Point Light Source Estimation from Two Images and Its Limits

In this paper, the performance of parameter estimation of a single static distant point light source from two video images is analyzed in terms of estimation theory. The illumination parameters are the intensity and direction of the light source.In the first part of this paper, estimators from the literature are reviewed. Most recent estimators evaluate as input data two video images as well as the 3D shape and the 3D motion of the visible moving objects.In the second part of the paper, the performance of these recent methods is analyzed. The input data to estimation as well as the inherent input data errors are described by a stochastic observation model. Based on this model, the performance is analyzed regarding the Cramér-Rao theoretical lower bound of estimation error variances. The bound is derived for a variety of cases of scene illumination, object motion and errors in input data. For simplification purpose, the bound is valid only for object motions with the rotation axis lying in the image plane. The analysis shows in which cases which estimation accuracy can be expected with current methods.Finally, a comparison of the bound with one of the recent estimators shows that recent estimators are suboptimal in case of errors in the 3D shape of the objects. In future work, the stochastic observation model presented in this paper can be used to improve illumination estimation.