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.
Creating photorealistic 3D assets requires bridging the appearance gap between real-world observations and synthetic models. A promising approach is to transfer visual attributes from real images onto synthetic 3D surfaces. Traditional methods struggle with resolution mismatch and the inherent discreteness of point correspondences. In contrast, resolution-robust functional maps enable smooth attribute propagation but rely on near-isometry assumptions and topological consistency. To address these limitations, we propose RealSkin, a self-supervised framework that performs correspondence optimization in a learned spectral domain, guided by spatial correspondences. We first introduce a spatial-guided registration algorithm to establish coarse correspondences under severe topological discrepancies. To relax strict isometric assumptions and handle partial correspondences, we further design a spectral-aware neural adjoint network that incorporates partial correspondences into a neural function space and models non-isometric residuals for correspondence refinement. Experimental results demonstrate that our method achieves state-of-the-art performance on challenging real-to-synthetic scenarios. The code will be publicly released.
Functional maps are the cornerstone of recent non-rigid 3D shape matching methods due to their efficiency and performance. However, existing methods struggle with challenging scenarios, such as partiality, topological noise, and raw point clouds. A primary bottleneck is that significant intrinsic distortion prevents truncated spectral bases from being accurately aligned via linear transformations (i.e., functional maps). To address this, we introduce a hyper-network that predicts non-linear neural functional maps (NFM), learned in an unsupervised manner, to better align spectral bases. Specifically, we model the NFM as an MLP with skip-connection to refine standard FM and employ a hyper-network to predict its weights, conditioned on standard FM. Our framework is trained using a novel unsupervised spectral alignment loss. Experiments demonstrate that our approach can be seamlessly integrated into state-of-the-art unsupervised deep functional map pipelines, substantially improving matching accuracy in demanding scenarios.