Robust point correspondence matching and similarity measuring for 3D models by relative angle-context distributions

Robust solutions for correspondence matching of deformable objects are prerequisite for many applications, particularly for analyzing and comparing soft tissue organs in the medical domain. However, this has proved very difficult for 3D model surfaces, especially for approximate symmetric organs such as the liver, the stomach and the head. In this paper, we propose a novel approach to establish the 3D point-correspondence for polygonal free-form models based on an analysis of the relative angle distribution around each vertex with respect to relative reference frame calculated from principal component analysis (PCA). Two kinds of distributions, the Relative Angle-Context Distribution (RACD) and the Neighborhood Relative Angle-Context Distribution (NRACD) have been defined respectively from the probability mass function of relative angles context. RACD describes the global geometric features while NRACD provides a hierarchical local to global shape description. The experiments and evaluation of adopting these features for the human head and liver models show that both distributions are capable of building robust point correspondence while the NRACD gives better performance because it contains additional information on the spatial relationship among vertices and has the ability to provide an effective neighborhood shape description. Furthermore, we propose a similarity measure between correspondence ready models based on relative angle-context distribution factors. The experimental results demonstrate that this approach is very promising for model analysis, 3D model retrieval and classification.