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.

A large number of 3D spectral descriptors have been proposed in the literature, which act as an essential component for 3D deformable shape matching and related applications. An outstanding descriptor should have desirable natures including high-level descriptive capacity, cheap storage, and robustness to a set of nuisances. It is, however, unclear which descriptors are more suitable for a particular application. This paper fills the gap by comprehensively evaluating nine state-of-the-art spectral descriptors on ten popular deformable shape datasets as well as perturbations such as mesh discretization, geometric noise, scale transformation, non-isometric setting, partiality, and topological noise. Our evaluated terms for a spectral descriptor cover four major concerns, i.e., distinctiveness, robustness, compactness, and computational efficiency. In the end, we present a summary of the overall performance and several interesting findings that can serve as guidance for the following researchers to construct a new spectral descriptor and choose an appropriate spectral feature in a particular application.

Traditional deep functional map frameworks are widely used for 3D shape matching; however, many methods fail to adaptively capture the relevant frequency information required for functional map estimation in complex scenarios, leading to poor performance, especially under significant deformations. To address these challenges, we propose a novel unsupervised learning-based framework, Deep Frequency Awareness Functional Maps (DFAFM), specifically designed to tackle diverse shape-matching problems. Our approach introduces the Spectral Filter Operator Preservation constraint, which ensures the preservation of critical frequency information. These constraints promote frequency awareness by learning a set of spectral filters and incorporating them as a loss function to jointly supervise the functional maps, pointwise maps, and spectral filters. The spectral filters are constructed using orthonormal Jacobi polynomials with learnable coefficients, enabling adaptive and efficient frequency representation. Furthermore, we propose a refinement strategy that leverages the learned spectral filters and constraints to enhance the accuracy of the final pointwise map. Extensive experiments conducted on multiple benchmark datasets demonstrate that our method outperforms state-of-the-art approaches, particularly in challenging scenarios involving non-isometric deformations and inconsistent topology.

The deployment of 5G New Radio in unlicensed spectrum is a promising solution to alleviate the spectrum crunch for cellular networks. With the openness of unlicensed spectrum, 5G New Radio Unlicensed (NR-U) will coexist with the incumbent Wi-Fi networks. It is therefore important to study how to maintain harmonious coexistence with the Wi-Fi network. To address this issue, this paper considers two alternative throughput optimization strategies under the 3GPP fairness by adjusting the access parameter: one is to maximize the total throughput of coexisting scenario, and the other is to maximize the throughput of NR-U network. It is shown that the throughput gain of both optimization strategies are related to the initial backoff window size and the network size of Wi-Fi. Moreover, the first strategy can maximize the total throughput yet it may be unfair to the NR-U network while the second strategy can maximize NR-U throughput yet may be harmful to the total throughput. In practical scenario where the IEEE 802.11 EDCA protocol is adopted in Wi-Fi, the performance of NR-U cannot be guaranteed when optimizing the total throughput, and thus optimizing the throughput of NR-U is suggested for fair coexistence.