Alternate method for constructing circular region mask from center positions and radii

I would like to be able to construct a mask for a given image full of different circular ROIs. I know the x,y coordinates for the centers and the radius length for each ROI. I know that the following expression can be utilized:

    temp = ((xgrid-data(i,1)).^2 + (ygrid-data(i,2)).^2) <= (radius(i)).^2;
    BW = BW+temp;

which will iterate through all ROIs and combine them into one full mask. I do not want to proceed in this particular way. I am wondering if a faster approach exists such that given the x,y coordinates and the radius for say 100 ROIs, can I instantaneously create the mask instead of iterating through each individual ROI?

[Chetna Jain]

Hey, Might be the function in the link below is what you are looking for : https://www.mathworks.com/matlabcentral/fileexchange/47905-createcirclesmask-m

[Serg Zhelezniak]

No, this function uses exactly the same logic as I've described above just in a slightly different format:

   mask = mask | hypot(xx - xc(ii), yy - yc(ii)) <= radii(ii);

It will have nearly identical computational time. I'm looking for some alternate means of doing this.

[Chetna Jain]

Can you share data file so that I can try computing and verify the difference in computational time.Also I can try finding out other options.

Answer 1

[Guillaume]

%random matrix of centre and radius coordinates for demo:
xyr = [randi(150, 10, 2) + 50, randi(20, 10, 1)];
masksize = [200, 200];

[x, y] = meshgrid(1:masksize(2), 1:masksize(1));  %create pixel coordinates
xyr = permute(xyr, [3 2 1]);  %move each circle along 3rd dimension
mask = any(hypot(x - xyr(1, 1, :), y - xyr(1, 2, :)) <= xyr(1, 3, :), 3);  %require R2016b or later
imshow(mask)

If you're on a version earlier than R2016b (or don't like implicit expansion):

mask = any(bsxfun(@le, hypot(bsxfun(@minus, x, xyr(1, 1, :)), bsxfun(@minus, y, xyr(1, 2, :))), xyr(1, 3, :)), 3);