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.

翻译：深度功能映射框架被广泛应用于三维形状匹配。然而，现有的大多数深度功能映射方法无法在特定匹配场景中自适应地捕捉用于功能映射估计的重要频率信息，即缺乏\textit{频率感知能力}，导致在处理大变形形状匹配时性能不佳。为此，我们提出了一种新颖的无监督学习框架，称为深度频率感知功能映射，能够优雅地应对各种形状匹配场景。我们首先引入了一种称为谱滤波算子保持的通用约束来计算理想的功能映射，其中谱滤波算子编码了信息丰富的频率信息，并通过学习一组滤波函数来增强深度功能映射框架的频率感知能力。接着，我们直接将所提出的约束作为损失函数，同时监督功能映射、逐点映射和滤波函数的学习，其中滤波函数源自正交雅可比基，而基函数的系数是可学习参数。最后，我们开发了一种有效的细化策略来改进最终的逐点映射，该策略结合了我们的约束和学习到的滤波函数，从而在推理过程中产生更鲁棒和准确的对应关系。在多个数据集上的大量实验结果表明，我们的方法优于现有的最先进方法，特别是在具有非等距变形和不一致拓扑等挑战性数据集中表现尤为突出。