Extremely fast 2D image convolution with a max filter. For each location computes J(y,x) = max(max(I(y-r:y+r,x-r:x+r))). The filtering is constant time per-window, independent of r. First, the filtering is separable, which brings the complexity down to O(r) per window from O(r*r). To bring the implemention down to constant time (independent of r) we use the van Herk/Gil-Werman algorithm. Ignoring boundaries, just 3 max operations are need per-window regardless of r. http://www.leptonica.com/grayscale-morphology.html#FAST-IMPLEMENTATION The output is exactly equivalent to the following Matlab operations: I=padarray(I,[r r],'replicate','both'); [h,w,d]=size(I); J=I; for z=1:d, for x=r+1:w-r, for y=r+1:h-r J(y,x,z) = max(max(I(y-r:y+r,x-r:x+r,z))); end; end; end J=J(r+1:h-r,r+1:w-r,:); The computation, however, is an order of magnitude faster than the above. USAGE J = convMax( I, r, [nomex] ) INPUTS I - [hxwxk] input k channel single image r - integer filter radius or radii along y and x nomex - [0] if true perform computation in matlab (for testing/timing) OUTPUTS J - [hxwxk] max image EXAMPLE I = single(imResample(imread('cameraman.tif'),[480 640]))/255; r = 5; % set parameter as desired tic, J1=convMax(I,r); toc % mex version (fast) tic, J2=convMax(I,r,1); toc % matlab version (slow) figure(1); im(J1); figure(2); im(abs(J2-J1)); See also conv2, convTri, convBox Piotr's Computer Vision Matlab Toolbox Version 3.00 Copyright 2014 Piotr Dollar & Ron Appel. [pdollar-at-gmail.com] Licensed under the Simplified BSD License [see external/bsd.txt]

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