what is zernike moments?

hello!

I have gotten the code of zernike moments from mathworks site it work good and it return tow value, but I don't know what is that and also I don't know how many moment it extract from image if it extract one moment how I edit this code that extract several moment. this is the code:

each function is in separate script.

sorry for my bad English!

thanks in advance.

a=imread('Oval_H.png');
p = im2bw(a,0.5);
a=imread('4.png');
figure(1);subplot(2,3,1);imshow(p);
title('Horizontal oval');
p = logical(not(p));
tic
[~, AOH, PhiOH] = Zernikmoment(p,n,m); % Call Zernikemoment fuction
Elapsed_time = toc;
xlabel({['A = ' num2str(AOH)]; ['\phi = ' num2str(PhiOH)]});
%***************************************************************************
function [Z A Phi] = Zernikmoment(p,n,m)
N = size(p,1);
x = 1:N; y = x;
[X,Y] = meshgrid(x,y);
R = sqrt((2.*X-N-1).^2+(2.*Y-N-1).^2)/N;
Theta = atan2((N-1-2.*Y+2),(2.*X-N+1-2));
R = (R<=1).*R;
Rad = radialpoly(R,n,m);    % get the radial polynomial
Product = p(x,y).*Rad.*exp(-1i*m*Theta);
Z = sum(Product(:));        % calculate the moments
cnt = nnz(R)+1;             % count the number of pixels inside the unit circle
Z = (n+1)*Z/cnt;            % normalize the amplitude of moments
A = abs(Z);                 % calculate the amplitude of the moment
Phi = angle(Z)*180/pi;      % calculate the phase of the mement (in degrees)
%**********************************************************************************
function rad = radialpoly(r,n,m)
rad = zeros(size(r));                     % Initilization
for s = 0:(n-abs(m))/2
c = (-1)^s*factorial(n-s)/(factorial(s)*factorial((n+abs(m))/2-s)*factorial((n-abs(m))/2-s));
rad = rad + c*r.^(n-2*s);
end

[Mansoor ahmadi]

Please answer my above question if someone know!

Answer 1

[student]

Hi Mansoor. I used the same code but i have different error which is : Index exceeds matrix dimensions.

Error in Zernikmoment (line 47) Product = p(x,y).*Rad.*exp(-1i*m*Theta);

Error in process_predict_leaf (line 80) [mom, amplitude, angle] = Zernikmoment(b,4,0); % Call Zernikemoment fuction n=4, m=0

Did you know why I got this error?

Answer 2

[ancy micheal]

unable to execute : Undefined function or variable 'n'.

Answer 3

[arun anoop m]

https://in.mathworks.com/matlabcentral/fileexchange/38900-zernike-moments

Answer 4

[arun anoop m]

hello Mansoor sir,

your code is working fine

But you need to keep it as seperate files.

%*******************************************************************************

zerniketest.m

a=imread('Oval_H.png');

p = im2bw(a,0.5);

% a=imread('4.png');

figure(1);subplot(2,3,1);imshow(p);

title('Horizontal oval');

p = logical(not(p));

tic

[~, AOH, PhiOH] = Zernikmoment(p,n,m); % Call Zernikemoment fuction

Elapsed_time = toc;

xlabel({['A = ' num2str(AOH)]; ['\phi = ' num2str(PhiOH)]});

%*******************************************************************************

radialpoly.m

function rad = radialpoly(r,n,m)

rad = zeros(size(r)); % Initilization

for s = 0:(n-abs(m))/2

c = (-1)^s*factorial(n-s)/(factorial(s)*factorial((n+abs(m))/2-s)*factorial((n-abs(m))/2-s));

rad = rad + c*r.^(n-2*s);

end

%*******************************************************************************

Zernikemoment.m

function [Z A Phi] = Zernikmoment(p,n,m)

N = size(p,1);

x = 1:N; y = x;

[X,Y] = meshgrid(x,y);

R = sqrt((2.*X-N-1).^2+(2.*Y-N-1).^2)/N;

Theta = atan2((N-1-2.*Y+2),(2.*X-N+1-2));

R = (R<=1).*R;

Rad = radialpoly(R,n,m); % get the radial polynomial

Product = p(x,y).*Rad.*exp(-1i*m*Theta);

Z = sum(Product(:)); % calculate the moments

cnt = nnz(R)+1; % count the number of pixels inside the unit circle

Z = (n+1)*Z/cnt; % normalize the amplitude of moments

A = abs(Z); % calculate the amplitude of the moment

Phi = angle(Z)*180/pi; % calculate the phase of the mement (in degrees)

%*******************************************************************************

Reference:

[1] Zernike Moments, version 1.5 (15.1 KB) by Amir Tahmasbi ,"MATLAB Code for the Fast Calculation of Zernike Moments of order n and repetition m on NxN images",Available:https://in.mathworks.com/matlabcentral/fileexchange/38900-zernike-moments

Answer 5

[arun anoop m]

One more thing sir,

The program will only for black and white images. So if u need to show other images, has to do the following,

a=imread('flowers.jpg');

p = im2bw(a,0.5);

figure(1);subplot(2,3,1);imshow(p);

title('Horizontal oval');

p = logical(not(p));

tic

[~, AOH, PhiOH] = Zernikmoment(p,n,m); % Call Zernikemoment fuction

Elapsed_time = toc;

xlabel({['A = ' num2str(AOH)]; ['\phi = ' num2str(PhiOH)]});

Actually i am searching a code for getting Angle(A) and magnitude(Phi) as image output. I dont know how to call array function in another file.

If all the programs are in same file, can use the following code,

figure,imshow(uint8(A)),title('Zernike Moment Angle');

instead

xlabel({['A = ' num2str(AOH)]; ['\phi = ' num2str(PhiOH)]});

Reference:

[1] Zernike Moments, version 1.5 (15.1 KB) by Amir Tahmasbi ,"MATLAB Code for the Fast Calculation of Zernike Moments of order n and repetition m on NxN images",Available:https://in.mathworks.com/matlabcentral/fileexchange/38900-zernike-moments