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.

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
\((N \times D)\), 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 \((N_i \times D)\) for \(i=1:M\) where \(M\) is the
number of sequences in the set.

This clustering framework is modular and divided in three parts:

Feature extraction

Distance computation

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.

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 np.sum(np.sqrt(np.sum((streamline[1:] - streamline[:-1]) ** 2)))
# or use a DIPY's function that computes the arc length of a 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)
```

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 http://en.wikipedia.org/wiki/Cosine_similarity.

Let’s start by importing the necessary modules.

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):
""" Computes 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):
""" Checks 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):
""" Computes 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)
```

- 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.