Integrating Bottom-Up/Top-Down for Object Recognition by Data Driven Markov Chain Monte Carlo

This article presents a mathematical paradigm called Data Driven Markov Chain Monte Carlo (DDMCMC) for object recognition. The obje ctives of this paradigm are two-fold. Firstly, it realizes traditional \hyp othesis-and-test"methods through wellbalanced Markov chain monte Carlo (MCMC) dynamics, thus it achieves robust and globally optimal solutions. Se condly, it utilizes data-driven (bottom-up) methods in computer vision, such as Hough transform and data clustering, to design e ective tr ansition probabilities for Markov chain dynamics. This drastically improves the e ectiveness of traditional MCMC algorithms in terms of two standard metrics: \burn-in" perio d and \mixing" rate. The article proceeds in three steps. Firstly, we analyze the structures of the solution space for obje ct recognition. is decomposed into a large number of subspaces of varying dimensions in a hierarchy. Se condly,we use data-driven techniques to compute importance proposal probabilities in these spaces, each expressed in a non-parametric form using weighted samples or particles. Thirdly, Markov chains are designed to travel in such heterogene ous structur ed solution space, with both jump and di usion dynamics. We use possibly the simplest objects the \ -world" as an example to illustrate the concepts, and we brie y present r esults on an applic ation of traÆc sign detection.