Probabilistic methods for discrete labeling problems in digital image processing and analysis

Abstract

Many problems in digital image processing and analysis can be interpreted as labeling problems, which aim to find the optimal mapping from a set of sites to a set of labels. A site represents a certain primitive, such as a pixel, while a label represents a certain quantity, such as disparity in stereo correspondence. Considering this labeling interpretation, instead of solving different problems individually, we propose a series of unified frameworks in the random walks (RW) context for labeling problems with regular sites and discrete labels. The first framework, which we term as the generalized random walks (GRW) framework, converts a discrete labeling problem into the calculation of steady-state probabilities of random walkers transiting on a graph. The performance of GRW is validated through experiments on stereo correspondence and multi-exposure fusion, which we formulate as labeling problems in the RW context. By incorporating hierarchical and multiscale schemes, the performance of GRW is further improved. This leads to two enhanced frameworks: the hierarchical random walks (HRW) framework, which reduces the computational cost of GRW but produces good approximations; and the multiscale random walks (MRW) framework, which produces robust solutions utilizing both inter- and intra-scale information. The performance of HRW is validated through perception-guided multi-exposure fusion, where we also introduce advanced perceptual metrics into multi-exposure fusion; the performance of MRW is verified through volumetric medical image fusion, where we also introduce a cross-scale fusion rule based on MRW. Furthermore, a multivariate Gaussian conditional random field model and its hierarchical version are proposed for more general multi-label problems, and their relationships with GRW and HRW are analyzed.