Enhancing QuickBundles with different metrics and features

QuickBundles [Garyfallidis12] is a flexible algorithm that requires only a distance metric and an adjacency threshold to perform clustering. There is a wide variety of metrics that could be used to cluster streamlines.

The purpose of this tutorial is to show how to easily create new Feature and new Metric classes that can be used by QuickBundles.

Clustering framework

DIPY provides a simple, flexible and fast framework to do clustering of sequential data (e.g. streamlines).

A sequential datum in DIPY is represented as a numpy array of size \((N imes D)\), where each row of the array represents a \(D\) dimensional point of the sequence. A set of these sequences is represented as a list of numpy arrays of size \((N_i imes D)\) for \(i=1:M\) where \(M\) is the number of sequences in the set.

This clustering framework is modular and divided in three parts:

1. Feature extraction

2. Distance computation

3. Clustering algorithm

The feature extraction part includes any preprocessing needed to be done on the data before computing distances between them (e.g. resampling the number of points of a streamline). To define a new way of extracting features, one has to subclass Feature (see below).

The distance computation part includes any metric capable of evaluating a distance between two sets of features previously extracted from the data. To define a new way of extracting features, one has to subclass Metric (see below).

The clustering algorithm part represents the clustering algorithm itself (e.g. QuickBundles, K-means, Hierarchical Clustering). More precisely, it includes any algorithms taking as input a list of sequential data and outputting a ClusterMap object.

Extending Feature

This section will guide you through the creation of a new feature extraction method that can be used in the context of this clustering framework. For a list of available features in DIPY see Tractography Clustering - Available Features.

Assuming a set of streamlines, the type of features we want to extract is the arc length (i.e. the sum of the length of each segment for a given streamline).

Let’s start by importing the necessary modules.

import numpy as np

from dipy.data import get_fnames
from dipy.io.streamline import load_tractogram
from dipy.tracking.streamline import Streamlines
from dipy.viz import window, actor, colormap
from dipy.segment.clustering import QuickBundles
from dipy.segment.featurespeed import Feature, VectorOfEndpointsFeature
from dipy.segment.metric import Metric, SumPointwiseEuclideanMetric
from dipy.tracking.streamline import length

We now define the class ArcLengthFeature that will perform the desired feature extraction. When subclassing Feature, two methods have to be redefined: infer_shape and extract.

Also, an important property about feature extraction is whether or not its process is invariant to the order of the points within a streamline. This is needed as there is no way one can tell which extremity of a streamline is the beginning and which one is the end.

class ArcLengthFeature(Feature):
    """ Computes the arc length of a streamline. """
    def __init__(self):
        # The arc length stays the same even if the streamline is reversed.
        super(ArcLengthFeature, self).__init__(is_order_invariant=True)

    def infer_shape(self, streamline):
        """ Infers the shape of features extracted from `streamline`. """
        # Arc length is a scalar
        return 1

    def extract(self, streamline):
        """ Extracts features from `streamline`. """
        return length(streamline)

The new feature extraction ArcLengthFeature is ready to be used. Let’s use it to cluster a set of streamlines by their arc length. For educational purposes we will try to cluster a small streamline bundle known from neuroanatomy as the fornix.

We start by loading the fornix streamlines.

fname = get_fnames('fornix')
fornix = load_tractogram(fname, 'same',
                         bbox_valid_check=False).streamlines

streamlines = Streamlines(fornix)

Perform QuickBundles clustering using the metric SumPointwiseEuclideanMetric and our ArcLengthFeature.

metric = SumPointwiseEuclideanMetric(feature=ArcLengthFeature())
qb = QuickBundles(threshold=2., metric=metric)
clusters = qb.cluster(streamlines)

We will now visualize the clustering result.

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

scene = window.Scene()
scene.SetBackground(1, 1, 1)
scene.add(actor.streamtube(streamlines, colormap_full))
window.record(scene, out_path='fornix_clusters_arclength.png', size=(600, 600))

# Enables/disables interactive visualization
interactive = False
if interactive:
    window.show(scene)

Showing the different clusters obtained by using the arc length.

Extending Metric

This section will guide you through the creation of a new metric that can be used in the context of this clustering framework. For a list of available metrics in DIPY see Tractography Clustering - Available Metrics.

Assuming a set of streamlines, we want a metric that computes the cosine distance giving the vector between endpoints of each streamline (i.e. one minus the cosine of the angle between two vectors). For more information about this distance check https://en.wikipedia.org/wiki/Cosine_similarity.

We now define the class CosineMetric that will perform the desired distance computation. When subclassing Metric, two methods have to be redefined: are_compatible and dist. Moreover, when implementing the dist method, one needs to make sure the distance returned is symmetric (i.e. dist(A, B) == dist(B, A)).

class CosineMetric(Metric):
    """Compute the cosine distance between two streamlines."""
    def __init__(self):
        # For simplicity, features will be the vector between endpoints of a
        # streamline.
        super(CosineMetric, self).__init__(feature=VectorOfEndpointsFeature())

    def are_compatible(self, shape1, shape2):
        """Check if two features are vectors of same dimension.

        Basically this method exists so that we don't have to check
        inside the `dist` method (speedup).
        """
        return shape1 == shape2 and shape1[0] == 1

    def dist(self, v1, v2):
        """Compute a the cosine distance between two vectors."""
        norm = lambda x: np.sqrt(np.sum(x**2))
        cos_theta = np.dot(v1, v2.T) / (norm(v1)*norm(v2))

        # Make sure it's in [-1, 1], i.e. within domain of arccosine
        cos_theta = np.minimum(cos_theta, 1.)
        cos_theta = np.maximum(cos_theta, -1.)
        return np.arccos(cos_theta) / np.pi  # Normalized cosine distance

The new distance CosineMetric is ready to be used. Let’s use it to cluster a set of streamlines according to the cosine distance of the vector between their endpoints. For educational purposes we will try to cluster a small streamline bundle known from neuroanatomy as the fornix.

We start by loading the fornix streamlines.

fname = get_fnames('fornix')
fornix = load_tractogram(fname, 'same', bbox_valid_check=False)
streamlines = fornix.streamlines

Perform QuickBundles clustering using our metric CosineMetric.

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

We will now visualize the clustering result.

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

scene = window.Scene()
scene.SetBackground(1, 1, 1)
scene.add(actor.streamtube(streamlines, colormap_full))
window.record(scene, out_path='fornix_clusters_cosine.png', size=(600, 600))
if interactive:
    window.show(scene)

Showing the different clusters obtained by using the cosine metric.

References

[Garyfallidis12]

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