbuffered in place operation on operand ‘a’ for elements specified by ‘indices’. For addition ufunc, this method is equivalent to a[indices] += b, except that results are accumulated for elements that are indexed more than once. For example, a[[0,0]] += 1 will only increment the first element once because of buffering, whereas add.at(a, [0,0], 1) will increment the first element twice.

New in version 1.8.0.

Parameters
aarray_like

The array to perform in place operation on.

indicesarray_like or tuple

Array like index object or slice object for indexing into first operand. If first operand has multiple dimensions, indices can be a tuple of array like index objects or slice objects.

barray_like

Second operand for ufuncs requiring two operands. Operand must be broadcastable over first operand after indexing or slicing.

Examples

Set items 0 and 1 to their negative values:

>>> a = np.array([1, 2, 3, 4])
>>> np.negative.at(a, [0, 1])
>>> a
array([-1, -2,  3,  4])

Increment items 0 and 1, and increment item 2 twice:

>>> a = np.array([1, 2, 3, 4])
>>> np.add.at(a, [0, 1, 2, 2], 1)
>>> a
array([2, 3, 5, 4])

Add items 0 and 1 in first array to second array, and store results in first array:

>>> a = np.array([1, 2, 3, 4])
>>> b = np.array([1, 2])
>>> a
array([2, 4, 3, 4])

### ndbincount

dipy.tracking.utils.ndbincount(x, weights=None, shape=None)

Like bincount, but for nd-indices.

Parameters
xarray_like (N, M)

M indices to a an Nd-array

weightsarray_like (M,), optional

Weights associated with indices

shapeoptional

the shape of the output

### near_roi

dipy.tracking.utils.near_roi(streamlines, affine, region_of_interest, tol=None, mode='any')

Provide filtering criteria for a set of streamlines based on whether they fall within a tolerance distance from an ROI

Parameters
streamlineslist or generator

A sequence of streamlines. Each streamline should be a (N, 3) array, where N is the length of the streamline.

affinearray (4, 4)

The mapping between voxel indices and the point space for seeds. The voxel_to_rasmm matrix, typically from a NIFTI file.

region_of_interestndarray

A mask used as a target. Non-zero values are considered to be within the target region.

tolfloat

Distance (in the units of the streamlines, usually mm). If any coordinate in the streamline is within this distance from the center of any voxel in the ROI, the filtering criterion is set to True for this streamline, otherwise False. Defaults to the distance between the center of each voxel and the corner of the voxel.

modestring, optional

One of {“any”, “all”, “either_end”, “both_end”}, where return True if:

“any” : any point is within tol from ROI. Default.

“all” : all points are within tol from ROI.

“either_end” : either of the end-points is within tol from ROI

“both_end” : both end points are within tol from ROI.

Returns
1D array of boolean dtype, shape (len(streamlines), )
This contains True for indices corresponding to each streamline
that passes within a tolerance distance from the target ROI, False
otherwise.

### path_length

dipy.tracking.utils.path_length(streamlines, affine, aoi, fill_value=-1)

Computes the shortest path, along any streamline, between aoi and each voxel.

Parameters
streamlinesseq of (N, 3) arrays

A sequence of streamlines, path length is given in mm along the curve of the streamline.

aoiarray, 3d

A mask (binary array) of voxels from which to start computing distance.

affinearray (4, 4)

The mapping between voxel indices and the point space for seeds. The voxel_to_rasmm matrix, typically from a NIFTI file.

fill_valuefloat

The value of voxel in the path length map that are not connected to the aoi.

Returns
plmarray

Same shape as aoi. The minimum distance between every point and aoi along the path of a streamline.

Create randomly placed seeds for fiber tracking from a binary mask.

Seeds points are placed randomly distributed in voxels of mask which are True. If seed_count_per_voxel is True, this function is similar to seeds_from_mask(), with the difference that instead of evenly distributing the seeds, it randomly places the seeds within the voxels specified by the mask.

Parameters

A binary array specifying where to place the seeds for fiber tracking.

affinearray, (4, 4)

The mapping between voxel indices and the point space for seeds. The voxel_to_rasmm matrix, typically from a NIFTI file. A seed point at the center the voxel [i, j, k] will be represented as [x, y, z] where [x, y, z, 1] == np.dot(affine, [i, j, k , 1]).

seeds_countint

The number of seeds to generate. If seed_count_per_voxel is True, specifies the number of seeds to place in each voxel. Otherwise, specifies the total number of seeds to place in the mask.

seed_count_per_voxel: bool

If True, seeds_count is per voxel, else seeds_count is the total number of seeds.

random_seedint

The seed for the random seed generator (numpy.random.seed).

Raises
ValueError

When mask is not a three-dimensional array

Examples

... seed_count_per_voxel=True, random_seed=1)
array([[-0.0640051 , -0.47407377,  0.04966248]])
... seed_count_per_voxel=True, random_seed=1)
array([[-0.0640051 , -0.47407377,  0.04966248],
[ 0.0507979 ,  0.20814782, -0.20909526],
[ 0.46702984,  0.04723225,  0.47268436],
[-0.27800683,  0.37073231, -0.29328084],
[ 0.39286015, -0.16802019,  0.32122912],
[-0.42369171,  0.27991879, -0.06159077]])
... seeds_count=2, seed_count_per_voxel=True, random_seed=1)
array([[-0.0640051 , -0.47407377,  0.04966248],
[-0.27800683,  1.37073231,  1.70671916],
[ 0.0507979 ,  0.20814782, -0.20909526],
[-0.48962585,  1.00187459,  1.99577329]])

### ravel_multi_index

dipy.tracking.utils.ravel_multi_index(multi_index, dims, mode='raise', order='C')

Converts a tuple of index arrays into an array of flat indices, applying boundary modes to the multi-index.

Parameters
multi_indextuple of array_like

A tuple of integer arrays, one array for each dimension.

dimstuple of ints

The shape of array into which the indices from multi_index apply.

mode{‘raise’, ‘wrap’, ‘clip’}, optional

Specifies how out-of-bounds indices are handled. Can specify either one mode or a tuple of modes, one mode per index.

• ‘raise’ – raise an error (default)

• ‘wrap’ – wrap around

• ‘clip’ – clip to the range

In ‘clip’ mode, a negative index which would normally wrap will clip to 0 instead.

order{‘C’, ‘F’}, optional

Determines whether the multi-index should be viewed as indexing in row-major (C-style) or column-major (Fortran-style) order.

Returns
raveled_indicesndarray

An array of indices into the flattened version of an array of dimensions dims.

unravel_index

Notes

New in version 1.6.0.

Examples

>>> arr = np.array([[3,6,6],[4,5,1]])
>>> np.ravel_multi_index(arr, (7,6))
array([22, 41, 37])
>>> np.ravel_multi_index(arr, (7,6), order='F')
array([31, 41, 13])
>>> np.ravel_multi_index(arr, (4,6), mode='clip')
array([22, 23, 19])
>>> np.ravel_multi_index(arr, (4,4), mode=('clip','wrap'))
array([12, 13, 13])
>>> np.ravel_multi_index((3,1,4,1), (6,7,8,9))
1621

### reduce_labels

dipy.tracking.utils.reduce_labels(label_volume)

Reduces an array of labels to the integers from 0 to n with smallest possible n.

Examples

>>> labels = np.array([[1, 3, 9],
...                    [1, 3, 8],
...                    [1, 3, 7]])
>>> new_labels, lookup = reduce_labels(labels)
>>> lookup
array([1, 3, 7, 8, 9])
>>> new_labels
array([[0, 1, 4],
[0, 1, 3],
[0, 1, 2]]...)
>>> (lookup[new_labels] == labels).all()
True

### reduce_rois

dipy.tracking.utils.reduce_rois(rois, include)

Reduce multiple ROIs to one inclusion and one exclusion ROI.

Parameters
roislist or ndarray

A list of 3D arrays, each with shape (x, y, z) corresponding to the shape of the brain volume, or a 4D array with shape (n_rois, x, y, z). Non-zeros in each volume are considered to be within the region.

includearray or list

A list or 1D array of boolean marking inclusion or exclusion criteria.

Returns
include_roiboolean 3D array

An array marking the inclusion mask.

exclude_roiboolean 3D array

An array marking the exclusion mask

Notes

The include_roi and exclude_roi can be used to perfom the operation: “(A or B or …) and not (X or Y or …)”, where A, B are inclusion regions and X, Y are exclusion regions.

Create seeds for fiber tracking from a binary mask.

Seeds points are placed evenly distributed in all voxels of mask which are True.

Parameters

A binary array specifying where to place the seeds for fiber tracking.

affinearray, (4, 4)

The mapping between voxel indices and the point space for seeds. The voxel_to_rasmm matrix, typically from a NIFTI file. A seed point at the center the voxel [i, j, k] will be represented as [x, y, z] where [x, y, z, 1] == np.dot(affine, [i, j, k , 1]).

densityint or array_like (3,)

Specifies the number of seeds to place along each dimension. A density of 2 is the same as [2, 2, 2] and will result in a total of 8 seeds per voxel.

Raises
ValueError

When mask is not a three-dimensional array

Examples

array([[ 0.,  0.,  0.]])

### streamline_near_roi

dipy.tracking.utils.streamline_near_roi(streamline, roi_coords, tol, mode='any')

Is a streamline near an ROI.

Implements the inner loops of the near_roi() function.

Parameters
streamlinearray, shape (N, 3)

A single streamline

roi_coordsarray, shape (M, 3)

ROI coordinates transformed to the streamline coordinate frame.

tolfloat

Distance (in the units of the streamlines, usually mm). If any coordinate in the streamline is within this distance from the center of any voxel in the ROI, this function returns True.

modestring

One of {“any”, “all”, “either_end”, “both_end”}, where return True if:

“any” : any point is within tol from ROI.

