tracking
¶
Tracking objects
Module: tracking._utils
¶
This is a helper module for dipy.tracking.utils.
Module: tracking.learning
¶
Learning algorithms for tractography
|
Detect corresponding tracks from list tracks1 to list tracks2 where tracks1 & tracks2 are lists of tracks |
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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
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A class for generating signals from streamlines in an efficient and speedy manner. |
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A class for representing and solving predictive models based on tractography solutions. |
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A fit of the LiFE model to diffusion data |
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Return the gradient of an N-dimensional array. |
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Calculate the gradients of the streamline along the spatial dimension |
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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] |
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The tensors generated by this fiber. |
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The signal from a single streamline estimate along each of its nodes. |
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Maps voxels to streamlines and streamlines to voxels, for setting up the LiFE equations matrix |
Module: tracking.local_tracking
¶
|
|
|
Module: tracking.mesh
¶
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Generate random triangles_indices and trilinear_coord |
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Compute points from triangles_indices and trilinear_coord |
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Compute the local area of each triangle |
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Change from values per vertex to values per triangle |
Module: tracking.metrics
¶
Metrics for tracks, where tracks are arrays of points
|
Total turning angle projected. |
|
Euclidean length of track line |
|
Size of track in bytes. |
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Midpoint of track |
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downsample for a specific number of points along the streamline Uses the length of the curve. |
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Center of mass of streamline |
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magnitude of vector |
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Frenet-Serret Space Curve Invariants Calculates the 3 vector and 2 scalar invariants of a space curve defined by vectors r = (x,y,z). |
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Calculates the mean curvature of a curve |
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Calculates the mean orientation of a curve |
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Combine sets of size n from items |
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Return longest track or length sorted track indices in bundle |
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If any segment of the track is intersecting with a sphere of specific center and radius return True otherwise False |
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If any point of the track is inside a sphere of a specified center and radius return True otherwise False. |
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If a track intersects with a sphere of a specified center and radius return the points that are inside the sphere otherwise False. |
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Generate B-splines as documented in https://scipy-cookbook.readthedocs.io/items/Interpolation.html |
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First point of the track |
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Parameters xyz array, shape(N,3) Track. |
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Select an arbitrary point along distance on the track (curve) |
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We use PCA to calculate the 3 principal directions for a track |
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Calculate distance from midpoint of a curve to arbitrary point p |
Module: tracking.streamline
¶
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Return the streamlines not as a list but as an array and an offset |
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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. |
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Move streamlines to the origin |
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Apply deformation field to streamlines |
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Apply affine transformation to streamlines |
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Select a random set of streamlines |
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Select streamlines based on logical relations with several regions of interest (ROIs). |
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Computes the cluster confidence index (cci), which is an estimation of the support a set of streamlines gives to a particular pathway. |
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Orient a set of streamlines according to a pair of ROIs |
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Orient a bundle of streamlines to a standard streamline. |
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Extract values of a scalar/vector along each streamline from a volume. |
|
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, let’s 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.]
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Count the number of unique streamlines that pass through each voxel. |
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Count the streamlines that start and end at each label pair. |
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Like bincount, but for nd-indices. |
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Reduce an array of labels to the integers from 0 to n with smallest possible n. |
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Split the segments of the streamlines into small segments. |
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Create seeds for fiber tracking from a binary mask. |
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Create randomly placed seeds for fiber tracking from a binary mask. |
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Filter streamlines based on whether or not they pass through an ROI. |
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Filter streamlines based on whether or not they pass through a ROI, using a line-based algorithm. |
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Is a streamline near an ROI. |
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Provide filtering criteria for a set of streamlines based on whether they fall within a tolerance distance from an ROI. |
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Calculate the lengths of many streamlines in a bundle. |
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Find the unique rows in an array. |
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Apply a linear transformation, given by affine, to streamlines. |
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Reduce multiple ROIs to one inclusion and one exclusion ROI. |
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Compute the shortest path, along any streamline, between aoi and each voxel. |
Get the maximum deviation angle from the minimum radius curvature. |
|
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Get minimum radius of curvature from a deviation angle. |
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 correspondence in the following way: the first column is the current index in tracks1 the second column is the corresponding index in tracks2
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)
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.)
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 correspondence in th following way the first column is the current index of tracks1 the second column is the corresponding index in tracks2
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)
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.)
See Also¶
distances.mam_distances
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.
- __init__(gtab, evals=(0.001, 0, 0), sphere=None)¶
Initialize a signal maker
Parameters¶
- gtabGradientTable class instance
The gradient table on which the signal is calculated.
