论文标题
频谱形状的总变化处理：理论和应用
Spectral Total-Variation Processing of Shapes: Theory and Applications
论文作者
论文摘要
我们介绍了非欧亚人参数化表面上的总变化（TV）的分析，这是3D图形中使用的形状的自然表示。我们的工作解释了形状光谱电视的最新实验发现[Fumero等，2020]和自适应各向异性光谱电视[Biton and Gilboa，2022]。通过表征表面上的电视特征函数来得出一种从平面到表面的概括凸度的新方法。发现电视，区域，特征值，本征及其不连续性之间的关系。此外，我们扩展了形状光谱电视工具包，以包括通过平滑和夸张的过滤器证明的多功能零均匀流。最后但并非最不重要的一点是，我们提出了第一种基于电视的形状变形方法，其特征是沿几何瓶颈变形。我们表明这些瓶颈与征税不连续性保持一致。这项研究在表面上及其在3D图形中的应用中推进了光谱电视领域，从而提供了形状过滤和变形的新观点。
We present an analysis of total-variation (TV) on non-Euclidean parameterized surfaces, a natural representation of the shapes used in 3D graphics. Our work explains recent experimental findings in shape spectral TV [Fumero et al., 2020] and adaptive anisotropic spectral TV [Biton and Gilboa, 2022]. A new way to generalize set convexity from the plane to surfaces is derived by characterizing the TV eigenfunctions on surfaces. Relationships between TV, area, eigenvalue, eigenfunctions and their discontinuities are discovered. Further, we expand the shape spectral TV toolkit to include versatile zero-homogeneous flows demonstrated through smoothing and exaggerating filters. Last but not least, we propose the first TV-based method for shape deformation, characterized by deformations along geometrical bottlenecks. We show these bottlenecks to be aligned with eigenfunction discontinuities. This research advances the field of spectral TV on surfaces and its application in 3D graphics, offering new perspectives for shape filtering and deformation.
