Illumination estimation and cast shadow detection through a higher-order graphical model

In this paper, we propose a novel framework to jointly recover the illumination environment and an estimate of the cast shadows in a scene from a single image, given coarse 3D geometry. We describe a higher-order Markov Random Field (MRF) illumination model, which combines low-level shadow evidence with high-level prior knowledge for the joint estimation of cast shadows and the illumination environment. First, a rough illumination estimate and the structure of the graphical model in the illumination space is determined through a voting procedure. Then, a higher order approach is considered where illumination sources are coupled with the observed image and the latent variables corresponding to the shadow detection. We examine two inference methods in order to effectively minimize the MRF energy of our model. Experimental evaluation shows that our approach is robust to rough knowledge of geometry and reflectance and inaccurate initial shadow estimates. We demonstrate the power of our MRF illumination model on various datasets and show that we can estimate the illumination in images of objects belonging to the same class using the same coarse 3D model to represent all instances of the class.