Sliding window in a sparse 3d volume

2013 4 8
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Hi, I have a 3d (MxNxL) matrix, and I want to compute for a list of x,y,z (actually all x,y, and a certain z, not for each x,y,z!) a function over a i*j*k window.
The sliding window should be of size(i*j*k) but not all values in the window are the neighborhood, for example, the window can be a sphere of radius r that is bound in that square window, or it could be a cylinder or some kind of other shape.
The results I need is a MxN matrix (2D, so no convn), where for each x,y location I have the result of the function applied on x,y 3d neighborhood. MxN could be very large, I don't want to do it with loops.
Example for a window I want to slide over the 3d volume:
[x,y,z] = meshgrid(1:r,1:r,1:r);
xc = floor(r./2)+1;
yc = floor(r./2)+1;
zc = floor(r./2)+1;
sphere_window = (x-xc).^2 + (y-yc).^2 + (z-zc).^2 <= r.^2;

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Sean de Wolski
Sean de Wolski 2013-4-8
What does the function look like? It might be something you could do with convn() or similar but we'll have to see the function.
Orly amsalem
Orly amsalem 2013-4-8
I actually have a 2 functions in mind: 1. compute for each neighborhood a: cx = sum(sum(sum(a.*x)))./sum(a(:)); cy = sum(sum(sum(a.*y)))./sum(a(:)); cz = sum(sum(sum(a.*z)))./sum(a(:)); and the finally the distance between (cx,cy,cz) and (0,0,0) (the center). where x,y,z are coordinates. 2. For each sliding window, compute pca for the points in the neighborhood, and take the ratio between the 2 largest eigenvalues.
I think convn would be too slow for that matter, and will operate for each x,y,z while I want for each x,y and one specific z. (x*y times and not x*y*z times)
Image Analyst
Image Analyst 2013-4-8
If you can do it with convn, I'd recommend that. It is highly optimized so it won't be as slow as you think. For example with a 10x10x10 cube, moving it over by 1 voxel only has to read in another 100 voxels, not a thousand.
Orly amsalem
Orly amsalem 2013-4-8
convn also performs for each x,y,z, i.e. return a 3d volume also, while I need a result of 2d matrix...
Orly amsalem
Orly amsalem 2013-4-8
The input is two 3d volumes and the input should be 2d matrix. Because I need the neighborhood to be 3d , but the function is performed for each x,y, not for each x,y,z
Orly amsalem
Orly amsalem 2013-4-8
besides, I have no idea if it possible to do what I want with convolution...

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