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，处理几何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，在这些框架下，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。     

三维网格模型的图像化表示

为使三维网格模型能被GPU进行渲染,提出了一种适用于GPU的针对零亏格的三角网格模型的绘制框架.传统的方法生成几何图像一般是从原始网格逐步切割至平面域,但是这样会产生复杂接缝的问题.论文通过对参数化后的球面进行映射,从而间接生成几何图像,避免了对原始网格进行复杂的切割.首先,将已经球面参数化后的球面信息映射至立方体,立方体平铺开即构成一个二维几何图像;然后,将二维纹理信息传输至GPU,利用GPU来还原三角网格模型.此文采用OpenGL和CUDA相结合的方式来实现最终效果,实验结果表明该绘制框架是可行的,参数化效果和还原效果较好.     

适用于复杂三维网格模型的盲水印算法

提出一种基于奇异值分解的网格模型盲水印算法，只对网格顶点的几何数据进行处理，适用于任意拓扑结构的网格模型。奇异值分解在与网格模型几何数据局部统计特征相似的球面坐标映射方阵中进行，水印序列嵌入到方阵生成的奇异值序列中。实验结果表明，算法可抵抗平移、旋转、各向一致缩放攻击及顶点重排序攻击，对噪声攻击也具有一定的鲁棒性。     

一种任意三维实体网格模型的体积特征提取算法

体积在不同轴向上的分布是三维网格模型的重要几何特征。在分析三维模型数据结构的基础上，提出一种提取任意三维实体网格模型体积分布特征的算法。算法首先应用主元分析法确定模型的主轴方向，并将模型按主轴方向旋转至特定姿态，再以一组等距的平行平面从三个坐标轴方向对模型进行剖分处理，并利用平面简单多边形的带符号面积公式求取相应的截面面积，进而求得模型的沿不同轴向的体积分布特征。模型在三个坐标轴向上的体积分布描述了模型的几何特征。实验表明，算法程序运行稳定、快速，可用于提取具有任意几何和拓扑复杂性的各类实体模型的体积分布特征。     

三维几何信号经验模式分解及其应用

针对三维几何信号非线性、非平稳的特点,提出基于经验模式分解的三维几何信号处理方法。将信号球面参数化,映射到平面,进行均匀规则采样。对平面信号进行限领域的经验模式分解,得到各个内蕴模式图层。从图层信号得到不规则的原始映射信号,逆映射回三维几何模型信号。将该方法用于几何模型的光顺及增强处理,实验结果表明,该方法能够有效处理三维几何信号。     

基于奇异值分解的三维网格模型数字水印算法

针对三维网格模型的版权保护提出了一种新的基于奇异值分解(SVD)的数字水印算法。算法利用几何信号处理框架将三维几何信号转换成平面规则采样信号，再用SVD技术嵌入水印。实验结果表明，算法具有较好的透明性和鲁棒性。     

一种基于小波变换的三维网格模型水印算法

提出了一种基于小波变换的强壮三维网格模型数字水印算法。首先采用一种平面参数化算法将三维网格模型映射为二维参数网格，三维网格模型表面的几何信号相应转换为二维信号，然后采用一种自适应小波水印算法加入水印。实验结果显示该水印算法能够抵抗各种几何信号处理攻击。     

网格环境下基于OAI的数字图书馆互操作机制

现有数字图书馆（DLs）互操作方案，在实现大规模数字图书馆集成方面都存在一定的局限性。该文将网格技术与OAI-PMH框架相结合，提出了一个数字图书馆网格（DL Grid）互操作框架，并对网格环境下元数据资源的发现、采集、重组等关键问题进行了分析和设计，初步实现了在集成的元数据基础上数字图书馆信息的共享。     

凸组合球面参数化

针对具有单边界的三角网格或与球面同胚的零亏格封闭网格，提出一种基于球面向量线性凸组合的三维网格球面参数化方法．把参数域从平面凸区域扩展到球面凸区域，并把具有凸性的重心坐标纳入到参数化框架中，使得参数化具有保形性质且变形小，同时证明了该参数化方法的存在性和惟一性．整个算法简单可靠．     

一种三角网格的球面参数化算法和应用*

三维网格的参数化是数字几何处理中一个基本问题,在纹理映射、重新网格化和几何变形等许多图形处理中都有着非常重要的应用。在现有参数化方法的基础上,根据球面与平面参数化之间的差异,列出了一个关于角度的有效球面三角化的充要条件,使用LM算法通过对非线性优化问题的求解,得到具有期望目标的球面参数化结果。并介绍算法的应用,给出实例说明了算法有效性。     

Geometric signal compression

Compression of mesh attributes becomes a challenging problem due to the great need for efficient storage and fast transmission. This paper presents a novel geometric signal compression framework for all mesh attributes, including position coordinates, normal, color, texture, etc. Within this framework, mesh attributes are regarded as geometric signals defined on mesh surfaces. A planar parameterization algorithm is first proposed to map 3D meshes to 2D parametric meshes. Geometric signals are then transformed into 2D signals, which are sampled into 2D regular signals using an adaptive sampling method. The JPEG2000 standard for still image compression is employed to effectively encode these regular signals into compact bit-streams with high rate/distortion ratios. Experimental results demonstrate the great application potentials of this framework.     