- evalsarray-like of 3 items, optional
The eigenvalues of the canonical tensor to use in calculating the signal.
- spheredipy.core.Sphere class instance, optional
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
FiberModel
¶
- class dipy.tracking.life.FiberModel(gtab)¶
Bases:
ReconstModel
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.
- 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.
- evalsarray-like (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, optional
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.
- evalsarray-like (3 items, optional)
The eigenvalues of the canonical tensor used as a response function. Default:[0.001, 0, 0].
- sphere: dipy.core.Sphere instance, optional
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
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)¶
Bases:
ReconstFit
A fit of the LiFE model to diffusion data
- __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_model : A FiberModel class instance
params : the parameters derived from a fit of the model to the data.
- predict(gtab=None, S0=None)¶
Predict the signal
Parameters¶
- gtabGradientTable
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
gradient¶
- dipy.tracking.life.gradient(f)¶
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¶
- gradientndarray
N arrays of the same shape as f giving the derivative of f with respect to each dimension.
Examples¶
>>> x = np.array([1, 2, 4, 7, 11, 16], dtype=float) >>> gradient(x) array([ 1. , 1.5, 2.5, 3.5, 4.5, 5. ])
>>> gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=float)) [array([[ 2., 2., -1.], [ 2., 2., -1.]]), array([[ 1. , 2.5, 4. ], [ 1. , 1. , 1. ]])]
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.
streamline_gradients¶
grad_tensor¶
- dipy.tracking.life.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]
Parameters¶
- grad1d array of shape (3,)
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.
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, optional
The estimated eigenvalues of a single fiber tensor.
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.
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¶
streamline : a single streamline
gtab : GradientTable class instance
- evalsarray-like of length 3, optional
The eigenvalues of the canonical tensor used as an estimate of the signal generated by each node of the streamline.
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, v2fn : tuple 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?
LocalTracking
¶
- class dipy.tracking.local_tracking.LocalTracking(direction_getter, stopping_criterion, seeds, affine, step_size, max_cross=None, maxlen=500, minlen=2, fixedstep=True, return_all=True, random_seed=None, save_seeds=False, unidirectional=False, randomize_forward_direction=False, initial_directions=None)¶
Bases:
object
- __init__(direction_getter, stopping_criterion, seeds, affine, step_size, max_cross=None, maxlen=500, minlen=2, fixedstep=True, return_all=True, random_seed=None, save_seeds=False, unidirectional=False, randomize_forward_direction=False, initial_directions=None)¶
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), optional
Points to seed the tracking. Seed points should be given in point space of the track (see
affine
).- affinearray (4, 4), optional
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, optional
Step size used for tracking.
- max_crossint or None, optional
The maximum number of direction to track from each seed in crossing voxels. By default all initial directions are tracked.
- maxlenint, optional
Maximum length of generated streamlines. Longer streamlines will be discarted if return_all=False.
- minlenint, optional
Minimum length of generated streamlines. Shorter streamlines will be discarted if return_all=False.
- fixedstepbool, optional
If true, a fixed stepsize is used, otherwise a variable step size is used.
- return_allbool, optional
If true, return all generated streamlines, otherwise only streamlines reaching end points or exiting the image.
- random_seedint, optional
The seed for the random seed generator (numpy.random.seed and random.seed).
- save_seedsbool, optional
If True, return seeds alongside streamlines
- unidirectionalbool, optional
If true, the tracking is performed only in the forward direction. The seed position will be the first point of all streamlines.
- randomize_forward_directionbool, optional
If true, the forward direction is randomized (multiplied by 1 or -1). Otherwise, the provided forward direction is used.
- initial_directions: array (N, npeaks, 3), optional
Initial direction to follow from the
seed
position. Ifmax_cross
is None, one streamline will be generated per peak per voxel. If None, direction_getter.initial_direction is used.
ParticleFilteringTracking
¶
- class dipy.tracking.local_tracking.ParticleFilteringTracking(direction_getter, stopping_criterion, seeds, affine, step_size, max_cross=None, maxlen=500, minlen=2, 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, min_wm_pve_before_stopping=0, unidirectional=False, randomize_forward_direction=False, initial_directions=None)¶
Bases:
LocalTracking
- __init__(direction_getter, stopping_criterion, seeds, affine, step_size, max_cross=None, maxlen=500, minlen=2, 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, min_wm_pve_before_stopping=0, unidirectional=False, randomize_forward_direction=False, initial_directions=None)¶
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, optional
The maximum number of direction to track from each seed in crossing voxels. By default all initial directions are tracked.
- maxlenint, optional
Maximum length of generated streamlines. Longer streamlines will be discarted if return_all=False.
