Homography Estimation from the Common Self-Polar Triangle of Separate Ellipses

Abstract

How to avoid ambiguity is a challenging problem for conic-based homography estimation. In this paper, we address the problem of homography estimation from two separate ellipses. We find that any two ellipses have a unique common self-polar triangle, which can provide three line correspondences. Furthermore, by investigating the location features of the common self-polar triangle, we show that one vertex of the triangle lies outside of both ellipses, while the other two vertices lies inside the ellipses separately. Accordingly, one more line correspondence can be obtained from the intersections of the conics and the common self-polar triangle. Therefore, four line correspondences can be obtained based on the common self-polar triangle, which can provide enough constraints for the homography estimation. The main contributions in this paper include: (1) A new discovery on the location features of the common self-polar triangle of separate ellipses. (2) A novel approach for homography estimation. Simulate experiments and real experiments are conducted to demonstrate the feasibility and accuracy of our approach.