Robust shadow and illumination estimation using a mixture model

Illuminant estimation from shadows typically relies on accurate segmentation of the shadows and knowledge of exact 3D geometry, while shadow estimation is difficult in the presence of texture. These can be onerous requirements; in this paper we propose a graphical model to estimate the illumination environment and detect the shadows of a scene with textured surfaces from a single image and only coarse 3D information. We represent the illumination environment as a mixture of von Mises-Fisher distributions. Then, each shadow pixel becomes the combination of samples generated from this illumination environment. We integrate a number of low-level, illumination-invariant 2D cues in a graphical model to detect and estimate cast shadows on textured surfaces. Both 2D cues and approximate 3D reasoning are combined to infer a set of labels that identify the shadows in the image and estimate the positions, shapes and intensities of the light sources. Our results demonstrate that the probabilistic combination of multiple cues, unlike prior approaches, manages to differentiate both hard and soft shadows from the underlying surface texture even when we can only coarsely anticipate the effect of 3D geometry. We also experimentally demonstrate how correct estimation of the sharpness and shape of the light sources improves the augmented reality results.