Structured Learning of Tree Potentials in CRF for Image Segmentation

We propose a new approach to image segmentation, which exploits the advantages of both conditional random fields (CRFs) and decision trees. In the literature, the potential functions of CRFs are mostly defined as a linear combination of some predefined parametric models, and then, methods, such as structured support vector machines, are applied to learn those linear coefficients. We instead formulate the unary and pairwise potentials as nonparametric forests-ensembles of decision trees, and learn the ensemble parameters and the trees in a unified optimization problem within the large-margin framework. In this fashion, we easily achieve nonlinear learning of potential functions on both unary and pairwise terms in CRFs. Moreover, we learn classwise decision trees for each object that appears in the image. Experimental results on several public segmentation data sets demonstrate the power of the learned nonlinear nonparametric potentials.