Geotensity: combining motion and lighting for 3D surface reconstruction

Abstract

This paper is about automatically reconstructing the full 3D surface of an object observed in motion by a single static camera. We introduce the geotensity constraint that governs the relationship between four images of a moving object under fairly general lighting conditions. We show that it is possible in theory to solve for 3D surface structure for both the case of a single point light source and a pair of point, light sources and propose that a solution exists for an arbitrary number point light sources. The surface may or may not be textured. We then give an example of automatic surface reconstruction of a face under a point light source. The geotensity constraint provides the theoretical foundation for the full automatic 3D reconstruction of Lambertian objects using a single fixed camera, and arbitrary unknown object motion under arbitrary lighting conditions.