A comparative analysis of B-spline deformation models in 3D shape matching

Abstract

Lattice-based B-spline driven deformation has become a useful method in shape matching applications. Here, the challenge is to find a configuration of the B-spline deformation model that effectuates a deformation that spatially aligns one shape (the source) to another shape (the target). Literature study indicates that few B-Spline deformation based algorithms were implemented that target polygonal meshes. In contrast, in the field of medical image registration, B-spline deformation has been extensively applied in matching shapes that use a voxel-based shape representation. For exploring the opportunities of applying these voxel-based methods to the shape matching of polygonal meshes, in this paper we propose to match polygon meshes by transforming them to voxel models and apply established techniques from the field of medical imaging. Two voxel-based methods are selected and implemented: Global Optimization methods, which globally optimize the B-spline model, and Markov Random Field methods, which locally optimize the B-spline model. These methods are compared to parameterized B-spline-based shape matching methods previously proposed by the authors. These methods directly match polygon meshes. Results indicate that the proposed methodology outperforms the parameterized approach in terms of accuracy and computation time and therefore is a promising alternative to existing methods.