3D surface filtering using spherical harmonics

This paper presents a novel approach for 3D surface filtering over two-manifold meshes. A robust spherical parameterization algorithm is proposed to transform the input surface into a spherical vector function/signal. This signal is then decomposed into frequency domain using spherical harmonic transforms. Finally, traditional filtering techniques are generalized to process such spherical signals in either the frequency or spatial domain. Our major contribution is the two-phase spherical parameterization algorithm, which can handle meshes with complex shapes by incorporating local parameterization into the progressive mesh. A number of experimental examples demonstrate the potential of our algorithm.     

Meshless methods for physics-based modeling and simulation of deformable models

As 3D digital photographic and scanning devices produce higher resolution images, acquired geometric data sets grow more complex in terms of the modeled objects’ size, geometry, and topology. As a consequence, point-sampled geometry is becoming ubiquitous in graphics and geometric information processing, and poses new challenges which have not been fully resolved by the state-of-art graphical techniques. In this paper, we address the challenges by proposing a meshless computational framework for dynamic modeling and simulation of solids and thin-shells represented as point samples. Our meshless framework can directly compute the elastic deformation and fracture propagation for any scanned point geometry, without the need of converting them to polygonal meshes or higher order spline representations. We address the necessary computational techniques, such as Moving Least Squares, Hierarchical Discretization, and Modal Warping, to effectively and efficiently compute the physical simulation in real-time. This meshless computational framework aims to bridge the gap between the point-sampled geometry with physics-based modeling and simulation governed by partial differential equations. Supported by the National Science Foundation (Grant Nos. CCF-0727098, IIS-0710819)     

GPU-accelerated blind and robust 3D mesh watermarking by geometry image

The prevalence of cheap and powerful consumer level graphics accelerated hardware introduces a significant growth of 3D applications. In this paper, we have proposed a GPU-accelerated blind and robust watermarking approach to the 3D polygon meshes on the basis of the geometry image transform and image watermarking, which performs watermark embedding and detection on the basis of the geometry image derived from a spherical parametrisation of the input mesh with the help of massive-parallel processing power of the GPUs on the display card. The experimental results show that our approach is successful in at least two aspects. First, the watermark is robust, the embedded watermark survives from common geometric attacks, cropping, simplification, and re-meshing attacks. Second, with the help of parallel computations on the GPUs, the embedding and detection process is extremely fast.     

一种利用FFT自适应阈值处理失真杂散信号的方法

在图像信号传输过程中,由于传输网络以及各种数模转换设备和数字处理设备的影响,可能会造成失真杂散信号的产生,其随机不确定性将导致某些专业图像检测处理设备工作的异常。文中首先分析了图像失真杂散信号产生的原因及其特征,然后针对此特征提出了一种FFT自适应阈值屏蔽算法,最后利用MATLAB仿真验证了此算法且进行了实际的FPGA实验。     

A diffusion wavelet approach for 3-D model matching

This paper proposes a new 3D shape retrieval approach based on diffusion wavelets which generalize wavelet analysis and associated signal processing techniques to functions on manifolds and graphs. Unlike current works on 3D matching, which are based either on the topological information of the model or its scatter point distribution information, this approach uses both information for more effective matching. Diffusion wavelets enable both global and local analyses on graphs, and can capture the topology of a surface with the diffusion map of its mesh representation. As a result, both multi-scale properties of the 3D geometric model and the topology among the meshes can be extracted for use in 3D geometric model retrieval. Tests using 3D benchmarks demonstrate that the approach based on diffusion wavelets is effective and performs better than those by spherical wavelet and spherical harmonics in 3D model matching.     

Processing of 3D meshed surfaces using spherical wavelets

This paper presents an efficient technique for processing of 3D meshed surfaces via spherical wavelets.More specifically,an input 3D mesh is firstly transformed into a spherical vector signal by a fast low distortion spherical parameterization approach based on symmetry analysis of 3D meshes.This signal is then sampled on the sphere with the help of an adaptive sampling scheme.Finally,the sampled signal is transformed into the wavelet domain according to spherical wavelet transform where many 3D mesh processing operations can be implemented such as smoothing,enhancement,compression,and so on.Our main contribution lies in incorporating a fast low distortion spherical parameterization approach and an adaptive sampling scheme into the frame for processing 3D meshed surfaces by spherical wavelets,which can handle surfaces with complex shapes.A number of experimental examples demonstrate that our algorithm is robust and efficient.     

Shape‐Up: Shaping Discrete Geometry with Projections

We introduce a unified optimization framework for geometry processing based on shape constraints. These constraints preserve or prescribe the shape of subsets of the points of a geometric data set, such as polygons, one‐ring cells, volume elements, or feature curves. Our method is based on two key concepts: a shape proximity function and shape projection operators. The proximity function encodes the distance of a desired least‐squares fitted elementary target shape to the corresponding vertices of the 3D model. Projection operators are employed to minimize the proximity function by relocating vertices in a minimal way to match the imposed shape constraints. We demonstrate that this approach leads to a simple, robust, and efficient algorithm that allows implementing a variety of geometry processing applications, simply by combining suitable projection operators. We show examples for computing planar and circular meshes, shape space exploration, mesh quality improvement, shape‐preserving deformation, and conformal parametrization. Our optimization framework provides a systematic way of building new solvers for geometry processing and produces similar or better results than state‐of‐the‐art methods.