Single Image Shadow Detection Using Multiple Cues in a Supermodular MRF

Abstract

We propose a single region shadow classifier based on a multikernel SVM. Our multikernel model is a linear combination of χ2 and Earth Mover’s Distance(EMD)[5] kernels that operate on texture and color histograms disjointly. This single region classifier already outperforms the more complex state of art methods, without performing MRF/CRF optimization. The local appearance of a single region is often ambiguous. Even for a human observer it can be hard to discern if a region is in shadow or not, without considering its context. Hence, it is sensible to look beyond the boundaries of a single region to decide its shadow label [1] [6]. In contrast to previous work we strive to use such contextual information sparingly. For MRF optimization reasons we prefer that most of the work is handled by the single region classifier (unary MRF potentials), with sparse pairwise connections that smooth the label changes across regions. We build on the work of [1] to propose our own improved pairwise classifiers but constrained to adjacent regions: for pairs of regions sharing the same material and same illumination condition, and for same material pairs viewed under different illumination (first lit, second in shadow). We also propose a shadow boundary classifier. Since shadow boundaries often overlap with reflectance changes confounding the effects of the illumination change, our classifier focuses on boundaries of shadows cast over surfaces with the same underlying material. We integrate our single region classifier, our pairwise classifiers, and our boundary classifier using an MRF. Confident positive predictions of the pairwise and boundary classifiers are used to define the pairwise potentials and the graph topology of the MRF. The unary potentials are defined based on the single region classifier. We want to minimize the following functional: