Establishing reliable correspondences is essential for registration tasks such as 3D and 2D3D registration. Existing methods commonly leverage geometric or semantic point features to generate potential correspondences. However, these features may face challenges such as large deformation, scale inconsistency, and ambiguous matching problems (e.g., symmetry). Additionally, many previous methods, which rely on single-pass prediction, may struggle with local minima in complex scenarios. To mitigate these challenges, we introduce a diffusion matching model for robust correspondence construction. Our approach treats correspondence estimation as a denoising diffusion process within the doubly stochastic matrix space, which gradually denoises (refines) a doubly stochastic matching matrix to the ground-truth one for high-quality correspondence estimation. It involves a forward diffusion process that gradually introduces Gaussian noise into the ground truth matching matrix and a reverse denoising process that iteratively refines the noisy matching matrix. In particular, the feature extraction from the backbone occurs only once during the inference phase. Our lightweight denoising module utilizes the same feature at each reverse sampling step. Evaluation of our method on both 3D and 2D3D registration tasks confirms its effectiveness. The code is available at https://github.com/wuqianliang/Diff-Reg.

翻译：在三维及二维-三维配准等任务中，建立可靠的对应关系至关重要。现有方法通常利用几何或语义点特征来生成潜在对应关系。然而，这些特征可能面临大形变、尺度不一致以及模糊匹配（如对称性）等挑战。此外，许多依赖单次预测的先前方法在复杂场景中可能陷入局部最优。为缓解这些问题，我们提出一种用于鲁棒对应关系构建的扩散匹配模型。该方法将对应关系估计视为双随机矩阵空间中的去噪扩散过程，通过逐步去噪（优化）将双随机匹配矩阵细化至真实匹配矩阵，从而实现高质量的对应关系估计。该过程包含前向扩散过程（逐步向真实匹配矩阵添加高斯噪声）和反向去噪过程（迭代优化含噪匹配矩阵）。特别地，在推理阶段，骨干网络的特征提取仅执行一次。我们设计的轻量化去噪模块在每次反向采样步骤中复用同一组特征。在三维及二维-三维配准任务上的实验评估验证了本方法的有效性。代码发布于 https://github.com/wuqianliang/Diff-Reg。