统一的数字几何处理框架

随着三维几何模型在工业界的广泛应用，处理几信号的算法变得越来越重要。尽管近几年数字几何处理研究有了很大的进展，仍然缺乏一个类似于数字图像处理的统一解决方案。该文提出了任意网格的数字信号处理框架，很好地满足了这一需求。该框架的核心思想是通过为任意网格模型构造一个全局球面（或平面）参数化，把模型的所有属性转化为定义在球面（或平面）上的信号，然后采用球面（或平面）正交分析工具对这些信号做分析处理。在这两个框架下，所有的数字图像处理技术都可以被扩展到网格模型。该文还给出了包括滤波、多分辨率编辑和压缩在内的几种典型应用的实现方法和试验结果。

A Unified Framework for Digital Geometry Processing

With the increasing use of 3D geometry in industry, algorithms processing geometric signals become more and more important. Despite the promising recent progress of digital geometry processing, it still lacks a unified solution to address all issues of geometry like digital image processing. With solid theoretic foundation, the framework for digital signal processing over arbitrary meshes presented in this paper meets this requirement. The key idea of the framework is to construct global spherical (or planar) parameterizations for meshes, transform all attributes of meshes into spherical (or planar) signals and use spherical (or planar) orthonormal analysis tool to process these signals. With the framework, all image processing techniques can be extended to 3D meshes. This paper also describes how to perform signal filtering, multi resolution editing and geometry compression and gives some experimental results.