cs.CVMar 19, 2026

Unsupervised Contrastive Learning for Efficient and Robust Spectral Shape Matching

Authors: Feifan Luo, Hongyang Chen

Organizations: College of Computer Science and Technology, Zhejiang University, Hangzhou 310027, China · Research Center for Data Hub and Security, Zhejiang Lab, Hangzhou 311121, China

Read PDF
Ask AI
Cite

Copy citation

DOINot available for this paper

Abstract

Estimating correspondences between pairs of non-rigid deformable 3D shapes remains a significant challenge in computer vision and graphics. While deep functional map methods have become the go-to solution for addressing this problem, they primarily focus on optimizing pointwise and functional maps either individually or jointly, rather than directly enhancing feature representations in the embedding space, which often results in inadequate feature quality and suboptimal matching performance. Furthermore, these approaches heavily rely on traditional functional map techniques, such as time-consuming functional map solvers, which incur substantial computational costs. In this work, we introduce, for the first time, a novel unsupervised contrastive learning-based approach for efficient and robust 3D shape matching. We begin by presenting an unsupervised contrastive learning framework that promotes feature learning by maximizing consistency within positive similarity pairs and minimizing it within negative similarity pairs, thereby improving both the consistency and discriminability of the learned features.We then design a significantly simplified functional map learning architecture that eliminates the need for computationally expensive functional map solvers and multiple auxiliary functional map losses, greatly enhancing computational efficiency. By integrating these two components into a unified two-branch pipeline, our method achieves state-of-the-art performance in both accuracy and efficiency. Extensive experiments demonstrate that our approach is not only computationally efficient but also outperforms current state-of-the-art methods across various challenging benchmarks, including near-isometric, non-isometric, and topologically inconsistent scenarios, even surpassing supervised techniques.

Figures & tables

 ProFUnsupWoSOl
FMNet✗✗✗-
GeomFmaps✗✗✗-
SRFeat✓✗✓-
DUO-FMNet✗✓✗✗
AttentiveFMaps✗✓✗✗
RFMNet✗✓✓✓
Table 1: Method comparison. Our method is the first unsupervised contrastive learning approach specifically for non-rigid deformable 3D shape matching, combining a distinctive set of properties that enhance its performance. Where ProF: Pro mote f eatures in the embedding space. Unsup: Full unsup ervised. WoS: W ith o ut functional map s olver. Ol: O nly single unsupervised functional map l oss.
Figure 1: A visual example illustrating the similarity score SXY\mathbf{S}_{\mathcal{XY}} , the positive similarity pair SXY+\mathbf{S}^{+}_{\mathcal{XY}} , and the negative similarity pair SXY−\mathbf{S}^{-}_{\mathcal{XY}} .
Figure 2: A visual example highlighting the functionality of two contrastive losses. The Euclidean distance between the feature of different points x1x_{1} on shape X\mathcal{X} , and y0y_{0} , y1y_{1} on shape Y\mathcal{Y} , to the source point x0x_{0} is computed, where hotter/colder colors mean smaller/larger distances.
Figure 3: An overview of our method. (1) Feature Extraction: Learned features FX\mathbf{F}_{\mathcal{X}} and FY\mathbf{F}_{\mathcal{Y}} are extracted from shapes X\mathcal{X} and Y\mathcal{Y} , respectively. (2) Unsupervised Contrastive Learning Branch: The learned features are used to generate positive and negative similarity pairs SXY+\mathbf{S}_{\mathcal{XY}}^{+} , SXY−\mathbf{S}_{\mathcal{XY}}^{-} , SXX−\mathbf{S}_{\mathcal{XX}}^{-} via the hybrid similarity generator. Two unsupervised contrastive losses Eq. ( 11 ) and Eq. ( 15 ) are then applied for feature enhancement. (3) Simplified Functional Map Branch: The differentiable pointwise map ΠXY{\Pi}_{\mathcal{XY}} is computed using the softmax operator Eq. ( 16 ), and the functional map CYX{\mathbf{C}}_{\mathcal{YX}} is calculated via spectral basis projection Eq. ( 17 ). A functional loss Eq. ( 18 ) is constructed to supervise both pointwise and functional map learning.
TrainFSFSSMALDT4D-H
TestFSS19FSS19F_aS_aF_aS_aintra-classinter-class
 Axiomatic Methods
ZoomOut6.17.5-6.17.5-8.715.08.715.047.74.029.0
SmoothShells2.54.7-2.54.7-5.45.05.45.034.91.16.3
DiscreteOp5.613.1-5.613.1-6.214.66.214.636.13.627.6
MWP3.14.1-3.14.1-8.28.78.28.720.91.725.4
Table 2: Evaluating the matching results across various benchmarks, including near-isometric shape matching, cross-dataset generalization, anisotropic meshing, and non-isometric shape matching, respectively. The numbers in the table are mean geodesic errors ( ×100\times 100 ). Bold : Best. Underline : Runner-up.
Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

