Pseudo zernike moment for an image

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ancy micheal 2020-12-8

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评论： Bjorn Gustavsson 2020-12-11

I want to extract Pseudo zernike moment for an image. I used the code from the link. https://in.mathworks.com/matlabcentral/fileexchange/33644-pseudo-zernike-functions. It works perfect for the given input but how do i extract moment fron an N*N imag

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Bjorn Gustavsson 2020-12-8

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The Zernike functions are defined on the unit-disk, i.e. circel with radius 1. Your image is likely square, so your choise is to calculate the Zernike expansion of your image inscribed into a unit-circle, or calculate the Zernike expansion of the region of your image that is inside an inscribed circle. In the second example in the help of the function the moments are calculated of an 101-by-101 pixels image of the peaks function (inscribed circle). If you step through that example you will see how to do this. If you after running that script run this snippet for a couple of i1s you will get the moments for the corresponding pseudo-Zernike-functions:

figure
i1 = 7;
scatter(r.*cos(theta),r.*sin(theta),23,P(:,i1),'filled'),
title(sprintf('n: %d, m: %d, Z_n^m: %f',n(i1),m(i1),M(i1)))

If you use this inscribed circle your moments will obviously not depend on what's in the corners of your image...

HTH

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Bjorn Gustavsson 2020-12-9

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The Zernike-moments/Zernike-functions are just a different set of amplitude/basis-function combination, just like the Fourier-coefficients/harmonic-functions.

Therefore different images of different faces will have different Zernike-moments. This might be a great, good, adequate, acceptable, poor or useless tool for extracting shape-features of faces, you will see. I assume that the first couple of moments will be roughly the same - most of our heads are reasonably ellipsoidal-egg-shaped, most of us have a nose above a mouth slightly below two eyes, that in turn are approximately half-way between the bottom of our chin and top of the head. If this argument is correct (enough) the differences will start to become more important at the higher moments.

You can try this snippet after example 2:

for idx = 1:numel(M)
  F_recovered(is_in_circle) = P(:,1:idx)*M(1:idx)';
  dF_recovered(is_in_circle) = P(:,idx)*M(idx)'; 
  subplot(3,2,2),
  imagesc(F_recovered),
  subplot(3,2,3),
  imagesc(F_recovered-F),
  subplot(3,2,4),
  imagesc(dF_recovered),
  colorbar,
  subplot(3,1,3),
  plot(1:numel(M),M,idx,M(idx),'.-'),
  grid on    
  pause(2)
end