用最大均值差异实现可微点云配准，计算快且适合端到端训练。
Scalable and Differentiable Point-Cloud Registration Using Maximum Mean Discrepancy
- 基于最大均值差异与随机傅里叶特征建模配准问题。
- 线性复杂度下实现高精度配准，支持弱初始对齐和部分重叠。
- 可嵌入神经网络作为可微层，适用于监督与无监督学习场景。
我们提出MMD-Reg，一种新型无对应关系的点云配准方法，具备可微性和线性计算复杂度。该方法基于最大均值差异（Maximum Mean Discrepancy）构建非线性最小二乘问题，并利用随机傅里叶特征进行近似。目标函数可通过标准优化方法（如Levenberg-Marquardt）高效求解，且解具有可微性，得益于隐函数定理。这使得MMD-Reg可作为可微优化层嵌入端到端可训练模型中，支持在弱初始对齐和部分重叠等挑战性条件下完成配准。我们通过将该层与集合变换器结合，在监督与无监督设置下进行训练，并与近期基于学习的方法进行对比。此外，还独立评估了MMD-Reg的精度与可扩展性，对比了广泛使用的非学习型配准方法。
原文摘要 · Abstract (English)
We present MMD-Reg, a novel correspondence-free approach to point-cloud registration that is differentiable and has linear computational complexity in the number of points. We model registration as a nonlinear least-squares problem based on the Maximum Mean Discrepancy, approximated using random Fourier features. The resulting objective can be solved efficiently with standard methods such as Levenberg-Marquardt, and the solution is differentiable via the implicit function theorem. This allows MMD-Reg to be used as a differentiable optimization layer within end-to-end trainable models, supporting registration under challenging conditions such as poor initial alignment and partial overlap. We demonstrate this Neural MMD-Reg formulation by integrating the layer with a set transformer, training the resulting model in supervised and unsupervised settings, and comparing its performance against recent learning-based methods. We also evaluate standalone MMD-Reg, comparing its accuracy and scalability against widely used non-learning-based registration methods.
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