A robust inlier identification algorithm for point cloud registration via \mathbf{\ell_0} -minimization

Correspondences in point cloud registration are prone to outliers, significantly reducing registration accuracy and highlighting the need for precise inlier identification. In this paper, we propose a robust inlier identification algorithm for point cloud registration by reformulating the conventional registration problem as an alignment error \ell_0 -minimization problem. The \ell_0 -minimization problem is formulated for each local set, where those local sets are built on a compatibility graph of input correspondences. To resolve the \ell_0 -minimization, we develop a novel two-stage decoupling strategy, which first decouples the alignment error into a rotation fitting error and a translation fitting error. Second, null-space matrices are employed to decouple inlier identification from the estimation of rotation and translation respectively, thereby applying Bayesian theory to \ell_0 -minimization problems and solving for fitting errors.