Which function can I use to implement the following image filter?

I have two questions,

(1) What kind of image filter is this? Is it a band-pass filter?

(2) Which MATLAB function can I use to implement this filter?

Reference:

http://stackoverflow.com/a/39339327/159072

Answer 1

[Image Analyst]

It looks like a radial low pass filter. If Cx and Cy are not zero then it's like it's filtering (masking) out a spot in the spectrum, so that's kind of like a bandpass filter, but not really since it's a spot not a band.

First they rotate the 2D spectrum by theta for some reason. Then they create H which looks like it's supposed to be multiplied by the image spectrum in Fourier space. You can fft the image, then create the H image, then call

fftImage = fft(grayImage);
outputSpectrum = fftImage .* H;
spatialDomainImage = ifft2(outputSpectrum);

See if you can create H yourself. It's not hard.

[Ba Ba Black Sheep!]

But, the StackOverflow link says that it is a reminiscent of Butterworth filter?

Butterworth filter is a band-pass filter isn't that so?

[Image Analyst]

Well it might be. I'm not that familiar with Butterworth. It could be that they're just shifting prior to rotating to do basically what the MATLAB function fftshift() does. In that case it's just moving the DC location to the center of the image, or to the corners, depending on how it started out, as long as Cx and Cy are halfway along the image.

[Ba Ba Black Sheep!]

function out = u_inverse(u, v, Cx, Cy, theta)
    left = (u-Cx) * cos(theta);
    right = (v-Cy) * sin(theta); 

      out = left + right;
  end

function out = v_inverse(u, v, Cx, Cy, theta)
    left = (-1) * (u-Cx) * sin(theta);
    right = (v-Cy) * cos(theta); 

      out = left + right;
  end

function out = H(u, v, Cx, Cy, theta, Du, Dv, N)
    u_inv = u_inverse(u, v, Cx, Cy, theta);
    v_inv = v_inverse(u, v, Cx, Cy, theta);

      u_part = u_inv/Du;
      v_part = v_inv/Dv;

      out = 1/((1 + (u_part + v_part)^(2*N))^(0.5));
  end

function out = KassWitkin(w, h)

      u = 0;
      v = 0;
      Cx = 0;
      Cy = 0;
      theta = 0;
      Du = 0;
      Dv = 0;
      N = 4;

      kernel(1:w, 1:h) = H(u, v, Cx, Cy, theta, Du, Dv, N);

      out = kernel;
  end