MATLAB: Calculating the eigenvalues of a composite matrix

Question

Hello everyone,

the problem is as follows:

I calcualted the first and second derivatives of an image (1024×1280 pixel) using imgrdarientxy.

[Gx,Gy] = imgradientxy(Bild);
[Gxx,Gxy] = imgradientxy(Gx);
[Gyx,Gyy] = imgradientxy(Gy);

Now i want to calculate the eigenvalues of the Hessian matrix, which consists of the second derivatives of the image.

Simply said it would look something like this.

HessianMatrix1 = [Gxx(1,1) Gxy(1,1); Gyx(1,1) Gyy(1,1)];
[V1,D1,W1] = eig(HessianMatrix1);
HessianMatrix2 = [Gxx(1,2) Gxy(1,2); Gyx(1,2) Gyy(1,2)];
[V2,D2,W2] = eig(HessianMatrix2);
.........
HessianMatrix1281 = [Gxx(2,1) Gxy(2,1); Gyx(2,1) Gyy(2,1)];
[V1281,D1281,W1281] = eig(HessianMatrix1281);

And so on. Basically the eigenvalues of the Hessian matrix (the second derivatives) for every pixel.

Now I don't know how to do this for the whole matrices.

I tryed it with a for loop but it only calcualtes the eigenvalue and eigenvector for the last iteration. I think I did a mistake in how the values are saved but i don't know how to fix it.

for j=1:n %n=1280
    for i=1:m %m=1024
      HesseM = [Gxx(i,j) Gxy(i,j); Gyx(i,j) Gyy(i,j)];
      [V,D,W] = eig(HesseM);
    end
end

Does anybody know how to implement this, so that it calcualtes all the eigenvalues (and eigenvectors) for every combination.

Thanks a lot,

Antonio

Answer 1

You are overwriting V,D,W every time. The simplest way to avoid this, ignoring the specific size of the variables, is to put the answers into a cell array:

for j=1:n %n=1280
    for i=1:m %m=1024
      HesseM = [Gxx(i,j) Gxy(i,j); Gyx(i,j) Gyy(i,j)];
      [V{j,i},D{j,i},W{j,i}] = eig(HesseM);
    end
end