Camera and light calibration from reflections on a sphere

This paper introduces a novel method for recovering light directions and camera parameters using 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. In this paper, it will be shown that light directions can be uniquely determined from specular highlights observed in a single view of a sphere without knowing or recovering the exact radius and center of the sphere. Besides, given multiple views of the sphere, it will be shown that the focal length and the relative positions and orientations of the cameras can be determined using the recovered sphere and light directions. Closed form solutions for estimation of light directions and camera poses are presented, and an optimization procedure for estimation of the focal length is introduced. Experimental results on synthetic and real data demonstrates both the accuracy and robustness of the proposed method.