Particle-Based Belief Propagation for Structure from Motion and Dense Stereo Vision with Unknown Camera Constraints

In this paper, we present a specific use of the Particle-based Belief Propagation (PBP) algorithm as an approximation scheme for the joint distribution over many random variables with very large or continuous domains. After formulating the problem to be solved as a probabilistic graphical model, we show that by running loopy Belief Propagation on the whole graph, in combination with an MCMC method such as Metropolis-Hastings sampling at each node, we can approximately estimate the posterior distribution of each random variable over the state space. We describe in details the application of PBP algorithm to the problem of sparse Structure from Motion and the dense Stereo Vision with unknown camera constraints. Experimental results from both cases are demonstrated. An experiment with a synthetic structure from motion arrangement shows that its accuracy is comparable with the state-of-the-art while allowing estimates of state uncertainty in the form of an approximate posterior density function.