A MATLAB user asked me how to determine which image pixels had local maxima that weren't unique. My answer involves a creative use of ordfilt2.
Let's review first the concept of a local maximum filter. This image operator replaces every pixel value with the maximum pixel value found in a neighborhood surrounding the pixel. For example:
a = magic(5)
a =
17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 21 3
11 18 25 2 9
What should the output be for a local maximum filter using 3-by-3 neighborhoods? The output in the 3rd row, 2nd column would be the maximum value found in this submatrix:
neighborhood = a(2:4, 1:3)
neighborhood =
23 5 7
4 6 13
10 12 19
The (3,2) output is 23:
max(neighborhood(:))
ans =
23
Local maximum filtering is the same as morphological dilation, so I usually use imdilate to compute the result for the entire image:
b = imdilate(a, ones(3,3))
b =
24 24 24 16 16
24 24 24 22 22
23 23 21 22 22
18 25 25 25 22
18 25 25 25 21
That's the background; now back to the original question. How do you determine which pixels have multiple maxima in their neighborhoods?
I suggest using ordfilt2 twice. This function is for ''two-dimensional order-statistic filtering.'' This operation replaces every pixel value with the n-th sorted pixel value in its neighborhood. It uses an ascending sort order, so if n is the number of pixels in the neighborhood, the operation is exactly equivalent to the local maximum filter.
The specific procedure is:
1. Call ordfilt2 to get the highest pixel values in each neighborhood.
2. Call ordfilt2 again to get the second-highest pixel values in each neighborhood.
3. Determine where the outputs of steps 1 and 2 are equal. Wherever they are equal, the local maximum is not unique.
Let's try an example. First, modify our original matrix a bit:
ap = a; ap(3,4) = 22
ap =
17 24 1 8 15
23 5 7 14 16
4 6 13 22 22
10 12 19 21 3
11 18 25 2 9
Get the highest pixel values in each 3-by-3 neighborhood:
highest = ordfilt2(ap, 9, ones(3,3))
highest =
24 24 24 16 16
24 24 24 22 22
23 23 22 22 22
18 25 25 25 22
18 25 25 25 21
Get the second-highest pixel values:
second_highest = ordfilt2(ap, 8, ones(3,3))
second_highest =
23 23 14 15 15
23 23 22 22 22
12 19 21 22 22
12 19 22 22 22
12 19 21 21 9
Determine where the highest and second highest pixel values are equal:
non_unique_maxima_mask = (highest == second_highest)
non_unique_maxima_mask =
0 0 0 0 0
0 0 0 1 1
0 0 0 1 1
0 0 0 0 1
0 0 0 0 0
Get
the MATLAB code
Published with MATLAB® 7.2
Mark – see the blog policies post.
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Hi steve,I am new in matlab and need your help.I want to find (row,col) of local maximums in an image matrix within N*N window. what do you do suggest?
Amir—I can think of multiple ways to interpret your question. Depending on what you really mean, you might find either the function imregionalmax or imdilate to be useful.
Thanks a lot Steve.It was very helpful.
Hi Steve,
The tutorial’s clear and absolutely useful. Thanks a lot.
I have a minor question, Steve. I wonder if there is any function finding extrema in stead of maxima as ‘imregionalmax’.
Regards.
Kevin.
Kevin—What is your definition of “extrema” in this context?
Hi Steve,
I meant ‘maxima and minima’. I need to search out both of them.
The fact that I can apply ‘imregionalmax’ and ‘imregionalmin’, then union 2 sets. But it’s great if there is any function that can do both of them probably :-).
Thank you for the quick reply.
Kevin
Kevin—As you suggest, just use both imregionalmax and imregionalmin.
Thank for your advice, Steve. It’s really informative.
Hi there,
I have a 3D matrix and I want to find the local extrema of it. I mean the coordinates of points that are bigger/smaller than its 26 neighboors.
Can anybody help me ?
Thanks in advance !
sorry for the previous question I did not read the help carefully.
Thank you
This is in reference to one of Amir’s earlier question, if I understood the question correctly. I found the max(x,y) of a given matrix A by using this method:
[max_val, x_max] = max(max(A)); %gives the column coordinate
[max_val, y_max] = max(max(A’)); %notice the transpose. gives the row coordinate
I know that the same value will be written twice on max_val, but this is another way of obtaining (x_max, y_max) coordinates.
I have an image 128*128.. which has a pixel with max intensity 233. How can i find the coordinates of the pixel..?
Vr—Try this: