Random field optimization using local label hierarchy

Abstract

Random field formulation has proven to be a powerful framework for solving various computer vision tasks, specifically those involving assigning labels to image pixels or superpixels subjected to spatial relationships and visual contexts, due to the ability to intuitively incorporate global and local information. Unfortunately, solving these problems can be impractical when large number of variables and possible labels are present as the computational complexity grows fast with the problem size. In this thesis, we propose a speedup scheme for random field optimization using local label hierarchy. We focus on problems in which the label space has a natural ordering structure that represents physical quantity and exploit characteristics of the underlying labeling problems to obtain a hierarchical energy minimization technique. This has enabled us to circumvent exhaustive search of label space and, therefore, achieve better performance in terms of running time. We give definitions and notations for local label hierarchy as well as present approaches for label-wise grouping, namely, local minimum search, cluster analysis, and maximum-difference subdivision. We also generalize the definition of energy function to include sets of labels as the domain and present heuristics for assigning group potentials. The added processing steps have significantly less theoretical computational complexity than the overall process. Our methodology was tested with a number of computer vision problems with structured label spaces. The experimental results have shown that our proposed scheme can provide up to an order of magnitude speedup of the computation time while providing comparable energy.