OpenCV's fitEllipse() sometimes returns completely wrong ellipses

Question

My goal is to recognize all the shapes present in an image. The idea is:

1. Extract contours
2. Fit each contour with different shapes
3. The correct

Answer 1

It may be a better idea to get a pixel-by-pixel comparison i.e. what percentage is the overlap between the contour and the "fitted" ellipse.

Another, simpler idea is to also compare the centroids of the contour and its ellipse fit.