Segmentation using Chebyshev moments

hello, I work on image processing domain,focusing on the segmentation of urban images. i have to make a shape constraint for segmentation using Chebyshev moments. Could you give me some ideas to implement that in MATLAB. Best regards;

Answer 1

[Vidhi Agarwal]

Hi @jihen aouni,

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!