Wavelet-based progressive compression scheme for triangle meshes: wavemesh

We propose a new lossy to lossless progressive compression scheme for triangular meshes, based on a wavelet multiresolution theory for irregular 3D meshes. Although remeshing techniques obtain better compression ratios for geometric compression, this approach can be very effective when one wants to keep the connectivity and geometry of the processed mesh completely unchanged. The simplification is based on the solving of an inverse problem. Optimization of both the connectivity and geometry of the processed mesh improves the approximation quality and the compression ratio of the scheme at each resolution level. We show why this algorithm provides an efficient means of compression for both connectivity and geometry of 3D meshes and it is illustrated by experimental results on various sets of reference meshes, where our algorithm performs better than previously published approaches for both lossless and progressive compression.     

Wavelet-based multiresolution analysis of irregular surface meshes

We extend Lounsbery's multiresolution analysis wavelet-based theory for triangular 3D meshes, which can only be applied to regularly subdivided meshes and thus involves a remeshing of the existing 3D data. Based on a new irregular subdivision scheme, the proposed algorithm can be applied directly to irregular meshes, which can be very interesting when one wants to keep the connectivity and geometry of the processed mesh completely unchanged. This is very convenient in CAD (computer-assisted design), when the mesh has attributes such as texture and color information, or when the 3D mesh is used for simulations, and where a different connectivity could lead to simulation errors. The algorithm faces an inverse problem for which a solution is proposed. For each level of resolution, the simplification is processed in order to keep the mesh as regular as possible. In addition, a geometric criterion is used to keep the geometry of the approximations as close as possible to the original mesh. Several examples on various reference meshes are shown to prove the efficiency of our proposal.     

Exact and Robust (Self‐)Intersections for Polygonal Meshes

We present a new technique to implement operators that modify the topology of polygonal meshes at intersections and self‐intersections. Depending on the modification strategy, this effectively results in operators for Boolean combinations or for the construction of outer hulls that are suited for mesh repair tasks and accurate mesh‐based front tracking of deformable materials that split and merge. By combining an adaptive octree with nested binary space partitions (BSP), we can guarantee exactness (= correctness) and robustness (= completeness) of the algorithm while still achieving higher performance and less memory consumption than previous approaches. The efficiency and scalability in terms of runtime and memory is obtained by an operation localization scheme. We restrict the essential computations to those cells in the adaptive octree where intersections actually occur. Within those critical cells, we convert the input geometry into a plane‐based BSP‐representation which allows us to perform all computations exactly even with fixed precision arithmetics. We carefully analyze the precision requirements of the involved geometric data and predicates in order to guarantee correctness and show how minimal input mesh quantization can be used to safely rely on computations with standard floating point numbers. We properly evaluate our method with respect to precision, robustness, and efficiency.     

Fun sheet matching: towards automatic block decomposition for hexahedral meshes

Depending upon the numerical approximation method that may be implemented, hexahedral meshes are frequently preferred to tetrahedral meshes. Because of the layered structure of hexahedral meshes, the automatic generation of hexahedral meshes for arbitrary geometries is still an open problem. This layered structure usually requires topological modifications to propagate globally, thus preventing the general development of meshing algorithms such as Delaunay??s algorithm for tetrahedral meshes or the advancing-front algorithm based on local decisions. To automatically produce an acceptable hexahedral mesh, we claim that both global geometric and global topological information must be taken into account in the mesh generation process. In this work, we propose a theoretical classification of the layers or sheets participating in the geometry capture procedure. These sheets are called fundamental, or fun-sheets for short, and make the connection between the global layered structure of hexahedral meshes and the geometric surfaces that are captured during the meshing process. Moreover, we propose a first generation algorithm based on fun-sheets to deal with 3D geometries having 3- and 4-valent vertices.     

Mean square error approximation for wavelet-based semiregular mesh compression

The objective of this paper is to propose an efficient model-based bit allocation process optimizing the performances of a wavelet coder for semiregular meshes. More precisely, this process should compute the best quantizers for the wavelet coefficient subbands that minimize the reconstructed mean square error for one specific target bitrate. In order to design a fast and low complex allocation process, we propose an approximation of the reconstructed mean square error relative to the coding of semiregular mesh geometry. This error is expressed directly from the quantization errors of each coefficient subband. For that purpose, we have to take into account the influence of the wavelet filters on the quantized coefficients. Furthermore, we propose a specific approximation for wavelet transforms based on lifting schemes. Experimentally, we show that, in comparison with a "naive" approximation (depending on the subband levels), using the proposed approximation as distortion criterion during the model-based allocation process improves the performances of a wavelet-based coder for any model, any bitrate, and any lifting scheme.     

