Topology-aware non-rigid point set registration via global–local topology preservation

Abstract

We propose a new topology-aware point set registration algorithm which can cope with multi-part articulated and non-rigid deformations. Point set registration is formulated as a maximum likelihood (ML) estimation problem where two topologically complementary constraints are jointly optimized in a probabilistic framework. The first is coherent point drift that keeps the overall spatial connectivity and associativity by moving the point set collectively and coherently. The second is local linear embedding that preserves the local topological structure during registration. Hence, the new algorithm is called global–local topology preservation (GLTP). Without any pre-segmentation and correspondence initialization, GLTP is particularly useful and effective in dealing with complex shape matching with non-coherent and non-rigid local deformations at different parts of a point set. We have derived the expectation maximization algorithm for the ML optimization constrained with both regularization terms. Experimental results on a large set of 2D and 3D examples show the advantages and robustness of GLTP over existing algorithms in the presence of outliers, noise and missing data, especially in the case of articulated non-rigid transformations.