double f_i(double *X1,double x1,double *X2,double x2,
int n,double h11,double h12,double h21,double h22,int i)
{
double sum = 0;
for(int j=0;j<n;j++){
if(j!=i) sum += epanechnikov(X1[j],x1,X2[j],x2,h11,h12,h21,h22);
}
return sum;
}
void computeSpatiogram(const cv::Mat &imagePatch, int m, spatiogram &sg){
int n = 256/m;
std::vector<double> bins;
linspace(bins, 0, 256, n);
int height = imagePatch.rows;
int width = imagePatch.cols;
cv::Mat X,Y, Xm, Ym, dist2, K;
meshgrid(cv::Range(1,width), cv::Range(1,height), X, Y);
meshgrid(cv::Range(-width/2,width/2), cv::Range(-height/2,height/2), Xm, Ym);
X.convertTo(X, CV_64FC1); Y.convertTo(Y, CV_64FC1);
robustnorm(Xm,Ym,dist2);
dist2 = dist2(cv::Rect(0,0,width,height));
epanechnikov(dist2, K);
// initialize spatiogram
sg.C = 1/cv::sum(K)[0];
sg.C = sg.C/(imagePatch.channels());
sg.cd = cv::Mat::zeros(1, m*imagePatch.channels(), CV_64FC1);
sg.mu = cv::Mat::zeros(2, m*imagePatch.channels(), CV_64FC1);
sg.cm = cv::Mat::zeros(2, m*imagePatch.channels(), CV_64FC1);
sg.bins = m*imagePatch.channels();
for (int l=0;l<imagePatch.channels();l++){
for (int j=0;j<m;j++){
cv::Mat temp;
binelements(imagePatch, bins, l, j, temp);
// zeroth order spatiogram
sg.cd.at<double>(0,l*m+j) = cv::sum( K.mul(temp) )[0];
double den = cv::sum(temp)[0];
if (den==0.0) den=std::numeric_limits<double>::epsilon();
if (sg.cd.at<double>(0,l*m+j)==0.0) sg.cd.at<double>(0,l*m+j)=std::numeric_limits<double>::epsilon();
// Mean vector of the pixels' coordinates mu: first order spatiogram
double mu_x = cv::sum( X.mul(temp) )[0]/den;
double mu_y = cv::sum( Y.mul(temp) )[0]/den;
sg.mu.at<double>(0, l*m+j) = mu_x;
sg.mu.at<double>(1, l*m+j) = mu_y;
// Covariance matrix of the pixels' coordinates Cm[2x2]: 2nd order spatiogram
cv::Mat C11; cv::pow(X - mu_x, 2, C11); //(x-mu_x)^2
cv::Mat C22; cv::pow(Y - mu_y, 2, C22); //(y-mu_y)^2
sg.cm.at<double>(0, l*m+j) = cv::sum(C11.mul(temp))[0]/den; //Cov(1,1)
sg.cm.at<double>(1, l*m+j) = cv::sum(C22.mul(temp))[0]/den; //Cov(2,2)
}
}
//normalize color distribution
sg.cd = sg.C*sg.cd;
}