 TOPKIDSFully intrinsic
Axiomatic Methods
ZoomOut33.7✓
DiscreteOp35.5✓
SmoothShells11.8✗
Unsupervised Methods
UnsupFMNet38.5✓
Appendix
Table 3: Topological noise on TOPKIDS ( Lähner et al. 2016 ) . The table presents the mean geodesic errors ( ×100\times 100 ). Bold : Best. Underline : Runner-up.
Figure 4: Comparisons with other methods on shape matching with topological noise ( Lähner et al. 2016 ) . Our results, with smoother and more accurate texture distributions, illustrate that our approach is more robust to topological noise compared to existing methods
Figure 5: Runtime comparison with different numbers of vertices. Left: Average training time per method (100 iterations). Right: Average inference time per method (100 shape pairs), where ULRSSM(+TTA) runtime (black line) is plotted against the right-hand axis due to its exceptional magnitude ( ≥\geq 50× longer than other methods), the remaining competing approaches are scaled against the left-hand axis. Our method achieves best performance
TrainFSSMAL
TestFS19SS19
pc=ps=10p_{c}=p_{s}=101.56.01.99.73.6
pc=ps=20p_{c}=p_{s}=201.56.21.98.23.7
pc=ps=30p_{c}=p_{s}=301.65.82.15.83.5
pc=ps=40p_{c}=p_{s}=401.65.02.16.33.8
pc=ps=50p_{c}=p_{s}=501.65.42.26.63.6
Appendix
Table 4: Parameter analysis on remeshed FAUST, SCAPE, SHREC’19, and SMAL, respectively.
 TOPKIDS
w.o LcrossL_{cross}17.7
w.o LselfL_{self}8.4
Ours7.6
Appendix
Table 5: Ablation study on TOPKIDS ( Lähner et al. 2016 ) dataset.
Figure 6: Comparisons of cross-dataset generalization performance with other methods. Top row: training on FAUST ( Ren et al. 2018 ) and testing on SHREC’19 ( Melzi et al. 2019a ) . Bottom row: Training on SCAPE ( Ren et al. 2018 ) and testing on SHREC’19. Our method exhibits fewer errors and less color distortion compared to other approaches, highlighting its robust performance.
Figure 7: Comparisons with other methods on the SMAL ( Zuffi et al. 2017 ) (top row) and DT4D-H ( Magnet et al. 2022 ) (bottom row) datasets. Our approach results in fewer errors and less texture distortion than other methods, demonstrating its superior performance for non-isometric shape matching.
More in this topic

Functional Maps

See all 12 papers

Explore similar work

CardsList
Mar 24, 2026

From Feature Learning to Spectral Basis Learning: A Unifying and Flexible Framework for Efficient and Robust Shape Matching

Shape matching is a fundamental task in computer graphics and vision, with deep functional maps becoming a prominent paradigm. However, existing methods primarily focus on learning informative feature representations by constraining pointwise and functional maps, while neglecting the optimization of the spectral basis-a critical component of the functional map pipeline. This oversight often leads to suboptimal matching results. Furthermore, many current approaches rely on conventional, time-consuming functional map solvers, incurring significant computational overhead. To bridge these gaps, we introduce Advanced Functional Maps, a framework that generalizes standard functional maps by replacing fixed basis functions with learnable ones, supported by rigorous theoretical guarantees. Specifically, the spectral basis is optimized through a set of learned inhibition functions. Building on this, we propose the first unsupervised spectral basis learning method for robust non-rigid 3D shape matching, enabling the joint, end-to-end optimization of feature extraction and basis functions. Our approach incorporates a novel heat diffusion module and an unsupervised loss function, alongside a streamlined architecture that bypasses expensive solvers and auxiliary losses. Extensive experiments demonstrate that our method significantly outperforms state-of-the-art feature-learning approaches, particularly in challenging non-isometric and topological noise scenarios, while maintaining high efficiency. Finally, we reveal that optimizing basis functions is equivalent to spectral convolution, where inhibition functions act as filters. This insight enables enhanced representations inspired by spectral graph networks, opening new avenues for future research. Our code is available at https://github.com/LuoFeifan77/Unsupervised-Spectral-Basis-Learning.

Feifan Luo, Hongyang Chen

College of Computer Science and Technology, Zhejiang University, China · Research Center for Computational Earth and Space Science, Zhejiang Lab, China

Functional MapsNon-Rigid Shape CorrespondenceUnsupervised Representation Learning
AskPDF
Jun 29, 2026

Hyper-Network Neural Functional Maps for Unsupervised Robust 3D Shape Matching

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.

Dongliang Cao, Florian Bernard

University of Bonn, Germany

Functional MapsNon-Rigid Shape CorrespondenceHypernetworks3D Shape Matching
AskPDF
Jun 25, 2026

Coarse-to-Fine: A Hybrid Self-Supervised Method for Non-rigid 3D Shape Matching

Non-rigid 3D shape matching is a fundamental task in computer vision and graphics. In this paper, we propose a hybrid self-supervised method based on a coarse-to-fine strategy, which ensures consistency between the coarse mapping and the refined correspondence produced by our refinement module. The architecture features a dual-branch design, consisting of two symmetric functional map learning streams: one based on the Laplacian basis and the other utilizing the elastic basis. Extensive experiments show that our approach not only maintains computational efficiency, but also achieves state-of-the-art performance across a variety of challenging scenarios, including non-isometric deformations and topological noise. Finally, we rigorously demonstrate that contrastive energies promote feature discrimination. Furthermore, integrating these energies with existing methods yields consistent improvements, validating the overall efficacy of our approach. Our code is available at https://github.com/LuoFeifan77/Coarse-to-Fine-Hybrid-Self-Supervised-Matching.

Feifan Luo, Ting Li, Zhao Li +1

Zhejiang University, China · Zhejiang Lab, China · Wenzhou University of Technology, China

Self-Supervised LearningFunctional MapsNon-Rigid Shape Correspondence3D Shape Matching
AskPDF