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

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Ba Ba Black Sheep! 2017-1-3

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https://ww2.mathworks.cn/matlabcentral/answers/318913-which-function-can-i-use-to-implement-the-following-image-filter

评论： Ba Ba Black Sheep! 2017-1-3

采纳的回答： Image Analyst

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

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Answer 1

Image Analyst 2017-1-3

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编辑：Image Analyst 2017-1-3

在 MATLAB Online 中打开

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.

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Image Analyst 2017-1-3

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! 2017-1-3

在 MATLAB Online 中打开

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