Sparse Update for Loopy Belief Propagation: Fast Dense Registration for Large State Spaces

A dense point-based registration is an ideal starting point for detailed comparison between two neuroanatomical objects. This paper presents a new algorithm for global dense point-based registration between anatomical objects without assumptions about their shape. We represent mesh models of the surfaces of two similar 3D anatomical objects using a Markov Random Field and seek correspondence pairs between points in each shape. However, for densely sampled objects the set of possible point by point correspondences is very large. We solve the global non-rigid matching problem between the two objects in an efficient manner by applying loopy belief propagation. Typically loopy belief propagation is of order m³ for each iteration, where m is the number of nodes in a mesh. By avoiding computation of probabilities of configurations that cannot occur in practice, we reduce this to order m². We demonstrate the method and its performance by registering hippocampi from a population of individuals aged 60-69. We find a corresponding rigid registration, and compare the results to a state-of-the-art technique and show comparable accuracy. Our method provides a global registration without prior information about alignment, and handles arbitrary shapes of spherical topology.