Efficiently finding optimal correspondences between point clouds is crucial for solving both rigid and non-rigid point cloud registration problems. Existing methods often rely on geometric or semantic feature embedding to establish correspondences and estimate transformations or flow fields. Recently, state-of-the-art methods have employed RAFT-like iterative updates to refine the solution. However, these methods have certain limitations. Firstly, their iterative refinement design lacks transparency, and their iterative updates follow a fixed path during the refinement process, which can lead to suboptimal results. Secondly, these methods overlook the importance of refining or optimizing correspondences (or matching matrices) as a precursor to solving transformations or flow fields. They typically compute candidate correspondences based on distances in the point feature space. However, they only project the candidate matching matrix into some matrix space once with Sinkhorn or dual softmax operations to obtain final correspondences. This one-shot projected matching matrix may be far from the globally optimal one, and these approaches do not consider the distribution of the target matching matrix. In this paper, we propose a novel approach that exploits the Denoising Diffusion Model to predict a searching gradient for the optimal matching matrix within the Doubly Stochastic Matrix Space. During the reverse denoising process, our method iteratively searches for better solutions along this denoising gradient, which points towards the maximum likelihood direction of the target matching matrix. Our method offers flexibility by allowing the search to start from any initial matching matrix provided by the online backbone or white noise. Experimental evaluations on the 3DMatch/3DLoMatch and 4DMatch/4DLoMatch datasets demonstrate the effectiveness of our newly designed framework.

翻译：高效寻找点云间的最优对应关系是解决刚性与非刚性点云配准问题的关键。现有方法通常依赖几何或语义特征嵌入来建立对应关系并估计变换场或流场。近期，最先进方法采用类似RAFT的迭代更新策略进行解优化。然而，这些方法存在以下局限：首先，其迭代优化设计缺乏透明度，且在优化过程中遵循固定路径进行迭代更新，易导致次优结果；其次，这些方法忽略了在求解变换场或流场前优化对应关系（或匹配矩阵）的重要性。它们通常基于点特征空间中的距离计算候选对应关系，但仅通过Sinkhorn或双softmax操作对候选匹配矩阵进行一次投影至特定矩阵空间以获取最终对应关系。这种单次投影得到的匹配矩阵可能与全局最优解偏差较大，且此类方法未考虑目标匹配矩阵的分布特性。本文提出一种新颖方法，利用去噪扩散模型在双随机矩阵空间中预测最优匹配矩阵的搜索梯度。在反向去噪过程中，本方法沿指向目标匹配矩阵最大似然方向的去噪梯度迭代搜索更优解。该方法支持从在线主干网络提供的任意初始匹配矩阵或白噪声开始搜索，具有灵活适应性。在3DMatch/3DLoMatch与4DMatch/4DLoMatch数据集上的实验评估验证了本框架的有效性。