MDND：基于不可微细化的无监督形状对应学习
MDND: Unsupervised Learning Guided by Non-Differentiable Refinement for Shape Correspondence
中文总结 AI 辅助
研究针对形状对应中深度功能映射框架受限于端到端可微性的问题，提出MDND范式，采用双分支架构，通过一致性损失进行无监督训练，能生成稳健对应，在非等距变形和拓扑噪声形状上表现出色，创造了新的先进水平。
中文摘要 AI 辅助
用于形状对应的深度功能映射框架（DFM）很强大，但因依赖端到端可微性而受限。该限制阻碍了高精度不可微细化技术的整合，限制了整体性能。为克服此问题，我们引入MDND，一种基于合并可微和不可微组件原理的新型DFM范式。它采用双分支架构，不可微细化分支利用多尺度迭代求解器生成稳健对应作为目标，可微分支从特征预测对应。通过一致性损失端到端无监督训练，迫使可微分支从不可微分支的结果学习。实验表明MDND创造了新的先进水平，在非等距变形和拓扑噪声形状上表现出强大的鲁棒性。
英文摘要
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.
