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Here a sample :

int main(int ac, char** av) 
{
Mat m,mc;

mc=imread("14282855632031481.jpg",cv::IMREAD_UNCHANGED);
cvtColor(mc, m, CV_BGR2GRAY);
vector<cv::Point2d> p;
Mat line_fit;
for (int i=0;i<m.rows;i++)
    for (int j=0;j<m.cols;j++)
        if (m.at<unsigned char>(i,j)!=0)
            p.push_back(Point2d(j,i));
cout<<"Coordinates : \n";
cout<<p;
fitLine(p, line_fit, CV_DIST_L2, 0, 0.01, 0.01);
double a,b,c;
b = -line_fit.at<float>(0, 0);
a = line_fit.at<float>(1, 0);
c = -(a*line_fit.at<float>(2, 0) + b*line_fit.at<float>(3, 0));
line(mc,Point2d(0,-c/b),Point2d(m.cols,(-a*m.cols-c)/b),Scalar(0,255,0),2);

imshow("Fit", mc);
waitKey();
}

Here a sample :without cheking (b, depth...):

int main(int ac, char** av) 
{
Mat m,mc;

mc=imread("14282855632031481.jpg",cv::IMREAD_UNCHANGED);
cvtColor(mc, m, CV_BGR2GRAY);
vector<cv::Point2d> p;
Mat line_fit;
for (int i=0;i<m.rows;i++)
    for (int j=0;j<m.cols;j++)
        if (m.at<unsigned char>(i,j)!=0)
            p.push_back(Point2d(j,i));
cout<<"Coordinates : \n";
cout<<p;
fitLine(p, line_fit, CV_DIST_L2, 0, 0.01, 0.01);
double a,b,c;
b = -line_fit.at<float>(0, 0);
a = line_fit.at<float>(1, 0);
c = -(a*line_fit.at<float>(2, 0) + b*line_fit.at<float>(3, 0));
line(mc,Point2d(0,-c/b),Point2d(m.cols,(-a*m.cols-c)/b),Scalar(0,255,0),2);

imshow("Fit", mc);
waitKey();
}