论文标题
通过电视变换的非线性光谱几何处理
Nonlinear Spectral Geometry Processing via the TV Transform
论文作者
论文摘要
我们基于与总变异功能相关的非线性操作员的推导，为数字处理引入了新的计算框架。此类操作员承认了光谱分解的广义概念，产生了类似于基于拉普拉斯的方法的稀疏多尺度表示，同时避免了此类技术典型的不良过度光滑效果。我们的方法需要在采用特别直观的形式的同时，需要准确，详细的保护分解和操纵：非本地语义细节被很好地分成不同的频段，然后可以通过直接线性步骤进行过滤并重新合成。我们的计算框架是灵活的，可以应用于各种信号，并且很容易适应不同的几何表示，包括三角形网格和点云。我们在图形中的多个应用程序中展示了我们的方法，从表面和信号降解到细节传输和立方样式。
We introduce a novel computational framework for digital geometry processing, based upon the derivation of a nonlinear operator associated to the total variation functional. Such operator admits a generalized notion of spectral decomposition, yielding a sparse multiscale representation akin to Laplacian-based methods, while at the same time avoiding undesirable over-smoothing effects typical of such techniques. Our approach entails accurate, detail-preserving decomposition and manipulation of 3D shape geometry while taking an especially intuitive form: non-local semantic details are well separated into different bands, which can then be filtered and re-synthesized with a straightforward linear step. Our computational framework is flexible, can be applied to a variety of signals, and is easily adapted to different geometry representations, including triangle meshes and point clouds. We showcase our method throughout multiple applications in graphics, ranging from surface and signal denoising to detail transfer and cubic stylization.
