A robust non-rigid point set registration method based on asymmetric gaussian representation

• An asymmetric Gaussian representation based method for point set registration.
• A robust estimator (L2E) is used to estimate the transformation in RKHS.
• Low-rank kernel matrix approximation trick to reduce the computational complexity.

Point set registration problem confronts with the challenge of large degree of degradations, such as deformation, noise, occlusion and outlier. In this paper, we present a novel robust method for non-rigid point set registration, and it includes four important parts are as follows: First, we used a mixture of asymmetric Gaussian model (MoAG) Kato et al. (2002) [1], a new probability model which can capture spatially asymmetric distributions, to represent each point set. Second, based on the representation of point set by MoAG, we used soft assignment technique to recover the correspondences, and correlation-based method to estimate the transformation parameters between two point sets. Point set registration is formulated as an optimization problem. Third, we solved the optimization problem under regularization theory in a feature space, i.e., Reproducing Kernel Hilbert Space (RKHS). Finally, we chose control points to build a kernel using low-rank kernel matrix approximation. Thus the computational complexity can be reduced down to O(N) approximately. Experimental results on 2D, 3D non-rigid point set, and real image registration demonstrate that our method is robust to a large degree of degradations, and it outperforms several state-of-the-art methods in most tested scenarios.