Geometric construction of the caustic curves for catadioptric sensors

Most of the catadioptric cameras rely on the single view-point constraint that is hardly fulfilled. There exists many works on non single viewpoint catadioptric sensors satisfying specific resolutions. The computation of the caustic curve becomes essential if precision and flexibility are aimed. Existing solutions are unfortunately too specific to a class of curves and need heavy precomputations. This paper presents a flexible geometric construction of the caustic surface of a catadioptric sensor that can be applied to the plane curves and under a tighter assumption, to space surfaces. The method holds for smooth mirror shapes that are surfaces of revolution. Tests and experimental results substantiate the possibilities of the approach.