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 objectives of this paradigm are two-fold. Firstly, it realizes traditional “hypothesis-and-test” methods through well-balanced Markov chain Monte Carlo (MCMC) dynamics, thus it achieves robust and globally optimal solutions. Secondly, it utilizes data-driven (bottom-up) methods in computer vision, such as Hough transform and data clustering, to design effective transition probabilities for Markov chain dynamics. This drastically improves the effectiveness of traditional MCMC algorithms in terms of two standard metrics: “burn-in” period and “mixing” rate. The article proceeds in three steps. Firstly, we analyze the structures of the solution space Ω for object recognition. Ω is decomposed into a large number of subspaces of varying dimensions in a hierarchy. Secondly, 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 heterogeneous structured solution space, with both jump and diffusion dynamics. We use possibly the simplest objects-the “Ψ-world” as an example to illustrate the concepts, and we briefly present results on an application of traffic sign detection