Using directional statistics to learn cast shadows from a multi-spectral light sources physical model

In this paper is proposed a novel statistical learning approach, to identify cast shadows, and model their generation. We exploit the theoretically well-founded directional statistics field, in order to formulate the generation of cast shadows as a Mixture of Von Mises-Fisher distributions (MovMF) on the unit sphere. This formulation is based on a bi-illuminant physical model of cast shadows, where no prior assumptions of the spectral power distribution (SPD) of the direct light sources and ambient illumination in the scene are made. Founded on a rigorous directional statistics approach, this parametric framework is capable of modelling the shaded surface behavior in complex illumination scenes and meet real time requirements. This better model discriminating cast shadows provides a more compact representation, and achieve better accuracy, with less data and much less computation time, compared with non-parametric models previously proposed. Theoretic analysis and experimental evaluations demonstrate the effectiveness of the proposed framework.