Below steps can help you in getting started with urban image segmentation with a focus on shape constraints using Chebyshev moments.
- Define the Chebyshev polynomials of the first kind Tn(x).
function T = chebyshevPoly(n, x)
if n == 0
T = ones(size(x));
elseif n == 1
T = x;
else
T = 2*x.*chebyshevPoly(n-1, x) - chebyshevPoly(n-2, x);
end
end
- For a grayscale image I, resize and normalize coordinates to [−1,1] range:
function M = chebyshevMoments(I, maxOrder)
I = double(I);
[rows, cols] = size(I);
% Normalize spatial coordinates to [-1,1]
x = linspace(-1, 1, cols);
y = linspace(-1, 1, rows);
[X, Y] = meshgrid(x, y);
M = zeros(maxOrder+1, maxOrder+1);
for m = 0:maxOrder
for n = 0:maxOrder
Tm = chebyshevPoly(m, X);
Tn = chebyshevPoly(n, Y);
M(m+1, n+1) = sum(sum(I .* Tm .* Tn));
end
end
end
- Use Moments as Shape Constraints. Let’s say, "M_target" is the moment matrix of a known shape (e.g., ideal building mask) and "M_seg" is the moment matrix of the current segmentation mask.
function loss = shapeConstraint(M_target, M_seg)
loss = sum((M_target(:) - M_seg(:)).^2); % L2 distance
end
- You can add this loss to your segmentation cost function or energy function in a graph cut, active contour, or deep learning pipeline.
Hope this helps!
