Introduction to non-linear optimization
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In this paper, the performance of parameter estimation of a single static distant point light source from two video imagesis analyzed in terms of estimation theory. The illuminationparameters are the intensity and direction of the light source.In the first part of this paper, estimators from the literature arereviewed. Most recent estimators evaluate as input data two video images aswell 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 methodsis analyzed. The input data to estimation as well as the inherent inputdata errors are described by a stochastic observation model. Based on thismodel, the performance is analyzed regarding the Cramér-Rao theoreticallower bound of estimation error variances. The bound is derived for avariety of cases of scene illumination, object motion and errors in inputdata. For simplification purpose, the bound is valid only for objectmotions with the rotation axis lying in the image plane. The analysis showsin which cases which estimation accuracy can be expected with currentmethods.Finally, a comparison of the bound with one of the recent estimators showsthat recent estimators are suboptimal in case of errors in the 3D shape ofthe objects. In future work, the stochastic observation model presented inthis paper can be used to improve illumination estimation.