SHC: soft-hard correspondences framework for simplifying point cloud registration

Point cloud registration is a multifaceted problem that involves a series of procedures. Many deep learning methods employ complex structured networks to achieve robust registration performance. However, these intricate structures can amplify the challenges of network learning and impede gradient propagation. To address this concern, the soft-hard correspondence (SHC) framework is introduced in the present paper to streamline the registration problem. The framework encompasses two modes: the hard correspondence mode, which transforms the registration problem into a correspondence pair search problem, and the soft correspondence mode, which addresses this new problem. The simplification of the problem provides two advantages. First, it eliminates the need for intermediate operations that lead to error fusion and counteraction, thereby improving gradient propagation. Second, a perfect solution is not necessary to solve the new problem, since accurate registration results can be achieved even in the presence of errors in the found pairs. The experimental results demonstrate that SHC successfully simplifies the registration problem. It achieves performance comparable to complex networks using a simple network and can achieve zero error on datasets with perfect correspondence pairs.