A real-time terrain visualization algorithm using wavelet-based compression

We propose a real-time terrain visualization algorithm combined with wavelet-based compression. Our approach updates a surface mesh model in real time by using wavelet coefficients and height data decoded from a compressed bitstream. To achieve this, a new mesh approximation method using restricted quadtree triangulation is designed on the basis of wavelet coefficients representing surface complexity. Also, a wavelet-based compression having a multiresolution structure is introduced to handle large terrain data interactively. Simulation results demonstrate that the proposed algorithm is prospective for applications in a network environment where narrow bandwidth and low computational power are usually allowed .     

有限元网格生成方法研究的新进展

总结了近10年来有限元网格生成方法的研究进展。首先，概述了目前研究与应用仍然较为活跃的通用网格生成方法，如映射法、基于栅格法、Delaunay三角化法和推进波前法的最新研究进展。其次，对当前的主要研究热点，如曲面网格生成、全六面体网格生成和并行网格生成等进行了阐述；最后，简要地探讨了该领域的发展趋势。     

稠密散乱数据点多分辨率曲面重构

将曲面重构看作是一种信号重构过程，针对大量散乱数据点，借助成熟的三角网格划分和网格化简算法，利用提升小波变换实现曲面重构，可以快速地构造出复杂拓扑结构的Calmull-Clark曲面；给出了小波系数估算方法以及基于网格拓扑结构的局部最优路径搜索算法．通过运行实例证明了文中算法的有效性．     

Adaptive terrain triangulation using the representation of quad trees by vertex textures and wavelet estimation of vertex significance

A method of adaptive terrain triangulation is proposed that can be implemented in hardware. The method is based on an estimate of the static error of a quad tree nodes using wavelet transforms and on the representation of the resulting quad tree by a vertex texture. The proposed method has the following characteristic features: the adjacent nodes of the generated adapted mesh can differ in any number of hierarchical levels; the triangulation process is not limited by the size of the decomposition segments, which solves the problem of joining segments without inserting additional nodes; the multiscale terrain representation used in the method makes it possible to store the levels of detail in the graphics processor memory as a multilevel vertex texture; thus, the costliest part of the algorithm can be efficiently implemented using a vertex shader. When constructing the triangulation, the algorithm takes into account both local features of the terrain and the camera location; also, it has a natural support of geomorphing.     

Adaptive chaotic noise reduction method based on dual-lifting wavelet

For the subjectivity of lifting wavelet coefficients selection, an adaptive noise reduction method is proposed for chaotic signals corrupted by nonstationary noises. Here, wavelet coefficients including coarse approximation and detail information are obtained by dual-lifting wavelet transform. The coarse parts are handled by the singular spectrum analysis, whereas the detail parts are analyzed combining with gradient decent algorithm in neural networks for the adaptive choice of wavelet coefficients. The chaotic signals generated by Lorenz model as well as the observed monthly series of sunspots are respectively applied for simulation analysis. The experimental results show a dramatic improvement of the proposed method, the advantages of which include the simple of achieving, the small reconstruction error and the efficiency for the noisy chaotic signals.     

MATLAB中9/7小波变换所得系数冗余问题研究

对MATLAB中直接采用正交小波计算模型处理双正交小波,导致小波分解系数冗余的问题进行了研究。针对该问题,提出采用9/7小波原型处理非周期信号的改进算法,与MATLAB所给算法相比,对于奇起点的偶数长信号和偶起点的奇数长信号,分解时可少计算2个近似系数和1个细节系数;对于奇起点的奇数长信号和偶起点的偶数长信号,可少计算1个近似系数。当用改进算法分解512×512点图像至第4级时,便可少计算4 256个系数,且重构图像的峰值信噪比要高于MATLAB中恢复图像。所以,改进算法既降低了计算量和数据存储量,又提高了恢复图像的质量。     

Generation of a finite element MESH from stereolithography (STL) files

The aim of the method proposed here is to show the possibility of generating adaptive surface meshes suitable for the finite element method, directly from an approximated boundary representation of an object created with CAD software. First, we describe the boundary representation, which is composed of a simple triangulation of the surface of the object. Then we will show how to obtain a conforming size-adapted mesh. The size adaptation is made considering geometrical approximation and with respect to an isotropic size map provided by an error estimator. The mesh can be used “as is” for a finite element computation (with shell elements), or can be used as a surface mesh to initiate a volume meshing algorithm (Delaunay or advancing front). The principle used to generate the mesh is based on the Delaunay method, which is associated with refinement algorithms, and smoothing. Finally, we will show that not using the parametric representation of the geometrical model allows us to override some of the limitations of conventional meshing software that is based on an exact representation of the geometry.     

Bezier曲面的适应性细分和三角形化的四叉树方法

计算机生成具有浓淡的参数曲面的方法之一是先对曲面进行适应性细分,并对所得到的曲面细分三角形化,得到曲面的三角形网表示,从而可以对每个三角形施行通常的浓淡处理算法。本文介绍了适应性细分双三次Bezier曲面的方法及曲面细分的四叉树表示,在此基础上给出了一个将曲面细分三角形化的算法。该算法防止了由于适应性细分而可能产生的曲面上的裂缝。     

基于分形维数的地表模型多分辨率动态绘制

以基于分形维数的树状结构组织三维地表网格模型,实现了与视点相关的连续多分辨率地表模型简化及实时绘制.算法分为预处理和实时绘制两个阶段.在预处理阶段,通过分形维数评价地表的复杂度,建立自适应的树状结构,计算出所有顶点的误差值.在绘制阶段,则根据视距、视角等因素动态地确定需保留的顶点集,并采用受限四叉树方法实时三角化得到所需分辨率下的三角网格近似模型.该算法具有两个优点:一个是地表模型的分层区域划分考虑了地形本身的复杂度;另一个是建立了视点相关各参数与所采用的分辨率表示的直接关系.实验表明,此算法简单、有效,支持对地表模型的交互式实时动态绘制.     

基于分形图像编码的小波补偿算法

提出了一种对图像进行分形“粗略”（概貌）编码,“细节”（边缘）信息通过小波变换提取图像高频信息进行补偿的编码算法。该编码算法中,小波变换产生的高频小波系数根据系数重要性采用类似嵌入式小波零树编码方式进行编码,从而具有比特率可控等特点。通过实验表明,新编码算法的编码效果优于分形自适应四叉树编码算法和小波变换编码算法。     

Wavelet denoising via sparse representation

Wavelet threshold denoising is a powerful method for suppressing noise in signals and images. However, this method often uses a coordinate-wise processing scheme, which ignores the structural properties in the wavelet coefficients. We propose a new wavelet denoising method using sparse representation which is a powerful mathematical tool recently developed. Instead of thresholding wavelet coefficients individually, we minimize the number of non-zero coefficients under certain conditions. The denoised signal is reconstructed by solving an optimization problem. It is shown that the solution to the optimization problem can be obtained uniquely and the estimates of the denoised wavelet coefficients are unbiased, i.e., the statistical means of the estimates are equal to the noise-free wavelet coefficients. It is also shown that at least a local optimal solution to the denoising problem can be found. Our experiments on test data indicate that this new denoising method is effective and efficient for a wide variety of signals including those with low signal-to-noise ratios. Supported by the U.S. National Institutes of Health (Grant No. U01 HL91736), and the National High-Tech Research & Development Program of China (Grant No. 2007AA01Z175)     

在任意拓扑三角形网格上的光滑样条曲面

介绍了一种在控制三角形网格上创建光滑样条曲面的算法,该控制网格能够刻画具有或没有边界的任意自由曲面.生成的曲面有一个4次参数多项式表示并且被表示成一个切平面连续的三角形Bézier片网.曲面对网格的逼近程度受到一个混合比控制,当混合比为0时,产生的曲面插值网格.该算法是一种局部方法,简单且效率高,适合于外形设计.     

Interactive Multiresolution Editing and Display of Large Terrains

In recent years, many systems have been developed for the real‐time display of very large terrains. While many of these techniques combine high‐quality rendering with impressive performance, most make the fundamental assumption that the terrain is represented by a fixed height map that cannot be altered at run time. Such systems frequently rely on extensive preprocessing of the raw terrain data. They are mostly designed for maximum performance. Consequently, these techniques are ill‐suited for the many applications such as geological simulations and games in which terrain surfaces must be altered interactively. We present a two‐component system that can achieve real‐time view‐dependent rendering while allowing on‐line multiresolution alterations of a large terrain. Our fundamental height map representation is a wavelet quadtree hierarchy, allowing one to easily apply arbitrary multiresolution edits to the terrain. Our display algorithm extracts a view‐dependent approximation of the terrain from the wavelet quadtree in real time. The algorithm dynamically alters this approximation based on any ongoing edits. To allow for flexibility and to limit performance loss, the two components of this system have been designed to be as independent as possible.     

