# Streamline length and size reduction¶

This example shows how to calculate the lengths of a set of streamlines and also how to compress the streamlines without considerably reducing their lengths or overall shape.

A streamline in DIPY is represented as a numpy array of size \((N \times 3)\) where each row of the array represent a 3D point of the streamline. A set of streamlines is represented with a list of numpy arrays of size \((N_i \times 3)\) for \(i=1:M\) where \(M\) is the number of streamlines in the set.

```
import numpy as np
from dipy.tracking.utils import length
from dipy.tracking.metrics import downsample
from dipy.tracking.distances import approx_polygon_track
```

Let’s first create a simple simulation of a bundle of streamlines using a cosine function.

```
def simulated_bundles(no_streamlines=50, n_pts=100):
t = np.linspace(-10, 10, n_pts)
bundle = []
for i in np.linspace(3, 5, no_streamlines):
pts = np.vstack((np.cos(2 * t/np.pi), np.zeros(t.shape) + i, t )).T
bundle.append(pts)
start = np.random.randint(10, 30, no_streamlines)
end = np.random.randint(60, 100, no_streamlines)
bundle = [10 * streamline[start[i]:end[i]]
for (i, streamline) in enumerate(bundle)]
bundle = [np.ascontiguousarray(streamline) for streamline in bundle]
return bundle
bundle = simulated_bundles()
print('This bundle has %d streamlines' % len(bundle))
```

This bundle has 50 streamlines.

Using the `length`

function we can retrieve the lengths of each streamline.
Below we show the histogram of the lengths of the streamlines.

```
lengths = list(length(bundle))
import matplotlib.pyplot as plt
fig_hist, ax = plt.subplots(1)
ax.hist(lengths, color='burlywood')
ax.set_xlabel('Length')
ax.set_ylabel('Count')
# plt.show()
plt.legend()
plt.savefig('length_histogram.png')
```

`Length`

will return the length in the units of the coordinate system that
streamlines are currently. So, if the streamlines are in world coordinates then
the lengths will be in millimeters (mm). If the streamlines are for example in
native image coordinates of voxel size 2mm isotropic then you will need to
multiply the lengths by 2 if you want them to correspond to mm. In this example
we process simulated data without units, however this information is good to have
in mind when you calculate lengths with real data.

Next, let’s find the number of points that each streamline has.

```
n_pts = [len(streamline) for streamline in bundle]
```

Often, streamlines are represented with more points than what is actually
necessary for specific applications. Also, sometimes every streamline has
different number of points which could be of a trouble for some algorithms
. The function `downsample`

can be used to set the number of points of a
streamline at a specific number and at the same time enforce that all the
segments of the streamline will have equal length.

```
bundle_downsampled = [downsample(s, 12) for s in bundle]
n_pts_ds = [len(s) for s in bundle_downsampled]
```

Alternatively, the function `approx_polygon_track`

allows to reduce the number
of points so that they are more points in curvy regions and less points in
less curvy regions. In contrast with `downsample`

it does not enforce that
segments should be of equal size.

```
bundle_downsampled2 = [approx_polygon_track(s, 0.25) for s in bundle]
n_pts_ds2 = [len(streamline) for streamline in bundle_downsampled2]
```

Both, `downsample`

and `approx_polygon_track`

can be thought as methods for
lossy compression of streamlines.

```
from dipy.viz import window, actor
# Enables/disables interactive visualization
interactive = False
ren = window.Renderer()
ren.SetBackground(*window.colors.white)
bundle_actor = actor.streamtube(bundle, window.colors.red, linewidth=0.3)
ren.add(bundle_actor)
bundle_actor2 = actor.streamtube(bundle_downsampled, window.colors.red, linewidth=0.3)
bundle_actor2.SetPosition(0, 40, 0)
bundle_actor3 = actor.streamtube(bundle_downsampled2, window.colors.red, linewidth=0.3)
bundle_actor3.SetPosition(0, 80, 0)
ren.add(bundle_actor2)
ren.add(bundle_actor3)
ren.set_camera(position=(0, 0, 0), focal_point=(30, 0, 0))
window.record(ren, out_path='simulated_cosine_bundle.png', size=(900, 900))
if interactive:
window.show(ren)
```

From the figure above we can see that all 3 bundles look quite similar. However, when we plot the histogram of the number of points used for each streamline, it becomes obvious that we have managed to reduce in a great amount the size of the initial dataset.

```
import matplotlib.pyplot as plt
fig_hist, ax = plt.subplots(1)
ax.hist(n_pts, color='r', histtype='step', label='initial')
ax.hist(n_pts_ds, color='g', histtype='step', label='downsample (12)')
ax.hist(n_pts_ds2, color='b', histtype='step', label='approx_polygon_track (0.25)')
ax.set_xlabel('Number of points')
ax.set_ylabel('Count')
# plt.show()
plt.legend()
plt.savefig('n_pts_histogram.png')
```

Finally, we can also show that the lengths of the streamlines haven’t changed considerably after applying the two methods of downsampling.

```
lengths_downsampled = list(length(bundle_downsampled))
lengths_downsampled2 = list(length(bundle_downsampled2))
fig, ax = plt.subplots(1)
ax.plot(lengths, color='r', label='initial')
ax.plot(lengths_downsampled, color='g', label='downsample (12)')
ax.plot(lengths_downsampled2, color='b', label='approx_polygon_track (0.25)')
ax.set_xlabel('Streamline ID')
ax.set_ylabel('Length')
# plt.show()
plt.legend()
plt.savefig('lengths_plots.png')
```

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.