体函数映射
Volumetric Functional Maps
把 functional maps 从曲面推广到体 Laplace 算子的特征函数空间，为体数据（四面体网格、医学体）之间的对应与信号迁移提供了可复用的谱域工具；做形状匹配时引入体谱还能提升纯曲面谱方法的精度。
原文依据 extending for the first time the functional maps framework from the surface to the volumetric setting
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论三维形状之间的体对应计算是医学与工业应用中的重要工具。本文为谱体映射开辟了道路，首次将函数映射框架从曲面推广到体设置。我们表明，体 Laplace 算子的特征函数定义了一个适合高质量信号迁移的函数空间。我们还试验了多种编辑该函数空间的技术，并将其移植到体域。我们在新的体数据集以及成熟曲面数据集的四面体化版本上验证了本方法，并展示了涉及离散与连续信号映射的实际应用，包括分割迁移、网格连通性迁移和实体纹理。最后，我们表明考虑体谱能大幅提升曲面间经典形状匹配任务的精度，持续优于仅使用曲面的现有谱方法。
英文原文摘要 1042 字符
The computation of volumetric correspondences between 3D shapes is a prominent tool for medical and industrial applications. In this work, we pave the way for spectral volume mapping, extending for the first time the functional maps framework from the surface to the volumetric setting. We show that the eigenfunctions of the volumetric Laplace operator define a functional space that is suitable for high-quality signal transfer. We also experiment with various techniques that edit this functional space, porting them to volume domains. We validate our method on novel volumetric datasets and on tetrahedralizations of well-established surface datasets, also showcasing practical applications involving both discrete and continuous signal mapping, for segmentation transfer, mesh connectivity transfer, and solid texturing. Last but not least, we show that considering the volumetric spectrum greatly improves the accuracy for classical shape matching tasks among surfaces, consistently outperforming existing surface-only spectral methods.