Pseudo zernike moment for an image

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

Answer 1

[Bjorn Gustavsson]

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

[ancy micheal]

Thanks for your reply sir. My choice is to calculate the zernike expansion of an image inscribed into a unit -circle. I get the moments using the above code but will the structure of the moments be same for all the face images as i want to extract the shape features from an face image using Pseudo Zernike Moment.

[Bjorn Gustavsson]

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

That should illustrate the general point.

HTH

[ancy micheal]

Then, lower order moments represent the global shape of a pattern and higher order moments represent the details. Will the final output of PZM will be same as the figure 2 in the paper titled "An Efficient Multiscale Scheme Using Local Zernike Moments for Face Recognition" ? I want to visualise the shape feature extracted using PZM. Kindly help me how to visualise the final output of PZM

[Bjorn Gustavsson]

Yes, just like an expansion in products of harmonics (like the Fourier-transform does), the Zernike-expansion has a similar ordering from large spatial structures to ever smaller structures.

If you want to do the same as that paper (for future citations, you'd be safer if you also include authors, year and journal) you'll have to do what they did - which seems to be to convert the first Zernike base-functions from the full image-size to 7x7 pixels and convolved their images with each of those (this limits the number of kernels to 49, at most). What they've done to use those filtered image-sets to for identification I wouldn't know. You could at least do the same in terms of down-sampling the Zernike-moments and image filterings without too much trouble.

HTH

[ancy micheal]

Kindly suggest me a code to visualise the output of PZM. I am able to visualise the structure of PZM with the given code but cannot visualise the output of PZM..

[Bjorn Gustavsson]

The code-snippet above shows you the image approximation for each included moment, and the incremental contribution at each level, the residual, and the amplitudes. That should give you enough options to modify and expand to display something that suits your needs - I cannot conjure up something that fits your desires for an objective I dont know. This is a suitable point for you to put in the work to get the figures and illustrations you need.

[ancy micheal]

Thank you sir for your timely response

[Bjorn Gustavsson]

My pleasure.