A Riemannian approach for free-space extraction and path planning using catadioptric omnidirectional vision

Abstract

This paper presents a Riemannian approach for free-space extraction and path planning using color catadioptric vision. The problem is formulated considering color catadioptric images as Riemannian manifolds and solved using the Riemannian Eikonal equation with an anisotropic fast marching numerical scheme. This formulation allows the integration of adapted color and spatial metrics in an incremental process. First, the traversable ground (namely free-space) is delimited using a color structure tensor built on the multi-dimensional components of the catadioptric image. Then, the Eikonal equation is solved in the image plane incorporating a generic metric tensor for central catadioptric systems. This built Riemannian metric copes with the geometric distortions in the catadioptric image plane introduced by the curved mirror in order to compute the geodesic distance map and the shortest path between image points. We present comparative results using Euclidean and Riemannian distance transforms and show the effectiveness of the Riemannian approach to produce safest path planning.