Simultaneous Sampling and Multi-Structure Fitting with Adaptive Reversible Jump MCMC

Multi-structure model fitting has traditionally taken a two-stage approach: First, sample a (large) number of model hypotheses, then select the subset of hypotheses that optimise a joint fitting and model selection criterion. This disjoint two-stage approach is arguably suboptimal and inefficient — if the random sampling did not retrieve a good set of hypotheses, the optimised outcome will not represent a good fit. To overcome this weakness we propose a new multi-structure fitting approach based on Reversible Jump MCMC. Instrumental in raising the effectiveness of our method is an adaptive hypothesis generator, whose proposal distribution is learned incrementally and online. We prove that this adaptive proposal satisfies the diminishing adaptation property crucial for ensuring ergodicity in MCMC. Our method effectively conducts hypothesis sampling and optimisation simultaneously, and yields superior computational efficiency over previous two-stage methods.