- minlenint, optional
Minimum length of generated streamlines. Shorter streamlines will be discarted if return_all=False.
- 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, optional
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, optional
Maximum number of trial for the particle filtering tractography (Prevents infinite loops).
- particle_countint, optional
Number of particles to use in the particle filter.
- return_allbool, optional
If true, return all generated streamlines, otherwise only streamlines reaching end points or exiting the image.
- random_seedint, optional
The seed for the random seed generator (numpy.random.seed and random.seed).
- save_seedsbool, optional
If True, return seeds alongside streamlines
- min_wm_pve_before_stoppingint, optional
Minimum white matter pve (1 - stopping_criterion.include_map - stopping_criterion.exclude_map) to reach before allowing the tractography to stop.
- unidirectionalbool, optional
If true, the tracking is performed only in the forward direction. The seed position will be the first point of all streamlines.
- randomize_forward_directionbool, optional
If true, the forward direction is randomized (multiplied by 1 or -1). Otherwise, the provided forward direction is used.
- initial_directions: array (N, npeaks, 3), optional
Initial direction to follow from the
seed
position. Ifmax_cross
is None, one streamline will be generated per peak per voxel. If None, direction_getter.initial_direction is used.
References¶
random_coordinates_from_surface¶
- dipy.tracking.mesh.random_coordinates_from_surface(nb_triangles, nb_seed, triangles_mask=None, triangles_weight=None, rand_gen=None)¶
Generate random triangles_indices and trilinear_coord
- Triangles_indices probability are weighted by triangles_weight,
for each triangles inside the given triangles_mask
Parameters¶
- nb_trianglesint (n)
The amount of triangles in the mesh
- nb_seedint
The number of random indices and coordinates generated.
- triangles_mask[n] numpy array
Specifies which triangles should be chosen (or not)
- triangles_weight[n] numpy array
Specifies the weight/probability of choosing each triangle
- rand_genint
The seed for the random seed generator (numpy.random.seed).
Returns¶
- triangles_idx: [s] array
Randomly chosen triangles_indices
- trilin_coord: [s,3] array
Randomly chosen trilinear_coordinates
See Also¶
seeds_from_surface_coordinates, random_seeds_from_mask
seeds_from_surface_coordinates¶
- dipy.tracking.mesh.seeds_from_surface_coordinates(triangles, vts_values, triangles_idx, trilinear_coord)¶
Compute points from triangles_indices and trilinear_coord
Parameters¶
- triangles[n, 3] -> m array
A list of triangles from a mesh
- vts_values[m, .] array
List of values to interpolates from coordinates along vertices, (vertices, vertices_normal, vertices_colors …)
- triangles_idx[s] array
Specifies which triangles should be chosen (or not)
- trilinear_coord[s, 3] array
Specifies the weight/probability of choosing each triangle
Returns¶
- pts[s, …] array
Interpolated values of vertices with triangles_idx and trilinear_coord
See Also¶
random_coordinates_from_surface
triangles_area¶
- dipy.tracking.mesh.triangles_area(triangles, vts)¶
Compute the local area of each triangle
Parameters¶
- triangles[n, 3] -> m array
A list of triangles from a mesh
- vts[m, .] array
List of vertices
Returns¶
- triangles_area[m] array
List of area for each triangle in the mesh
See Also¶
random_coordinates_from_surface
vertices_to_triangles_values¶
- dipy.tracking.mesh.vertices_to_triangles_values(triangles, vts_values)¶
Change from values per vertex to values per triangle
Parameters¶
- triangles[n, 3] -> m array
A list of triangles from a mesh
- vts_values[m, .] array
List of values to interpolates from coordinates along vertices, (vertices, vertices_normal, vertices_colors …)
Returns¶
- triangles_values[m] array
List of values for each triangle in the mesh
See Also¶
random_coordinates_from_surface
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.
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])
bytes¶
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. ])
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.
dipy.tracking.metrics.downsample is deprecated, Please use dipy.tracking.streamline.set_number_of_points instead
deprecated from version: 1.2
Raises <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
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.])
magn¶
- dipy.tracking.metrics.magn(xyz, n=1)¶
magnitude of vector
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. Similar to https://www.mathworks.com/matlabcentral/fileexchange/11169-frenet 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 ———- xyz : array-like shape (N,3) array representing x,y,z of N points in a track Returns ——- T : array shape (N,3) array representing the tangent of the curve xyz N : array shape (N,3) array representing the normal of the curve xyz B : array shape (N,3) array representing the binormal of the curve xyz k : array shape (N,1) array representing the curvature of the curve xyz t : array 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)
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¶
generate_combinations¶
- dipy.tracking.metrics.generate_combinations(items, n)¶
Combine sets of size n from items
Parameters¶
items : sequence n : int
Returns¶
ic : iterator
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]
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]...)
