A 100 x 100 matrix has (2*100-1) = 199 diagonals. 199 is prime. Therefore you will not be able to group the diagonals into any number of bands with the same number of diagonals for each band (except, of course, taking one band at a time or taking all 199 bands at a time.)
An N x N matrix has (2*N-1) diagonals. That is always going to be an odd number. Therefore you will never be able to group the diagonals into any even number of bands with the same number of diagonals in each band.
To be able to group into 19 bands of equal width, you would have to pad your 100 x 100 matrix out to 105 x 105, at which point you could construct 19 bands of 11 diagonals per band.
YourImage = rand(105,105) > 0.5;
N = size(YourImage,1);
numbands = 19;
bandwidth = (2*N - 1) / numbands;
if bandwidth ~= floor(bandwidth)
error(sprintf('Matrix size of %d x %d cannot be divided into %d equal-width bands', N, N, numbands));
end
bandoffset = N + bandwidth;
B = fliplr(YourImage);
diags = cell(numbands,1);
for J = 1 : numbands
T = cell(bandwidth,1);
for K = 1:bandwidth
T{K} = diag(B, J*bandwidth + K - bandoffset);
end
diags{J} = vertcat(T{:});
end
To get the number of white pixels per group,
diagsum = cellfun(@sum, diags);
For left-leaning bands, use B = YourImage; without the fliplr();
