Recovering Light Directions and Camera Poses from a Single Sphere

This paper introduces a novel method for recovering both the light directions and camera poses from a single sphere. Traditional methods for estimating light directions using spheres either assume both the radius and center of the sphere being known precisely, or they depend on multiple calibrated views to recover these parameters. It will be shown in this paper that the light directions can be uniquely determined from the specular highlights observed in a single view of a sphere without knowing or recovering the exact radius and center of the sphere. Besides, if the sphere is being observed by multiple cameras, its images will uniquely define the translation vector of each camera from a common world origin centered at the sphere center. It will be shown that the relative rotations between the cameras can be recovered using two or more light directions estimated from each view. Closed form solutions for recovering the light directions and camera poses are presented, and experimental results on both synthetic and real data show the practicality of the proposed method.