MDND: Unsupervised Learning Guided by Non-Differentiable Refinement for Shape Correspondence
Qinsong Li, Jing Meng, Haibo Wang, Shengjun Liu
Abstract
Deep functional map frameworks (DFM) for shape correspondence are powerful, yet fundamentally limited by their reliance on end-to-end differentiability. This constraint prevents the integration of highly accurate, non-differentiable refinement techniques, capping their overall performance, especially on challenging non-isometric shapes. To overcome this, we introduce MDND, a novel DFM paradigm built on the principle of merging differentiable and non-differentiable components. Our framework facilitates unsupervised learning guided by an internal, non-differentiable refinement. Specifically, MDND employs a dual-branch architecture: a non-differentiable refinement branch leverages a novel, multiscale iterative solver to produce highly robust correspondences, acting as a refined target. Concurrently, a fully differentiable branch learns to predict correspondences from features. The entire system is trained end-to-end without supervision by enforcing a consistency loss that compels the differentiable branch to learn from the superior, refined results of the non-differentiable branch. Extensive experiments show that MDND sets a new state-of-the-art, demonstrating remarkable robustness on shapes with non-isometric deformations and topological noise.
Topics
Classified with taxonomy v2 on Sat, 5 Sept 2026.