Multilevel Optimization for Registration of Deformable Point Clouds

Handling deformation is one of the biggest challenges associated with point cloud registration. When deformation happens due to the motion of an animated object which actively changes its location and general shape, registration of two instances of the same object turns out to be a challenging task. The focus of this work is to address the problem by leveraging the complementary attributes of local and global geometric structures of the point clouds. We define an energy function which consists of local and global terms, as well as a semi-local term to model the intermediate level geometry of the point cloud. The local energy estimates the transformation parameters at the lowest level by assuming a reduced deformation model. The parameters are estimated in a closed form solution, which are then used to assign the initial probability of a stochastic model working at the intermediate level. The global energy term estimates the overall transformation parameters by minimizing a nonlinear least square function via Gauss-Newton optimization framework. The total energy is optimized in a block coordinate descent fashion, updating one term at a time while keeping others constant. Experiments on three publicly available datasets show that the method performs significantly better than several state-of-the-art algorithms in registering pairwise point cloud data.