Particle-Based Shape Analysis of Multi-object Complexes

This paper presents a new method for optimizing surface point correspondences for shape modeling of multiobject anatomy, or shape complexes. The proposed method is novel in that it optimizes correspondence positions in the full, joint shape space of the object complex. Researchers have previously only considered the correspondence problem separately for each structure, thus ignoring the interstructural shape correlations that are increasingly of interest in many clinical contexts, such as the study of the effects of disease on groups of neuroanatomical structures. The proposed method uses a nonparametric, dynamic particle system to simultaneously sample object surfaces and optimize correspondence point positions. This paper also suggests a principled approach to hypothesis testing using the Hotelling T2 test in the PCA space of the correspondence model, with a simulation-based choice of the number of PCA modes. We also consider statistical analysis of object poses. The modeling and analysis methods are illustrated on brain structure complexes from an ongoing clinical study of pediatric autism.