[WM]: Zernike Moments

["Mostafa mohsen" <orange1704@hotmail.com>]

Hi watermarker

                     I tried to make a watermarking schema that is invariant 
to rotational attack so I decided to use Zernike moments as to embed the 
watermark I have implemented the attached code for Zernike moments; but the 
problem that the values of the Zernike moments are not matched with correct 
values for example for constant gray level 127 for 128*128 image the value 
of the Zernike moments is 127.24 but using my implementation it was 124.7896 
for n=0 and m=0
Same for n=12 and m=12 correct value is 0.0153 but my value is 0.7069 i.e. 
my value is always greater than the correct value except for n=0 and m=0.

Could you please help me to find the problem in the following matlab code?

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [A]=calculateZernikMoment(I,n,m)
I=double(I);
V=calculateZernikePoly(I,n,m);
Vconj=conj(V);
[l w]=size(I);
Xdelta=2/(l);
Ydelta=2/(w);
A=sum(sum(Vconj.*I));
A=((n+1)/pi)*Xdelta*Ydelta*A;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [V]=calculateZernikePoly(I,n,m)
[l w]=size(I);
V=zeros(l,w);
radialPoly=zeros(l,w);
step=2/(l-1);
[x y]=meshgrid(-1:step:1);
y=y';
y=fliplr(y);
y=y';
r=x+i*y;
rm=abs(r);
theta=angle(r);
for row=1:l
    for col=1:w
        rmValue=rm(row,col);
        thetaValue=theta(row,col);
        if(rmValue<=1.00)
            radialPoly(row,col)=calculateRadialPoly(rmValue,n,m);
            V(row,col)=radialPoly(row,col)*exp(i*m*thetaValue);
        end
    end
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function[radialPoly] =calculateRadialPoly(r,n,m)
radialPoly=0;
mAbs=abs(m);
for s=0:(n-mAbs)/2
    nem=(-1)^s * nCr(n-s) * r^(n-2*s);
    dem=nCr(s) * nCr(((n+mAbs)/2)-s) * nCr(((n-mAbs)/2)-s);
    radialPoly=radialPoly+( nem/dem );
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [result]=nCr(n)
result=1;
for counter=n:-1:1
    result=counter*result;
end




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