Efficient, General Point Cloud Registration with Kernel Feature Maps

This paper proposes a novel and efficient point cloud registration algorithm based on the kernel-induced feature map. Point clouds are mapped to a high-dimensional (Hilbert) feature space, where they are modeled with Gaussian distributions. A rigid transformation is first computed in feature space by elegantly computing and aligning a small number of eigenvectors with kernel PCA (KPCA) and is then projected back to 3D space by minimizing a consistency error. SE(3) on-manifold optimization is employed to search for the optimal rotation and translation. This is very efficient; once the object-specific eigenvectors have been computed, registration is performed in linear time. Because of the generality of KPCA and SE(N) on-manifold method, the proposed algorithm can be easily extended to registration in any number of dimensions (although we only focus on 3D case). The experimental results show that the proposed algorithm is comparably accurate but much faster than state-of-the-art methods in various challenging registration tasks.