Scalable and Differentiable Point-Cloud Registration Using Maximum Mean Discrepancy

• URL: http://arxiv.org/abs/2606.27818v1
• Date: Fri, 26 Jun 2026 07:59:30 GMT
• Title: Scalable and Differentiable Point-Cloud Registration Using Maximum Mean Discrepancy
• Abstract summary: MMD-Reg is a correspondence-free approach to point-cloud registration that is differentiable and has linear computational complexity in the number of points.<n>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.
• Score: 9.317249642627058
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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