Dear all,

I have been playing around with the watershed segmentation by markers with the code proposed as example:

http://scikit-image.org/docs/dev/auto_examples/segmentation/plot_watershed.html

Unfortunately, if we use for example floating values for the radii of the circles (like r1, r2 = 20.7, 24.7), the separation is not perfect, as it gives 4 labels.

If we use the chamfer distance transform instead of the Euclidean distance transform, it is even worse.

It appears that the markers detection by regional maximum (peak_local_max) fails in the presence of plateaus. Its algorithm is basically D(I)==I, where D is the morphological dilation.

A better algorithm would be to use morphological reconstruction (see SOILLE, Pierre. Morphological image analysis: principles and applications. Springer Science & Business Media, 2003, p202, Eq 6.13). A proposition of the code can be the following (it should deal with float values):

import numpy as np

def rmax(I):

"""

This avoids plateaus problems of peak_local_max

I: original image, float values

returns: binary array, with True for the maxima

"""

I = I.astype('float');

I = I / np.max(I) * 2**31;

I = I.astype('int32');

rec = morphology.reconstruction(I-1, I);

maxima = I - rec;

return maxima>0

This code is relatively fast. Notice that the matlab function imregionalmax seem to work the same way (the help is not explicit, but the results on a few tests seem to be similar).

I am afraid I do not have time to integrate it on gitlab, but this should be a good start if someone wants to work on it. If you see any problem with this code, please correct it.

thank you

best regards

-- 
Yann