“all” : all points are within tol from ROI.

“either_end” : either of the end-points is within tol from ROI

“both_end” : both end points are within tol from ROI.

Returns
outboolean

### subsegment

dipy.tracking.utils.subsegment(streamlines, max_segment_length)

Splits the segments of the streamlines into small segments.

Replaces each segment of each of the streamlines with the smallest possible number of equally sized smaller segments such that no segment is longer than max_segment_length. Among other things, this can useful for getting streamline counts on a grid that is smaller than the length of the streamline segments.

Parameters
streamlinessequence of ndarrays

The streamlines to be subsegmented.

max_segment_lengthfloat

The longest allowable segment length.

Returns
output_streamlinesgenerator

A set of streamlines.

Notes

Segments of 0 length are removed. If unchanged

Examples

>>> streamlines = [np.array([[0,0,0],[2,0,0],[5,0,0]])]
>>> list(subsegment(streamlines, 3.))
[array([[ 0.,  0.,  0.],
[ 2.,  0.,  0.],
[ 5.,  0.,  0.]])]
>>> list(subsegment(streamlines, 1))
[array([[ 0.,  0.,  0.],
[ 1.,  0.,  0.],
[ 2.,  0.,  0.],
[ 3.,  0.,  0.],
[ 4.,  0.,  0.],
[ 5.,  0.,  0.]])]
>>> list(subsegment(streamlines, 1.6))
[array([[ 0. ,  0. ,  0. ],
[ 1. ,  0. ,  0. ],
[ 2. ,  0. ,  0. ],
[ 3.5,  0. ,  0. ],
[ 5. ,  0. ,  0. ]])]

### target

Filters streamlines based on whether or not they pass through an ROI.

Parameters
streamlinesiterable

A sequence of streamlines. Each streamline should be a (N, 3) array, where N is the length of the streamline.

affinearray (4, 4)

The mapping between voxel indices and the point space for seeds. The voxel_to_rasmm matrix, typically from a NIFTI file.

A mask used as a target. Non-zero values are considered to be within the target region.

includebool, default True

If True, streamlines passing through target_mask are kept. If False, the streamlines not passing through target_mask are kept.

Returns
streamlinesgenerator

A sequence of streamlines that pass through target_mask.

Raises
ValueError

When the points of the streamlines lie outside of the target_mask.

density_map

### target_line_based

Filters streamlines based on whether or not they pass through a ROI, using a line-based algorithm. Mostly used as a replacement of target for compressed streamlines.

This function never returns single-point streamlines, whatever the value of include.

Parameters
streamlinesiterable

A sequence of streamlines. Each streamline should be a (N, 3) array, where N is the length of the streamline.

affinearray (4, 4)

The mapping between voxel indices and the point space for seeds. The voxel_to_rasmm matrix, typically from a NIFTI file.

A mask used as a target. Non-zero values are considered to be within the target region.

includebool, default True

If True, streamlines passing through target_mask are kept. If False, the streamlines not passing through target_mask are kept.

Returns
streamlinesgenerator

A sequence of streamlines that pass through target_mask.

References

[Bresenham5] Bresenham, Jack Elton. “Algorithm for computer control of a

digital plotter”, IBM Systems Journal, vol 4, no. 1, 1965.

[Houde15] Houde et al. How to avoid biased streamlines-based metrics for

streamlines with variable step sizes, ISMRM 2015.

### transform_tracking_output

dipy.tracking.utils.transform_tracking_output(tracking_output, affine, save_seeds=False)

Applies a linear transformation, given by affine, to streamlines. Parameters ———- streamlines : Streamlines generator

Either streamlines (list, ArraySequence) or a tuple with streamlines and seeds together

affinearray (4, 4)

The mapping between voxel indices and the point space for seeds. The voxel_to_rasmm matrix, typically from a NIFTI file.

save_seedsbool, optional

If set, seeds associated to streamlines will be also moved and returned

streamlinesgenerator

A generator for the sequence of transformed streamlines. If save_seeds is True, also return a generator for the transformed seeds.

### unique_rows

dipy.tracking.utils.unique_rows(in_array, dtype='f4')

This (quickly) finds the unique rows in an array

Parameters
in_array: ndarray

The array for which the unique rows should be found

dtype: str, optional

This determines the intermediate representation used for the values. Should at least preserve the values of the input array.

Returns
u_return: ndarray

Array with the unique rows of the original array.

### warn

dipy.tracking.utils.warn(/, message, category=None, stacklevel=1, source=None)

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

### wraps

dipy.tracking.utils.wraps(wrapped, assigned=('__module__', '__name__', '__qualname__', '__doc__', '__annotations__'), updated=('__dict__', ))

Decorator factory to apply update_wrapper() to a wrapper function

Returns a decorator that invokes update_wrapper() with the decorated function as the wrapper argument and the arguments to wraps() as the remaining arguments. Default arguments are as for update_wrapper(). This is a convenience function to simplify applying partial() to update_wrapper().