Scalable and Differentiable Point-Cloud Registration Using Maximum Mean Discrepancy

2026-06-26

AI Summary

This work addresses the challenge of point cloud registration by proposing the first differentiable method based on Maximum Mean Discrepancy (MMD) that operates without explicit correspondences and scales efficiently to large-scale data. By approximating MMD via random Fourier features, the registration problem is cast as a nonlinear least-squares optimization with linear computational complexity. Differentiability of the solution is ensured through the integration of the Levenberg–Marquardt algorithm with the implicit function theorem, enabling end-to-end training. The resulting method can be embedded as a differentiable optimization layer within neural networks, outperforming existing learning-based approaches in both supervised and unsupervised settings. When used standalone, it also surpasses state-of-the-art non-learning registration algorithms in terms of accuracy and scalability.

Abstract

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.

Problem

• point-cloud registration
• differentiable optimization
• scalability
• correspondence-free
• partial overlap

Innovation

• point-cloud registration
• Maximum Mean Discrepancy
• differentiable optimization
• random Fourier features
• correspondence-free