A Unified Robust Coordinate Measurement Framework for Point Cloud Registration via Maximum Correntropy Criterion with Variable Center

Recently, estimating coordinate measurement transformation parameters has been a core step in three-dimensional (3D) point cloud registration between the source and target point clouds. The transformation model is commonly represented in practical applications by either a rigid model or a similarity model. However, most existing studies treat these two models separately, while a unified and robust formulation remains insufficiently explored. In addition, many conventional transformation estimation methods are developed under least squares (LS)-based criteria. They can provide reliable results when the correspondences (common points) are accurate, and the errors are close to Gaussian noise, but their performance may degrade seriously when mismatched correspondences or gross errors are present. To address these issues, this paper proposes a unified robust coordinate transformation framework using the maximum correntropy criterion with variable center (MCCVC) for point cloud registration. The rigid and similarity transformation models are first formulated within a general 12-parameter coordinate transformation framework, where six equality constraints are imposed for the rigid transformation and five for the similarity transformation. Building on this unified constrained formulation, the Laplacian kernel-based MCCVC objective function is constructed to reduce the influence of outliers. The kernel center, kernel bandwidth, and transformation parameters are estimated through an alternating optimization strategy. Simulated experiments on rigid and similarity transformations, together with real-data tests on publicly available point cloud datasets, demonstrate that the proposed MCCVC framework achieves higher registration accuracy and greater robustness than the compared methods.