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

• URL: http://arxiv.org/abs/2603.23383v2
• Date: Wed, 25 Mar 2026 09:30:14 GMT
• Title: From Feature Learning to Spectral Basis Learning: A Unifying and Flexible Framework for Efficient and Robust Shape Matching
• Abstract summary: We introduce Advanced Functional Maps, a framework that generalizes standard functional maps by replacing fixed basis functions with learnable ones.<n>We propose the first unsupervised spectral basis learning method for robust non-rigid 3D shape matching.<n>Our approach incorporates a novel heat diffusion module and an unsupervised loss function, alongside a streamlined architecture that bypasses expensive solvers and auxiliary losses.
• Score: 35.320288409500314
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

Related papers

• Don't Fix the Basis -- Learn It: Spectral Representation with Adaptive Basis Learning for PDEs [0.2581652423269287]
  We propose Adaptive Basis Learning (ABLE), a framework that learns data-dependent spectral representations instead of relying on predefined bases.<n>ABLE constructs a spatially adaptive Parseval frame via a learned ancillary density, enabling the operator to act in a lifted spectral space.<n>Our results highlight that the data-driven choice of representation, rather than operator complexity alone, is a key bottleneck in neural operator design.
  arXiv  Detail & Related papers  (2026-05-11T12:20:57Z)
• Unsupervised Contrastive Learning for Efficient and Robust Spectral Shape Matching [35.320288409500314]
  Estimating correspondences between pairs of non-rigid deformable 3D shapes remains a significant challenge in computer vision and graphics.<n>We introduce, for the first time, a novel unsupervised contrastive learning-based approach for efficient and robust 3D shape matching.
  arXiv  Detail & Related papers  (2026-03-19T14:02:12Z)
• Outcome-Aware Spectral Feature Learning for Instrumental Variable Regression [37.76825470697479]
  We introduce Augmented Spectral Feature Learning, a framework that makes the feature learning process outcome-aware.<n>We provide a theoretical analysis of this framework and validate our approach on challenging benchmarks.
  arXiv  Detail & Related papers  (2025-11-30T14:54:03Z)
• DiffuMatch: Category-Agnostic Spectral Diffusion Priors for Robust Non-rigid Shape Matching [53.39693288324375]
  We show that both in-network regularization and functional map training can be replaced with data-driven methods.<n>We first train a generative model of functional maps in the spectral domain using score-based generative modeling.<n>We then exploit the resulting model to promote the structural properties of ground truth functional maps on new shape collections.
  arXiv  Detail & Related papers  (2025-07-31T16:44:54Z)
• A Refreshed Similarity-based Upsampler for Direct High-Ratio Feature Upsampling [54.05517338122698]
  A popular similarity-based feature upsampling pipeline has been proposed, which utilizes a high-resolution feature as guidance.<n>We propose an explicitly controllable query-key feature alignment from both semantic-aware and detail-aware perspectives.<n>We develop a fine-grained neighbor selection strategy on HR features, which is simple yet effective for alleviating mosaic artifacts.
  arXiv  Detail & Related papers  (2024-07-02T14:12:21Z)
• Deep Frequency-Aware Functional Maps for Robust Shape Matching [17.276162941967943]
  We propose a novel unsupervised learning-based framework called Deep Frequency-Aware Functional Maps. We first introduce a general constraint called Spectral Filter Operator Preservation to compute desirable functional maps. We then directly utilize the proposed constraint as a loss function to supervise functional maps, pointwise maps, and filter functions simultaneously.
  arXiv  Detail & Related papers  (2024-02-06T11:16:18Z)
• Understanding and Improving Features Learned in Deep Functional Maps [31.61255365182462]
  We show that features learned within deep functional map approaches can be used as point-wise descriptors across different shapes. We propose effective modifications to the standard deep functional map pipeline, which promote structural properties of learned features.
  arXiv  Detail & Related papers  (2023-03-29T08:32:16Z)
• Offline Reinforcement Learning with Differentiable Function Approximation is Provably Efficient [65.08966446962845]
  offline reinforcement learning, which aims at optimizing decision-making strategies with historical data, has been extensively applied in real-life applications. We take a step by considering offline reinforcement learning with differentiable function class approximation (DFA) Most importantly, we show offline differentiable function approximation is provably efficient by analyzing the pessimistic fitted Q-learning algorithm.
  arXiv  Detail & Related papers  (2022-10-03T07:59:42Z)
• Stabilizing Q-learning with Linear Architectures for Provably Efficient Learning [53.17258888552998]
  This work proposes an exploration variant of the basic $Q$-learning protocol with linear function approximation. We show that the performance of the algorithm degrades very gracefully under a novel and more permissive notion of approximation error.
  arXiv  Detail & Related papers  (2022-06-01T23:26:51Z)
• Functional Regularization for Reinforcement Learning via Learned Fourier Features [98.90474131452588]
  We propose a simple architecture for deep reinforcement learning by embedding inputs into a learned Fourier basis. We show that it improves the sample efficiency of both state-based and image-based RL.
  arXiv  Detail & Related papers  (2021-12-06T18:59:52Z)
• iffDetector: Inference-aware Feature Filtering for Object Detection [70.8678270164057]
  We introduce a generic Inference-aware Feature Filtering (IFF) module that can easily be combined with modern detectors. IFF performs closed-loop optimization by leveraging high-level semantics to enhance the convolutional features. IFF can be fused with CNN-based object detectors in a plug-and-play manner with negligible computational cost overhead.
  arXiv  Detail & Related papers  (2020-06-23T02:57:29Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.