First mistake, this should work, but the discretization of the 'continuous' values should be handled with care.

def rmax(I):

"""

Own version of regional maximum

This avoids plateaus problems of peak_local_max

I: original image, int values

returns: binary array, with 1 for the maxima

"""

I = I.astype('float');

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

I = I.astype('int32');

h = 1;

rec = morphology.reconstruction(I, I+h);

maxima = I + h - rec;

return maxima

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

from skimage import morphology

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

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-- 
Yann GAVET
Assistant Professor - Ecole Nationale Supérieure des Mines de Saint-Etienne
158 Cours Fauriel, CS 62362, 42023 SAINT-ETIENNE cedex 2
Tel: (33) - 4 7742 0170