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Tractography Clustering - Available Metrics

This page lists available metrics that can be used by the tractography clustering framework. For every metric a brief description is provided explaining: what it does, when it’s useful and how to use it. If you are not familiar with the tractography clustering framework, check this tutorial Clustering framework.

Note: All examples assume a function get_streamlines exists. We defined here a simple function to do so. It imports the necessary modules and load a small streamline bundle.

def get_streamlines():
    from nibabel import trackvis as tv
    from dipy.data import get_data

    fname = get_data('fornix')
    streams, hdr = tv.read(fname)
    streamlines = [i[0] for i in streams]
    return streamlines

Average of Pointwise Euclidean Metric

What: Instances of AveragePointwiseEuclideanMetric first compute the pointwise Euclidean distance between two sequences of same length then return the average of those distances. This metric takes as inputs two features that are sequences containing the same number of elements.

When: By default the QuickBundles clustering will resample your streamlines on-the-fly so they have 12 points. If for some reason you want to avoid this and you made sure all your streamlines have already the same number of points, you can manually provide an instance of AveragePointwiseEuclideanMetric to QuickBundles. Since the default Feature is the IdentityFeature the streamlines won’t be resampled thus saving some computational time.

Note: Inputs must be sequences of same length.

from dipy.viz import fvtk
from dipy.segment.clustering import QuickBundles
from dipy.segment.metric import AveragePointwiseEuclideanMetric

# Get some streamlines.
streamlines = get_streamlines()  # Previously defined.

# Make sure our streamlines have the same number of points.
from dipy.tracking.streamline import set_number_of_points
streamlines = set_number_of_points(streamlines, nb_points=12)

# Create the instance of `AveragePointwiseEuclideanMetric` to use.
metric = AveragePointwiseEuclideanMetric()
qb = QuickBundles(threshold=10., metric=metric)
clusters = qb.cluster(streamlines)

print("Nb. clusters:", len(clusters))
print("Cluster sizes:", map(len, clusters))
Nb. clusters: 4

Cluster sizes: [64, 191, 44, 1]

Sum of Pointwise Euclidean Metric

What: Instances of SumPointwiseEuclideanMetric first compute the pointwise Euclidean distance between two sequences of same length then return the sum of those distances.

When: This metric mainly exists because it is used internally by AveragePointwiseEuclideanMetric.

Note: Inputs must be sequences of same length.

from dipy.segment.clustering import QuickBundles
from dipy.segment.metric import SumPointwiseEuclideanMetric

# Get some streamlines.
streamlines = get_streamlines()  # Previously defined.

# Make sure our streamlines have the same number of points.
from dipy.tracking.streamline import set_number_of_points
nb_points = 12
streamlines = set_number_of_points(streamlines, nb_points=nb_points)

# Create the instance of `SumPointwiseEuclideanMetric` to use.
metric = SumPointwiseEuclideanMetric()
qb = QuickBundles(threshold=10.*nb_points, metric=metric)
clusters = qb.cluster(streamlines)

print("Nb. clusters:", len(clusters))
print("Cluster sizes:", map(len, clusters))
Nb. clusters: 4

Cluster sizes: [64, 191, 44, 1]

Minimum Average Direct Flip Metric (MDF)

What: It is the metric used in the QuickBundles algorithm [Garyfallidis12]. Instances of MinimumAverageDirectFlipMetric first compute the direct distance d1 by taking the average of the pointwise Euclidean distances between two sequences of same length. Reverse one of the two sequences and compute the flip distance d2 using the same approach as for d1. Then, return the minimum between d1 and d2.

When: This metric mainly exists because it is used internally by AveragePointwiseEuclideanMetric.

Note: Inputs must be sequences of same length.

from dipy.segment.metric import MinimumAverageDirectFlipMetric

# Get some streamlines.
streamlines = get_streamlines()  # Previously defined.

# Make sure our streamlines have the same number of points.
from dipy.tracking.streamline import set_number_of_points
streamlines = set_number_of_points(streamlines, nb_points=20)

# Create the instance of `MinimumAverageDirectFlipMetric` to use.
metric = MinimumAverageDirectFlipMetric()
d = metric.dist(streamlines[0], streamlines[1])

print("MDF distance between the first two streamlines: ", d)
MDF distance between the first two streamlines: 11.681308709622542

Cosine Metric

What: Instances of CosineMetric compute the cosine distance between two vectors (for more information see the wiki page).

When: This metric can be useful when you only need information about the orientation of a streamline.

Note: Inputs must be vectors (i.e. 1D array).

import numpy as np
from dipy.viz import fvtk
from dipy.segment.clustering import QuickBundles
from dipy.segment.metric import VectorOfEndpointsFeature
from dipy.segment.metric import CosineMetric

# Get some streamlines.
streamlines = get_streamlines()  # Previously defined.

feature = VectorOfEndpointsFeature()
metric = CosineMetric(feature)
qb = QuickBundles(threshold=0.1, metric=metric)
clusters = qb.cluster(streamlines)

# Color each streamline according to the cluster they belong to.
colormap = fvtk.create_colormap(np.arange(len(clusters)))
colormap_full = np.ones((len(streamlines), 3))
for cluster, color in zip(clusters, colormap):
    colormap_full[cluster.indices] = color

# Visualization
ren = fvtk.ren()
fvtk.clear(ren)
ren.SetBackground(0, 0, 0)
fvtk.add(ren, fvtk.streamtube(streamlines, colormap_full))
fvtk.record(ren, n_frames=1, out_path='cosine_metric.png', size=(600, 600))
../_images/cosine_metric.png

Showing the streamlines colored according to their orientation.

References

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

Example source code

You can download the full source code of this example. This same script is also included in the dipy source distribution under the doc/examples/ directory.