[scikit-image] local maxima improvements

[Yann GAVET]

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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