Effective Bayesian Inference by Data-Driven Markov Cain Monte Carlo for Object Recognition and Image Segmentation

摘要

This artical presents a mathermatical paradidm called Data Driven Markow Chain Monte Carlo (DDMCMC) for effective stochastic inference in the Bayesian framework. We apply the DDMCMC paradigm to two typical problems in image analysis: object recognition and image semgnetation. In both problems, the solution spaces are not only high dimensional but heterogeneously-structured in the sense that they are composed of many subspaces of varying dimensions. Each of the subs0pace is product of what we called the object spaces. The latter is further decomposed inthe the co-called atomic spaces. The DDMCMC paradigm simulated Markov chins for exploring the solution spaces using bothjump and diffusion dynamics. Unlike tranditional MCMC algorithms, the DDMCMC paradigm utilizes data driven (or bottom-up) techniques, such as Hough transform, edge detection, and color clustering, to design effective transition probabilitis for Markov chain dynamics. This drastically improves the effectiveness of traditional MCMC algorithms in terms of two standazrd metrics: "burn-in" period and "mixing" rate. The article proceeds in three steps. Firstly, we analyze the structures of the solution space OMETA for the two tasks. Secondly, we study how data-driven techniques are utilized to compte impor5tance proposal probabilities in the solution spaces, the object spaces and atomic spaces. These proposal probabilities are expressed in non-gparametric form using weighted samples or particles. Thirdly, we design Markov chains to travel in such heterogeneous structured solution space as an ergoic and reversible process. The paper first review the DDMCMC theory using a simple object recognition problem-the PSI -world reported in (14), then we briefly intrudce the result5s on image semgnetation.