### ellipse approximation of blob using contours moments : confusing orientation angle

Dear all,

I want to draw the ellipse approximating an isolated blob (the largest contour found with findContours). Using the formulas of paper :http://goo.gl/yvcUO5 for the major and minor axes I obtain consistent axes lengths. However using the formula to compute the orientation angle from the same paper( and which I find almost everywhere) I obtain odd results. This is the formula : theta = 0.5*atan (2*mu11 / (mu20-mu02)) ;

As long as the blob (which represents a human silhouette) is not close to horizontal, the formula returns a consistent value of the orientation angle but as soon as the blob becomes almost horizontal the sign of the orientation angle is flipped suddenly. I know the reason of such a behavior. If we refer to the formula above : when the blob is not horizontal mu20 is smaller than mu02. This is true while the blob starts climbing (falling) counter clockwise until it reaches an orientation of about -45 degrees. When it reaches that value the pxels distribution of the blob becomes horizontal rather than vertical and mu20 becomes larger than mu02 which implies inversion of the angle's sign. I don't know if this formula is correct.

Thanks a lot for your help.