Vectorizing multiple gaussian calculations - matlab

Question

I am attempting to vectorize some of my code that adds the intensity of many Gaussian distributions over an image. I currently loop over the function 'gaussIt2D' for each Gaussian, which is vectorized for a single 2D gaussian:
windowSize=10;
imSize=[512,512];
%pointsR is an nx2 array of coordinates [x1,y1;x2,y2;...;xn,yn]
pointsR=rand(100,2)*511+1;
%sigmaR is the standard deviation of the gaussian being created
sigmaR = 1;
outputImage=zeros(imSize);
for n=1:size(pointsR,1)
rangeX = floor(pointsR(n,1)-windowSize):ceil(pointsR(n,1)+ windowSize);
rangeX = rangeX(rangeX > 0 & rangeX <= imSize(1));
rangeY = floor(pointsR(n,2)-windowSize):ceil(pointsR(n,2)+windowSize);
rangeY = rangeY(rangeY > 0 & rangeY <= imSize(2));
outputImage(rangeX,rangeY) = outputImage(rangeX,rangeY)+gaussIt2D(rangeX(1),rangeX(end),rangeY(1),rangeY(end),[sigmaR,pointsR(n,1),pointsR(n,2)]);
end
function [result] = gaussIt2D(xInit,xFinal,yInit,yFinal,sigma,xCenter,yCenter)
%Returns gaussian intenisty values for the region defined by [xInit:xFinal,yInit:yFinal] using the gaussian properties sigma,centerX,centerY
[gridX,gridY]=ndgrid(xInit:xFinal,yInit:yFinal);
result=exp( -( (gridX-xCenter).^2 + (gridY-yCenter).^2 ) ./ (2*sigma.^2) );
end
I am trying to further vectorize this process by allowing the gaussIt2D function to accept a vector of x and y values and a vector of x and y centers and do all of them together. My thought process so far has been to try to stack the grids and replicate the centers and do the element-wise gaussian calculations. For (a simplified) example if:
xInits = [1,2,3];
xFinals = [2,3,4];
xCenters = [1.2,2.8,3.1];
yInits = [1,2,3];
yFinals = [2,3,4];
yCenters = [1.5,2.4,3.6];
Then I was thinking to create grids and centers following the form:
gridX = [1,2
1,2
2,3
2,3
3,4
3,4]
xCenters = [1.2,1.2
1.2,1.2
2.8,2.8
2.8,2.8
3.1,3.1
3.1,3.1]
This could then be used in the same gaussian equation used in the original function. However, generating these arrays is tripping me up. What I have right now is:
function [result]=gaussIt2DVectorized(xInits,xFinals,yInits,yFinals,sigmas,xCenters,yCenters)
%Incomplete
%Returns gaussian intenisty values for the region defined by
%[xInit:xFinal,yInit:yFinal] using the values array:[sigma,centerX,centerY]
[gridX,gridY]=arrayfun('ndgrid',xInits:xFinals,yInits:yFinals);
xCenters = repelem(xCenters,numel(xInits(1):xFinals(1)), numel(yInits(1):yFinals(1)));
yCenters = repelem(yCenters,numel(xInits(1):xFinals(1)), numel(yInits(1):yFinals(1)));
result=exp( -( (gridX-xCenters).^2 + (gridY-yCenters).^2 ) ./ (2*sigmas^2) );
end
This doesn't actually work though, and the I also anticipate difficulty accounting for ranges (ie xInit:xFinal) of different lengths.
Any help, tips, or alternate methods would be appriciated.
Thanks.

Answer 1

Since you cannot be sure that the grids will all be the same size, it's probably best to store them in a cell array rather than stacking them in a matrix. With cells arrays, you can still run your calculation without looping using cellfun.
For example:
function [result] = gaussIt2D_better(xInits,xFinals,yInits,yFinals,sigmas,xCenters,yCenters)
[gridsX, gridsY] = arrayfun(#(x) ndgrid(xInits(x):xFinals(x), yInits(x):yFinals(x)),1:length(xInits),'UniformOutput',0);
f=#(gridX, gridY, xCenter, yCenter, sigma) exp( -( (gridX-xCenter).^2 + (gridY-yCenter).^2 ) ./ (2*sigma.^2) );
result=cellfun(f, gridsX, gridsY, num2cell(xCenters), num2cell(yCenters), num2cell(sigmas), 'UniformOutput',0);
end
Note that in this example, the value returned is a cell array with the same length as the input vectors, one result for each.