MATCHING PARAMETERIZED SHAPES BY NONPARAMETRIC BELIEF PROPAGATION

Abstract

In this paper we generalize the belief propagation based rigid shape matching algorithm to a nonparametric belief propagation based on parameterized shape matching. We construct a local-global shape descriptor based cost function to compare the distances among landmarks in each data set, which is equivalent to the Hamiltonian of a spin glass. The constructed cost function is immune to rigid transformations, therefore the parameterized shape matching can be achieved by searching for the optimal shape parameter and the correspondence assignment that minimize the cost function. The optimization procedure is then approximated by a Monte Carlo simulation based MAP estimation on a graphical model, i.e. the nonparametric belief propagation. Experiments on a principal component analysis (PCA) based point distribution model (PDM) of the proximal femur illustrate the effects of two key factors, the topology of the graphical model and the renormalization of the shape parameters of the parameterized shape. Other factors that can influence its performance and its computational complexity are also discussed.