Using Conic Correspondence in Two Images to Estimate the Epipolar Geometry

In this paper it is shown how to use corresponding conics in two images to estimate the epipolar geometry, the fundamental/essential matrix and reconstruct the scene. The corresponding conics can be images of either a planar conic or silhouettes of a quadric. It is shown that one conic correspondence gives two constraints on the fundamental matrix and a method to estimate the fundamental matrix from four (or more) corresponding conics is presented. Furthermore, a new type of fundamental matrix for describing conic correspondences is presented. Finally, it is shown that the problem of estimating the fundamental matrix from 5 point correspondences and 1 conic correspondence in general has 10 diierent solutions. A method to calculate these solutions is also given together with an experimental validation.