Non-rigid Point Set Registration with Global-Local Topology Preservation

We propose a new point set registration method, Global-Local Topology Preservation (GLTP), which can cope with complex non-rigid transformations including highly articulated deformation. The registration is formulated as a Maximum Likelihood (ML) estimation problem with two topologically complementary constraints. The first is the previous Coherent Point Drift (CPD) that encodes a global topology constraint by moving one point set coherently to align with the second set. The second, which is inspired by the idea of Local Linear Embedding (LLE), is introduced to handle highly articulated non-rigid deformation while sustaining the local structure. Without any pre-segmentation, the newly introduced LLE constraint is particularly useful and effective when there are multiple non-coherent and non-rigid local deformations (i.e, the CPD assumption may be violated). We have derived the EM algorithm for the ML optimization constrained with both CPD and LLE terms, leading to the new GLTP algorithm. Experimental results on 2D and 3D examples show its accuracy and robustness in the presence of outliers and noise, especially in the case of highly-articulated non-rigid transformation.