Matlab code runs too slow on three dimensional array - matlab

Question

I'm trying to vectorize the following code:
% code before
% code before
% a lot of code before we got to the current comment
%
% houghMatrix holds some values
for i=1:n
for j=1:m
for k = 1:maximalRadius
% get the maximal threshold
if houghMatrix(i,j,k) > getMaximalThreshold(k)
lhs = [j i k];
% verify that the new circle is not listed
isCircleExist = verifyCircleExists(circles,lhs,circleCounter);
% not listed - then we put it in the circles vector
if isCircleExist == 0
circles(circleCounter,:) = [j i k];
fprintf('Circle % d: % d, % d, % d \n', circleCounter, j, i, k);
circleCounter = circleCounter + 1;
end
end
end
end
end
Using tic tac I got the below outputs :
>> x = findCircles(ii);
Circle 1: 38, 38, 35
Circle 2: 89, 51, 34
Circle 3: 72, 66, 11
Circle 4: 33, 75, 30
Circle 5: 90, 81, 31
Circle 6: 54, 96, 26
Elapsed time is 3.111176 seconds.
>> x = findCircles(ii);
Circle 1: 38, 38, 35
Circle 2: 89, 51, 34
Circle 3: 72, 66, 11
Circle 4: 33, 75, 30
Circle 5: 90, 81, 31
Circle 6: 54, 96, 26
Elapsed time is 3.105642 seconds.
>> x = findCircles(ii);
Circle 1: 38, 38, 35
Circle 2: 89, 51, 34
Circle 3: 72, 66, 11
Circle 4: 33, 75, 30
Circle 5: 90, 81, 31
Circle 6: 54, 96, 26
Elapsed time is 3.135818 seconds.
Meaning - average of 3.1 seconds .
I tried to vectorize the code , but the problem is that I need to use
the index i,j,k in the body of the inner for (the 3rd for) .
Any suggestions how to vectorize the code would be greatly appreciated
Thanks
EDIT :
% -- function [circleExists] = verifyCircleExists(circles,lhs,total) --
%
%
function [circleExists] = verifyCircleExists(circles,lhs,total)
MINIMUM_ALLOWED_THRESHOLD = 2;
circleExists = 0;
for index = 1:total-1
rhs = circles(index,:);
absExpr = abs(lhs - rhs);
maxValue = max( absExpr );
if maxValue <= MINIMUM_ALLOWED_THRESHOLD + 1
circleExists = 1;
break
end
end
end

Answer 1

Heres what I think you want to do: For each valid coordinate triplet, you want to check whether there has been a nearby triplet already, otherwise, you add it to the list. This operation can be fully vectorized if there's no possibility of "chaining", i.e. if each cluster of possible candidate voxels can only accomodate one center. In this case, you simply use:
%# create a vector of thresholds
maximalThreshold = getMaximalThreshold(1:maximalRadius);
%# make it 1-by-1-by-3
maximalThreshold = reshape(maximalThreshold,1,1,[]);
%# create a binary array the size of houghMatrix with 1's
%# wherever we have a candidate circle center
validClusters = bsxfun(#gt, houghMatrix, maximalThreshold);
%# get the centroids of all valid clusters
stats = regionprops(validClusters,'Centroid');
%# collect centroids, round to get integer pixel values
circles = round(cat(1,stats.Centroid));
Alteratively, if you want to follow your scheme of selecting valid circles, you can get the ijk indices from validClusters as follows:
[potentialCircles(:,1),potentialCircles(:,2), potentialCircles(:,3)]= ...
sub2ind(size(houghMatrix),find(validClusters));
nPotentialCircles = size(potentialCircles,1);
for iTest = 2:nPotentialCircles
absDiff = abs(bsxfun(#minus,potentialCircles(1:iTest-1,:),potentialCircles(iTest,:)));
if any(absDiff(:) <= MINIMUM_ALLOWED_THRESHOLD + 1)
%# mask the potential circle
potentialCircles(iTest,:) = NaN;
end
end
circles = potentialCircles(isfinite(potentialCircles(:,1)),:);