Question about polar or radial angle calculation in the image coordinate system

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I am not sure this is the exact answer for you question but may be helpful. If you consider an image and you want to find the angle at any point from 0,0 you can consider the image as third quadrant and you will get angle in the range of -90 to -179.99 using atan2(). And if your reference is centre of the image the upper quadrants will be in the range of 0 to 180 and the lower quadrants gives approximately -.1 to -179.99. The below code may give you the idea about the arc tangent of any point in the given image. You can use mouse click to point out the co-ordinates.

#include "opencv2/highgui/highgui.hpp"
#include "opencv2/imgproc/imgproc.hpp"

using namespace std;
using namespace cv;

Point p1;
Mat frame, src;
Point cent = Point(300,300);// for calculating tangent from center of image    
double angle=0;
char name[20];

void mouseHandler(int event, int x, int y, int flags, void *param)
  {
    switch(event) {
    /* left button down */
    case CV_EVENT_LBUTTONDOWN:

            p1.x=x;
            p1.y=y;

         frame.copyTo(src);
         line(src, p1, cent,Scalar(255,0,0),2, 8 );
         angle = atan2(cent.y - p1.y,cent.x - p1.x) * 180.0 / CV_PI;

         sprintf(name,"Angle  = %f degree",angle);
         putText(src,name, Point(30,30), FONT_HERSHEY_SIMPLEX,1, Scalar(0,255,0),2);
         imshow("out", src);
         break;
  }
}

int main(int argc, char** argv)
{
  frame= Mat(600,600,CV_8UC3);
  frame.copyTo(src);
  namedWindow("out", 0);
  imshow("out", src);
  setMouseCallback( "out", mouseHandler, NULL );
  waitKey(0);
  return 0;
 }

Hope these Helpful.....