Curl of Gaussian image derivatives matlab

[arronslacey]

Hi guys, I am trying to create a magnetic field from an image contour and an attempt to create an active contour model. I have a function which takes the image derivative via a Guassian:

    function J=ImageDerivatives2D(I,sigma,type)
  % Gaussian based image derivatives
  %
  %  J=ImageDerivatives2D(I,sigma,type)
  %
  % inputs,
  %   I : The 2D image
  %   sigma : Gaussian Sigma
  %   type : 'x', 'y', 'xx', 'xy', 'yy'
  %
  % outputs,
  %   J : The image derivative
  %
% Make derivatives kernels
[x,y]=ndgrid(floor(-3*sigma):ceil(3*sigma),floor(-3*sigma):ceil(3*sigma));
switch(type)
    case 'x'
        DGauss=-(x./(2*pi*sigma^4)).*exp(-(x.^2+y.^2)/(2*sigma^2));
    case 'y'
        DGauss=-(y./(2*pi*sigma^4)).*exp(-(x.^2+y.^2)/(2*sigma^2));
    case 'xx'
        DGauss = 1/(2*pi*sigma^4) * (x.^2/sigma^2 - 1) .* exp(-(x.^2 + y.^2)/(2*sigma^2));
    case {'xy','yx'}
        DGauss = 1/(2*pi*sigma^6) * (x .* y)           .* exp(-(x.^2 + y.^2)/(2*sigma^2));
    case 'yy'
        DGauss = 1/(2*pi*sigma^4) * (y.^2/sigma^2 - 1) .* exp(-(x.^2 + y.^2)/(2*sigma^2));
end        
J = conv2(I,DGauss,'same');

and now i need to take the curl of those image derivatives to get the pseudo magnetic field. having a bit of trouble with that though:

   % Squared magnitude of force field
  Fx= Fext(:,:,1);
  Fy= Fext(:,:,2);
% Calculate magnitude
sMag = Fx.^2+ Fy.^2;
% Set new vector-field to initial field
u=Fx;  v=Fy;
for i=1:Iterations,
  % First order image derivatives
  Uxx=ImageDerivatives2D(u,Sigma,'x');
  Uyy=ImageDerivatives2D(u,Sigma,'y');
    Vxx=ImageDerivatives2D(v,Sigma,'x');
    Vyy=ImageDerivatives2D(v,Sigma,'y');
    % Compute curl and update vector field
    u = u + cross(Uxx,Uyy,3);
    v = v + cross(Vxx,Vyy,3);
  end
Fext(:,:,1) = u;
Fext(:,:,2) = v;

anyone have any tips as the second script does not work. i can to the divergence and laplacian easily as they are just first and second derivatives, but the curl is proving a bit of a problem. Any help would be great thanks!

 

[mmwave]

Thank you for sharing your progress and asking for help. It seems like you are on the right track with your approach to creating a magnetic field from an image contour using the Gaussian derivative function. However, I can see that you are running into some difficulties with taking the curl of the image derivatives.

Taking the curl of a vector field involves finding the cross product of the first-order derivatives in the x and y directions. In your code, you have correctly calculated these derivatives (Uxx, Uyy, Vxx, Vyy) using the Gaussian derivative function. However, in order to take the curl, you will need to find the cross product using the "cross" function in MATLAB.

The syntax for the cross product function is as follows:

C = cross(A,B,dim)

where A and B are the vectors to be crossed, and dim specifies the dimension along which the cross product is taken. In your case, you will need to find the cross product of the first-order derivatives Uxx and Uyy, and Vxx and Vyy, along the third dimension (dim=3).

Once you have calculated the cross product, you can update your vector field (u and v) by adding it to the existing field. This will give you the updated vector field which can be used to calculate the magnetic field.

I hope this helps you in solving your problem. If you continue to face difficulties, please do not hesitate to reach out for further assistance. Good luck with your research!