[scikit-image] local maxima improvements
Yann GAVET
gavet at emse.fr
Wed Apr 11 03:24:57 EDT 2018
Thank you Juan,
all my researches from a well-known web search engine gave me
peak_local_max as a solution, in particular, the example attached to the
watershed function.
Sorry about this. Maybe this function should be marked as deprecated in
favor of local_maxima.
About peak_local_max, there is an option indices=False that results in
an array with the same shape as the image in argument.
yann
Le 11/04/2018 à 04:44, Juan Nunez-Iglesias a écrit :
> Hi Yann, and thanks for the interest!
>
> We actually already have this algorithm implemented in
> skimage.morphology.local_maxima.
>
> peak_local_max is a bit different and I must admit I don’t understand
> the logic in it. I *particularly* don’t understand the following result:
>
> In [1]: 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
> ...:
> ...:
>
> In [2]: image = np.zeros((6, 6))
> In [3]: image[1, 1] = 1
> In [4]: image[3:] = 2
> In [6]: image[3:-1, 3:-1] = 4
>
> In [7]: image
> Out[7]:
> array([[ 0., 0., 0., 0., 0., 0.],
> [ 0., 1., 0., 0., 0., 0.],
> [ 0., 0., 0., 0., 0., 0.],
> [ 2., 2., 2., 4., 4., 2.],
> [ 2., 2., 2., 4., 4., 2.],
> [ 2., 2., 2., 2., 2., 2.]])
>
> In [8]: rmax(image)
> Out[8]:
> array([[ 0., 0., 0., 0., 0., 0.],
> [ 0., 1., 0., 0., 0., 0.],
> [ 0., 0., 0., 0., 0., 0.],
> [ 0., 0., 0., 1., 1., 0.],
> [ 0., 0., 0., 1., 1., 0.],
> [ 0., 0., 0., 0., 0., 0.]])
>
> In [12]: morphology.local_maxima(image)
> Out[12]:
> array([[0, 0, 0, 0, 0, 0],
> [0, 1, 0, 0, 0, 0],
> [0, 0, 0, 0, 0, 0],
> [0, 0, 0, 1, 1, 0],
> [0, 0, 0, 1, 1, 0],
> [0, 0, 0, 0, 0, 0]], dtype=uint8)
>
> In [15]: feature.peak_local_max(image)
> Out[15]:
> array([[4, 4],
> [4, 3],
> [4, 1],
> [3, 4],
> [3, 3],
> [3, 1],
> [1, 1]])
>
> In [16]: image_peak = np.zeros_like(image)
>
> In [17]: image_peak[tuple(feature.peak_local_max(image).T)] = 1
>
> In [18]: image_peak
> Out[18]:
> array([[ 0., 0., 0., 0., 0., 0.],
> [ 0., 1., 0., 0., 0., 0.],
> [ 0., 0., 0., 0., 0., 0.],
> [ 0., 1., 0., 1., 1., 0.],
> [ 0., 1., 0., 1., 1., 0.],
> [ 0., 0., 0., 0., 0., 0.]])
>
>
> Anyone else on the list care to comment???
>
> Juan.
>
> On 10 Apr 2018, 11:49 PM +1000, Yann GAVET <gavet at emse.fr>, wrote:
>> 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
>>
>>
>> Le 10/04/2018 à 15:35, Yann GAVET a écrit :
>>>
>>> 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
>>>
>>>
>>> _______________________________________________
>>> scikit-image mailing list
>>> scikit-image at python.org
>>> https://mail.python.org/mailman/listinfo/scikit-image
>>
>> --
>> 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
>> _______________________________________________
>> scikit-image mailing list
>> scikit-image at python.org
>> https://mail.python.org/mailman/listinfo/scikit-image
>
>
> _______________________________________________
> scikit-image mailing list
> scikit-image at python.org
> https://mail.python.org/mailman/listinfo/scikit-image
--
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
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