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Distance Transform

The example in this section is present in the source under mahotas/demos/

We start with an image, a black&white image that is mostly black except for two white spots:

import numpy as np
import mahotas

f = np.ones((256,256), bool)
f[200:,240:] = False
f[128:144,32:48] = False
.. plot::

    from pylab import imshow, gray, show
    import numpy as np

    f = np.ones((256,256), bool)
    f[200:,240:] = False
    f[128:144,32:48] = False


There is a simple distance() function which computes the distance map:

import mahotas
dmap = mahotas.distance(f)

Now dmap[y,x] contains the squared euclidean distance of the pixel (y,x) to the nearest black pixel in f. If f[y,x] == True, then dmap[y,x] == 0.

.. plot:: ../../mahotas/demos/

Distance Transform and Watershed

The distance transform is often combined with the watershed for segmentation. Here is an example (which is available with the source in the mahotas/demos/ directory as

.. plot:: ../../mahotas/demos/

The code is not very complex. Start by loading the image and preprocessing it with a Gaussian blur:

import mahotas
import mahotas.demos

nuclear = mahotas.demos.nuclear_image()
nuclear = nuclear[:,:,0]
nuclear = mahotas.gaussian_filter(nuclear, 1.)
threshed  = (nuclear > nuclear.mean())

Now, we compute the distance transform:

distances = mahotas.stretch(mahotas.distance(threshed))

We find and label the regional maxima:

Bc = np.ones((9,9))
maxima = mahotas.morph.regmax(distances, Bc=Bc)
spots,n_spots = mahotas.label(maxima, Bc=Bc)

Finally, to obtain the image above, we invert the distance transform (because of the way that cwatershed is defined) and compute the watershed:

surface = (distances.max() - distances)
areas = mahotas.cwatershed(surface, spots)
areas *= threshed

We used a random colormap with a black background for the final image. This is achieved by:

import random
from matplotlib import colors as c
colors = map(cm.jet,range(0, 256, 4))
colors[0] = (0.,0.,0.,1.)
rmap = c.ListedColormap(colors)
imshow(areas, cmap=rmap)

API Documentation

.. automodule:: mahotas
    :members: distance