Medial Axis Construction in Three Dimensions and its Application to Mesh Generation

An algorithm for the construction of the medial axis of a three-dimensional body given by a triangulation of its bounding surface is described. The indirect construction is based on the Delaunay-triangulation of a set of sample points on the bounding surface. The point set is refined automatically so as to capture the correct topology of the medial axis. The computed medial axis (or better medial surface) is then used for hex-dominant mesh generation. Quad-dominant meshes are generated on the medial subfaces first and extruded to the boundary of the body at both sides. The resulting single cell layer is subdivided in direction normal to the boundary, yielding columns of hexahedral and three-sided prismatic cells. The resulting volume mesh is orthogonal at the boundary and ‘semi-structured’ between boundary and medial surface. Mixed cell types (tets, pyramids, degenerate hexahedra) may result along the medial surface. An advancing front algorithm (paving) is used for meshing the subfaces of the medial surface. Development of the mesh generator has not been fully completed with respect to degenerate parts of the medial axis. First medium-complexity bodies have been meshed, however, showing moderate meshing times.     

基于自适应分解层数和阈值的小波去噪算法

为了更好地降低电能质量扰动信号中的噪声,提出了一种基于自适应分解层数和阈值的小波去噪算法.通过计算小波细节系数的峰值比,自适应地确定最佳小波分解层数,根据各层细节系数中有用信息和噪声信息的分布特性以及细节系数的正、负峰值比,动态调整各层细节系数的上、下阈值.应用Matlab对暂态振荡和脉冲信号进行去噪处理,并与传统硬、软阈值算法和一种改进小波阈值算法相比.结果表明:本文提出的自适应分解层数和阈值的小波去噪算法得到的信噪比和均方根误差均优于以上3种方法,重构后信号更接近原始信号,并且较好地保留了扰动期间信号的特征信息.     

A highly solid model boundary preserving method for large-scale parallel 3D Delaunay meshing on parallel computers

In this paper, we propose a novel parallel 3D Delaunay triangulation algorithm for large-scale simulations on parallel computers. Our method keeps the 3D boundary representation model information during the whole parallel 3D Delaunay triangulation process running on parallel computers so that the solid model information can be accessed dynamically and the meshing results can be very approaching to the model boundary with the increase of meshing scale. The model is coarsely meshed at first and distributed on CPUs with consistent partitioned shared interfaces and partitioned model boundary meshes across processors. The domain partition aims at minimizing the edge-cuts across different processors for minimum communication cost and distributing roughly equal number of mesh vertices for load balance. Then a parallel multi-scale surface mesh refinement phase is iteratively performed to meet the mesh density criteria followed by a parallel surface mesh optimization phase moving vertices to the model boundary so as to fit model geometry feature dynamically. A dynamic load balancing algorithm is performed to change the partition interfaces if necessary. A 3D local non-Delaunay mesh repair algorithm is finally done on the shared interfaces across processors and model boundaries. The experimental results demonstrate our method can achieve high parallel performance and perfect scalability, at the same time preserve model boundary feature and generate high quality 3D Delaunay mesh as well.     

Optimized surface discretization of functionally defined multi-material objects

We present in this paper an algorithm for meshing implicit surfaces based on the Delaunay triangulation of a point-set adaptively sampled on an implicit surface. To improve the quality of the resulting triangular mesh, we use at each iteration a mesh optimization algorithm with the following objectives: optimizing the connectivity, retrieving the sharp features, regularizing the triangles shapes and minimizing the approximation error. Then, we extend this algorithm in order to handle functionally defined heterogeneous object surfaces, while maintaining a good quality for the triangles’ shapes and the mesh features (geometrical sharp features and boundaries between different materials).     

雷达辐射源信号小波变换特征提取方法

在小波域滤波算法的基础上提出一种对雷达辐射源信号进行脉内特征提取方法,该方法能够从信号中有效地提取定量信息。将小波变换后低频逼近小波系数的能量分布熵与经过尺度相关去噪计算后反映信号边缘的高频细节小波系数能量分布熵构成雷达辐射源信号的二维特征向量。通过对10种雷达辐射源信号的特征提取和分类仿真实验分析表明：提取的样本特征在0 dB下具有很好的抗噪性和可聚类性,方法是有效的。该方法能够简化分类器的设计,有利于工程应用。