模板匹配之zernike矩

zernike矩具有旋转不变性，广泛用于目标识别模板匹配，抗噪能力强。

zernike矩的原理就不过多赘述，上代码。

//求n的阶乘
long TemplateMatch::factorial(int n)
{
int result=1;
while(n>1)
{
result *= n;
n-=1;
}
return result;
}

//zernike矩径向多项式
double TemplateMatch::RadialPolynomial(double p, int n, int m)
{
double radial=0;
int s;
double c;

for (s=0; s<=(n-m)/2; s++)
{
c=pow((double)(-1),(double)(s))*factorial(n-s)/((double)(factorial(s)*factorial((n+m)/2-s)*factorial((n-m)/2-s)));
radial=radial+c*pow(p,n-2*s);
}
return radial;
}

//n阶m次zernike矩
double TemplateMatch::ZernikeMoments(double *im,int imW,int imH, int n, int m)
{
#define im(ROW,COL) im[imW*(ROW)+(COL)]
double zr=0;
double zi=0;
int cnt=0;
int x,y;
double p;
double radial=0;
double theta=0;

for (y=0; y<imH; y++)
{
for(x=0; x<imW; x++)
{
p=sqrt((double)((2*x-imW+1)*(2*x-imW+1)+(imH-1-2*y)*(imH-1-2*y)))/imW;
if (p<=1)
{
radial=RadialPolynomial(p,n,m);
theta=atan2((double)(imH-1-2*y),(double)(2*x-imW+1));
zr+=im(y,x)*radial*cos(m*theta);
zi+=im(y,x)*radial*sin(m*theta);
cnt++;
}
}
}
double A=(n+1)*sqrt((double)(zr*zr+zi*zi))/cnt;
return A;
}