Feifan Luo

Feifan Luo, Hongyang Chen

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

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.

Feifan Luo, Qinsong Li, Ling Hu et al.

Deep functional map frameworks are widely employed for 3D shape matching. However, most existing deep functional map methods cannot adaptively capture important frequency information for functional map estimation in specific matching scenarios, i.e., lacking \textit{frequency awareness}, resulting in poor performance when dealing with large deformable shape matching. To this end, we propose a novel unsupervised learning-based framework called Deep Frequency-Aware Functional Maps, which can gracefully cope with various shape matching scenarios. We first introduce a general constraint called Spectral Filter Operator Preservation to compute desirable functional maps, where the spectral filter operator encodes informative frequency information and can promote frequency awareness for deep functional map frameworks by learning a set of filter functions. Then, we directly utilize the proposed constraint as a loss function to supervise functional maps, pointwise maps, and filter functions simultaneously, where the filter functions are derived from the orthonormal Jacobi basis, and the coefficients of the basis are learnable parameters. Finally, we develop an effective refinement strategy to improve the final pointwise map, which incorporates our constraint and learned filter functions, leading to more robust and accurate correspondences during the inference process. Extensive experimental results on various datasets demonstrate that our approach outperforms the existing state-of-the-art methods, especially in challenging settings like datasets with non-isometric deformation and inconsistent topology.