Determining the Orientation of a Painted Sphere from a Single Image: A Graph Coloring Problem

In our work on robotic manipulation, we required a method for determining the orientation of a marked sphere from a single visual image. Our solution utilizes features of different colors painted on the sphere at the vertices of the Platonic solids. The main result of this paper is the minimization of the number of feature colors needed to solve the correspondence problem. The minimization of colors is a graph coloring problem. Index Terms — Graph coloring, feature correspondence, Platonic solids, surface markings, sphere orientation.