A speedup scheme for MRF stereo using local label hierarchy

Abstract

Random field formulation has proven to be a powerful framework for solving stereo correspondence problems because of its ability to intuitively incorporate global smoothness constraint with local matching costs. However, solving such problems for cases where large number of pixel variables and possible disparity labels are common can be impractical as the computational complexity grows fast with the number of labels. We proposed a speedup scheme using local label hierarchy in which we exploit characteristics of stereo vision problem to obtain a hierarchical energy minimization technique. In doing so, we give definitions and notations for local label hierarchy as well as approaches for label-wise grouping. We also generalize the definition of energy function to include sets of labels and present heuristics for assigning group potentials. Our approach builds different “local” hierarchy for each variable using information from the energy function which enables us to achieve better performance when compared to using the same hierarchy for every variable. The added processing steps have significantly less theoretical computational complexity than the overall process. Our method was tested with different combinations of cost functions, and our experiment has shown that our heuristics can assist in speeding up the computation time while providing comparable energy and error.