intersect_sphere¶
- dipy.tracking.metrics.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
Parameters¶
- xyzarray, shape (N,3)
representing x,y,z of the N points of the track
- centerarray, shape (3,)
center of the sphere
- radiusfloat
radius 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]) >>> sph_radius = 1 >>> intersect_sphere(line,sph_cent,sph_radius) True
Notes¶
The ray to sphere intersection method used here is similar with https://paulbourke.net/geometry/circlesphere/ https://paulbourke.net/geometry/circlesphere/source.cpp we just applied it for every segment neglecting the intersections where the intersecting points are not inside the segment
inside_sphere¶
- dipy.tracking.metrics.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. Mathematically 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 ———- xyz : array, shape (N,3) representing x,y,z of the N points of the track center : array, shape (3,) center of the sphere radius : float radius 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]) >>> sph_radius = 1 >>> inside_sphere(line,sph_cent,sph_radius) True
inside_sphere_points¶
- dipy.tracking.metrics.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. Mathematically 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 ———- xyz : array, shape (N,3) representing x,y,z of the N points of the track center : array, shape (3,) center of the sphere radius : float radius of the sphere Returns ——- xyzn : array, 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]) >>> sph_radius = 1 >>> inside_sphere_points(line,sph_cent,sph_radius) array([[1, 1, 1]])
spline¶
- dipy.tracking.metrics.spline(xyz, s=3, k=2, nest=-1)¶
Generate B-splines as documented in https://scipy-cookbook.readthedocs.io/items/Interpolation.html
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
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
See Also¶
scipy.interpolate.splprep scipy.interpolate.splev
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
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
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)
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
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]))
unlist_streamlines¶
relist_streamlines¶
center_streamlines¶
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
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
select_random_set_of_streamlines¶
- dipy.tracking.streamline.select_random_set_of_streamlines(streamlines, select, rng=None)¶
Select a random set of streamlines
Parameters¶
- streamlinesStreamlines
Object of 2D ndarrays of shape[-1]==3
- selectint
Number of streamlines to select. If there are less streamlines than
select
thenselect=len(streamlines)
.- rngRandomState
Default None.
Returns¶
selected_streamlines : list
Notes¶
The same streamline will not be selected twice.
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.
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.
Returns¶
- generator
Generates the streamlines to be included based on these criteria.
See also¶
dipy.tracking.utils.near_roi()
dipy.tracking.utils.reduce_rois()
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) >>> mask2 = np.zeros_like(mask1) >>> mask1[0, 0, 0] = True >>> mask2[1, 0, 0] = True >>> selection = select_by_rois(streamlines, np.eye(4), [mask1, mask2], ... [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.]])] >>> selection = select_by_rois(streamlines, np.eye(4), [mask1, mask2], ... [True, False], ... tol=0.87) >>> list(selection) [array([[ 0., 0., 0.], [ 0., 1., 1.], [ 0., 2., 2.]])] >>> selection = select_by_rois(streamlines, np.eye(4), [mask1, mask2], ... [True, True], ... mode="both_end", ... tol=1.0) >>> list(selection) [array([[ 0. , 0. , 0.9], [ 1.9, 0. , 0. ]])] >>> mask2[0, 2, 2] = True >>> selection = select_by_rois(streamlines, np.eye(4), [mask1, mask2], ... [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.]])]
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.
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.
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.
nbytes¶
- dipy.tracking.streamline.nbytes(streamlines)¶
density_map¶
- dipy.tracking.utils.density_map(streamlines, affine, vol_dims)¶
Count 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.
connectivity_matrix¶
- dipy.tracking.utils.connectivity_matrix(streamlines, affine, label_volume, inclusive=False, symmetric=True, return_mapping=False, mapping_as_streamlines=False)¶
Count 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. 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 ifi < j
mapping will have key(i, j)
but not key(j, i)
.
ndbincount¶
reduce_labels¶
- dipy.tracking.utils.reduce_labels(label_volume)¶
Reduce 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
subsegment¶
- dipy.tracking.utils.subsegment(streamlines, max_segment_length)¶
Split 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. ]])]
seeds_from_mask¶
- dipy.tracking.utils.seeds_from_mask(mask, affine, density=(1, 1, 1))¶
Create seeds for fiber tracking from a binary mask.
Seeds points are placed evenly distributed in all voxels of
mask
which areTrue
.Parameters¶
- maskbinary 3d array_like
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.
See Also¶
random_seeds_from_mask
Raises¶
- ValueError
When
mask
is not a three-dimensional array
Examples¶
>>> mask = np.zeros((3,3,3), 'bool') >>> mask[0,0,0] = 1 >>> seeds_from_mask(mask, np.eye(4), [1,1,1]) array([[ 0., 0., 0.]])
random_seeds_from_mask¶
- dipy.tracking.utils.random_seeds_from_mask(mask, affine, seeds_count=1, seed_count_per_voxel=True, random_seed=None)¶
Create randomly placed seeds for fiber tracking from a binary mask.
Seeds points are placed randomly distributed in voxels of
mask
which areTrue
. Ifseed_count_per_voxel
isTrue
, this function is similar toseeds_from_mask()
, with the difference that instead of evenly distributing the seeds, it randomly places the seeds within the voxels specified by themask
.Parameters¶
- maskbinary 3d array_like
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.Generator).
See Also¶
seeds_from_mask
Raises¶
- ValueError
When
mask
is not a three-dimensional array
Examples¶
>>> mask = np.zeros((3,3,3), 'bool') >>> mask[0,0,0] = 1 >>> random_seeds_from_mask(mask, np.eye(4), seeds_count=1, ... seed_count_per_voxel=True, random_seed=1) array([[-0.23838787, -0.20150886, 0.31422574]]) >>> random_seeds_from_mask(mask, np.eye(4), seeds_count=6, ... seed_count_per_voxel=True, random_seed=1) array([[-0.23838787, -0.20150886, 0.31422574], [-0.41435083, -0.26318949, 0.30127447], [ 0.44305611, 0.01132755, 0.47624371], [ 0.30500292, 0.30794079, 0.01532556], [ 0.03816435, -0.15672913, -0.13093276], [ 0.12509547, 0.3972138 , 0.27568569]]) >>> mask[0,1,2] = 1 >>> random_seeds_from_mask(mask, np.eye(4), ... seeds_count=2, seed_count_per_voxel=True, random_seed=1) array([[ 0.30500292, 1.30794079, 2.01532556], [-0.23838787, -0.20150886, 0.31422574], [ 0.3702492 , 0.78681721, 2.10314815], [-0.41435083, -0.26318949, 0.30127447]])
target¶
- dipy.tracking.utils.target(streamlines, affine, target_mask, include=True)¶
Filter 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.
- target_maskarray-like
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.
See Also¶
density_map
target_line_based¶
- dipy.tracking.utils.target_line_based(streamlines, affine, target_mask, include=True)¶
Filter 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.
- target_maskarray-like
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.
See Also¶
dipy.tracking.utils.density_map dipy.tracking.streamline.compress_streamlines
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¶
out : boolean
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.
length¶
unique_rows¶
- dipy.tracking.utils.unique_rows(in_array, dtype='f4')¶
Find 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.
transform_tracking_output¶
- dipy.tracking.utils.transform_tracking_output(tracking_output, affine, save_seeds=False)¶
Apply a linear transformation, given by affine, to streamlines.
Parameters¶
- tracking_outputStreamlines 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
Returns¶
- streamlinesgenerator
A generator for the sequence of transformed streamlines. If save_seeds is True, also return a generator for the transformed seeds.
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 perform the operation: “(A or B or …) and not (X or Y or …)”, where A, B are inclusion regions and X, Y are exclusion regions.
path_length¶
- dipy.tracking.utils.path_length(streamlines, affine, aoi, fill_value=-1)¶
Compute 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.
max_angle_from_curvature¶
- dipy.tracking.utils.max_angle_from_curvature(min_radius_curvature, step_size)¶
Get the maximum deviation angle from the minimum radius curvature.
Parameters¶
- min_radius_curvature: float
Minimum radius of curvature in mm.
- step_size: float
The tracking step size in mm.
Returns¶
- max_angle: float
The maximum deviation angle in radian, given the radius curvature and the step size.
References¶
For more information: https://onlinelibrary.wiley.com/doi/full/10.1002/ima.22005
min_radius_curvature_from_angle¶
- dipy.tracking.utils.min_radius_curvature_from_angle(max_angle, step_size)¶
Get minimum radius of curvature from a deviation angle.
Parameters¶
- max_angle: float
The maximum deviation angle in radian. theta should be between [0 - pi/2] otherwise default will be pi/2.
- step_size: float
The tracking step size in mm.
Returns¶
- min_radius_curvature: float
Minimum radius of curvature in mm, given the maximum deviation angle theta and the step size.
References¶
More information: https://onlinelibrary.wiley.com/doi/full/10.1002/ima.22005