Point cloud registration is a central theme in computer vision, with alignment algorithms continuously improving for greater robustness. Commonly used methods evaluate Euclidean distances between point clouds and minimize an objective function, such as Root Mean Square Error (RMSE). However, these approaches are most effective when the point clouds are well-prealigned and issues such as differences in density, noise, holes, and limited overlap can compromise the results. Traditional methods, such as Iterative Closest Point (ICP), require choosing one point cloud as fixed, since Euclidean distances lack commutativity. When only one point cloud has issues, adjustments can be made, but in real scenarios, both point clouds may be affected, often necessitating preprocessing. The authors introduce a novel differential entropy-based metric, designed to serve as the objective function within an optimization framework for fine rigid pairwise 3D point cloud registration, denoted as Iterative Differential Entropy Minimization (IDEM). This metric does not depend on the choice of a fixed point cloud and, during transformations, reveals a clear minimum corresponding to the best alignment. Multiple case studies are conducted, and the results are compared with those obtained using RMSE, Chamfer distance, and Hausdorff distance. The proposed metric proves effective even with density differences, noise, holes, and partial overlap, where RMSE does not always yield optimal alignment.

翻译：点云配准是计算机视觉领域的核心课题，其配准算法正不断提升以增强鲁棒性。常用方法通过评估点云间的欧氏距离并最小化目标函数（如均方根误差）来实现配准。然而，这些方法在点云已良好预配准时效果最佳，而密度差异、噪声、孔洞及有限重叠等问题可能影响结果。传统方法如迭代最近点算法需要指定固定点云，因为欧氏距离不具备交换性。当仅单一点云存在缺陷时可通过调整处理，但在实际场景中双方点云常同时存在问题，往往需要进行预处理。本文提出一种基于微分熵的新型度量标准，旨在作为精细刚性成对三维点云配准优化框架中的目标函数，称为迭代微分熵最小化方法。该度量不依赖于固定点云的选择，且在变换过程中能呈现明确的最小值对应最佳配准状态。通过多组案例研究，将所得结果与使用均方根误差、倒角距离和豪斯多夫距离的方法进行对比。实验表明，即使在存在密度差异、噪声、孔洞和部分重叠的情况下，所提出的度量方法仍能保持有效性，而均方根误差在此类场景中并不总能实现最优配准。