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 an operator admits a generalized notion of spectral decomposition, yielding a convenient 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 through multiple applications in graphics, ranging from surface and signal denoising to enhancement, detail transfer, and cubic stylization.

中文翻译：

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通过 TV 变换进行非线性光谱几何处理

我们基于与总变差泛函相关的非线性算子的推导，引入了一种用于数字几何处理的新型计算框架。这样的算子承认谱分解的广义概念，产生类似于基于拉普拉斯的方法的方便的多尺度表示，同时避免了这种技术典型的不希望的过度平滑效应。我们的方法需要准确，细节保留3D 形状几何的分解和操作，同时采用一种特别直观的形式：非局部语义细节很好地分离到不同的波段，然后可以通过简单的线性步骤对其进行过滤和重新合成。我们的计算框架很灵活，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。我们通过图形中的多种应用展示我们的方法，从表面和信号去噪到增强、细节传输和三次风格化。