Coherent Point Drift (CPD) is widely used for rigid point cloud registration because of its soft correspondences and closed-form parameter updates. However, CPD's target-side marginal constraint forces every observation, including outliers, to receive exactly unit probability mass. This assumption degrades registration accuracy under heavy outliers and partial overlap. Optimal transport (OT) methods can handle missing mass through unbalanced formulations, but require hand-tuned annealing schedules. In this paper, we propose Sinkhorn-CPD, which replaces CPD's target-side marginal constraint with dual Kullback-Leibler penalties, allowing the algorithm to discard outliers on both sides. The resulting formulation is a fully unbalanced entropic optimal transport problem, which can be efficiently solved by generalized Sinkhorn iterations. Moreover, Sinkhorn-CPD preserves the closed-form Procrustes and variance updates of CPD. In our method, the variance sigma^2 plays the role of the entropic regularization parameter, which induces an automatic annealing schedule from diffuse to sharp correspondences without manual temperature tuning. Experiments on synthetic, cross-category, and scan-to-CAD benchmarks show that Sinkhorn-CPD achieves state-of-the-art accuracy, with strong robustness to outliers and partial overlap.

翻译：相干点漂移（CPD）因具有软对应关系与闭合形式参数更新而被广泛用于刚体点云配准。然而，CPD的目标侧边缘约束迫使每个观测点（包括离群点）必须精确接收单位概率质量。在存在严重离群点和部分重叠情况下，这一假设会降低配准精度。最优传输（OT）方法虽可通过非平衡形式处理缺失质量，但需人工调节退火调度策略。本文提出Sinkhorn-CPD，将CPD的目标侧边缘约束替换为双重Kullback-Leibler惩罚项，使算法能够丢弃两侧离群点。由此得到的公式是完全非平衡熵最优传输问题，可通过广义Sinkhorn迭代高效求解。此外，Sinkhorn-CPD保留了CPD中Procrustes分析与方差更新的闭合形式。在我们方法中，方差σ²扮演熵正则化参数的角色，自动生成从弥散到尖锐对应关系的退火调度策略，无需手动调节温度参数。在合成数据、跨类别数据及扫描件到CAD数据的基准测试中，Sinkhorn-CPD取得了最先进的配准精度，并对离群点与部分重叠具有强鲁棒性。