How can I find local maxima in an image in MATLAB?

I have an image in MATLAB:

y = rgb2gray(imread('some_image_file.jpg'));

and I want to do some processing on it:

pic = some_processing(y);

and find the local maxima of the output. That is, all the points in y that are greater than all of their neighbors.

I can't seem to find a MATLAB function to do that nicely. The best I can come up with is:

[dim_y,dim_x]=size(pic);
enlarged_pic=[zeros(1,dim_x+2);
              zeros(dim_y,1),pic,zeros(dim_y,1);
              zeros(1,dim_x+2)];

% now build a 3D array
% each plane will be the enlarged picture
% moved up,down,left or right,
% to all the diagonals, or not at all

[en_dim_y,en_dim_x]=size(enlarged_pic);

three_d(:,:,1)=enlarged_pic;
three_d(:,:,2)=[enlarged_pic(2:end,:);zeros(1,en_dim_x)];
three_d(:,:,3)=[zeros(1,en_dim_x);enlarged_pic(1:end-1,:)];
three_d(:,:,4)=[zeros(en_dim_y,1),enlarged_pic(:,1:end-1)];
three_d(:,:,5)=[enlarged_pic(:,2:end),zeros(en_dim_y,1)];
three_d(:,:,6)=[pic,zeros(dim_y,2);zeros(2,en_dim_x)];
three_d(:,:,7)=[zeros(2,en_dim_x);pic,zeros(dim_y,2)];
three_d(:,:,8)=[zeros(dim_y,2),pic;zeros(2,en_dim_x)];
three_d(:,:,9)=[zeros(2,en_dim_x);zeros(dim_y,2),pic];

And then see if the maximum along the 3rd dimension appears in the 1st layer (that is: three_d(:,:,1)):

(max_val, max_i) = max(three_d, 3);
result = find(max_i == 1);

Is there any more elegant way to do this? This seems like a bit of a kludge.

matlab image-processing mathematical-optimization

Edit Report

If you have the Image Processing Toolbox, you could use the IMREGIONALMAX function:

BW = imregionalmax(y);

The variable BW will be a logical matrix the same size as y with ones indicating the local maxima and zeroes otherwise.

NOTE: As you point out, IMREGIONALMAX will find maxima that are greater than or equal to their neighbors. If you want to exclude neighboring maxima with the same value (i.e. find maxima that are single pixels), you could use the BWCONNCOMP function. The following should remove points in BW that have any neighbors, leaving only single pixels:

CC = bwconncomp(BW);
for i = 1:CC.NumObjects,
  index = CC.PixelIdxList{i};
  if (numel(index) > 1),
    BW(index) = false;
  end
end

answered 2009-12-06T19:00:23.083

How can I find local maxima in an image in MATLAB?

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