arXiv:2606.16672cs.CV2026-06

用熵正则化最优传输改进点云配准,自动处理异常值和部分重叠。

Sinkhorn-CPD: Robust point cloud registration via unbalanced entropic optimal transport

论文配图:Sinkhorn-CPD: Robust point cloud registration via unbalanced entropic optimal transport
图 1 · 摘自论文原文
  • 用双侧KL散度替代固定概率约束,实现双向异常值剔除。
  • 无需手动调温,方差参数自动引导对应关系从模糊到清晰。
  • 在合成数据与真实扫描数据上均达到当前最佳配准精度。

协同点漂移(CPD)因软对应关系和闭式参数更新被广泛用于刚性点云配准。然而,其目标侧边缘约束要求每个观测点(包括异常值)必须接收恰好单位概率质量,这在存在大量异常值或部分重叠时会降低配准精度。最优传输(OT)方法可通过非平衡形式处理缺失质量,但需人工调节退火策略。本文提出Sinkhorn-CPD,将CPD的目标侧边缘约束替换为双侧Kullback-Leibler惩罚,允许算法在两侧丢弃异常值。该公式转化为完全非平衡的熵正则最优传输问题,可由广义Sinkhorn迭代高效求解。同时,该方法保留了CPD的闭式Procrustes与方差更新。其中方差σ²充当熵正则化参数,自动实现从模糊到尖锐对应关系的退火过程,无需手动调节温度。在合成数据、跨类别及扫描到CAD基准测试中,Sinkhorn-CPD均实现最先进精度,并对异常值和部分重叠具有强鲁棒性。

原文摘要 · Abstract (English)

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.

点云配准最优传输鲁棒性熵正则

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