3D model retrieval based on color + geometry signatures

Color plays a significant role in the recognition of 3D objects and scenes from the perspective of cognitive psychology. In this paper, we propose a new 3D model retrieval method, focusing on not only the geometric features but also the color features of 3D mesh models. Firstly, we propose a new sampling method that samples the models in the regions of either geometry-high-variation or color-high-variation. After collecting geometry + color sensitive sampling points, we cluster them into several classes by using a modified ISODATA algorithm. Then we calculate the feature histogram of each model in the database using these clustered sampling points. For model retrieval, we compare the histogram of an input model to the stored histograms in the database to find out the most similar models. To evaluate the retrieval method based on the new color + geometry signatures, we use the precision/recall performance metric to compare our method with several classical methods. Experiment results show that color information does help improve the accuracy of 3D model retrieval, which is consistent with the postulate in psychophysics that color should strongly influence the recognition of objects.     

Uniform remeshing with an adaptive domain: a new scheme for view-dependent level-of-detail rendering of meshes

We present a new algorithm for view-dependent level-of-detail rendering of meshes. Not only can it effectively resolve complex geometry features similar to edge collapse-based schemes, but it also produces meshes that modern graphics hardware can render efficiently. This is accomplished through a novel hybrid approach: for each frame, we view-dependently refine the progressive mesh (PM) representation of the original mesh and use the output as the base domain of uniform regular refinements. The algorithm exploits frame-to-frame coherence and only updates portions of the output mesh corresponding to modified domain triangles. The PM representation is built using a custom volume preservation-based error function. A simple k-d tree enhanced jump-and-walk scheme is used to quickly map from the dynamic base domain to the original mesh during regular refinements. In practice, the PM refinement provides a view-optimized base domain for later regular refinements. The regular refinements ensure almost-everywhere regularity of output meshes, allowing optimization for vertex cache coherence and caching of geometry data in high-performance graphics memory. Combined, they also have the effect of allowing our algorithm to operate on uniform clusters of triangles instead of individual ones, reducing CPU workload.     

三角形条带网格模型几何压缩方法研究

三角形条带为三角形网格提供了一种紧凑的表示方法，使快速的绘制和传输三角形网格成为可能，因此对由三角形条带构成的网格压缩进行研究具有重要的意义．本文使用Triangle Fixer方法对三角形条带构成的三维模型拓扑信息进行了压缩，并采用3阶自适应算术编码进一步提高压缩率；同时结合量化、平行四边形顶点坐标预测以及算术编码来实现三角形网格几何信息的压缩，在几何模型质量基本没有损失的情况下，获得了很好的压缩性能．     

Fast Polyhedral Cell Sorting for Interactive Rendering of Unstructured Grids

Direct volume rendering based on projective methods works by projecting, in visibility order, the polyhedral cells of a mesh onto the image plane, and incrementally compositing the cell's color and opacity into the final image. Crucial to this method is the computation of a visibility ordering of the cells. If the mesh is "well-behaved" (acyclic and convex), then the MPVO method of Williams provides a very fast sorting algorithm; however, this method only computes an approximate ordering in general datasets, resulting in visual artifacts when rendered. A recent method of Silva et al. removed the assumption that the mesh is convex, by means of a sweep algorithm used in conjunction with the MPVO method; their algorithm is substantially faster than previous exact methods for general meshes.
In this paper we propose a new technique, which we call BSP-XMPVO, which is based on a fast and simple way of using binary space partitions on the boundary elements of the mesh to augment the ordering produced by MPVO. Our results are shown to be orders of magnitude better than previous exact methods of sorting cells.     

基于小波变换的非渐进网格压缩

为了取得较好的三角形网格压缩性能，提出了一种基于小波变换的三角形网格非渐进压缩方法。该压缩方法先利用重新网格化来去除大部分连接信息，然后利用小波变换的强去相关能力来压缩几何信息。在进行重新网格化和小波变换后，再按一个确定的次序将所有的小波系数扫描为一个序列，然后对其做量化和算术编码。另外，对重新网格化得到的自适应半正规采样模式，还设计了一种自适应细分信息编码算法，以便使解码端知道每一个小波系数应该放置在哪一个顶点上。实验表明，用该压缩方法对由三维扫描仪获取的复杂网格进行压缩，取得了比Edgebreaker方法明显要好的率失真性能；10比特量化时，压缩倍数在200倍左右，为Edgebreaker方法的2倍多。     

R-D optimized progressive compression of 3D meshes using prioritized gate selection and curvature prediction

A rate-distortion (R-D) optimized progressive coding algorithm for three-dimensional (3D) meshes is proposed in this work. We propose the prioritized gate selection and the curvature prediction to improve the connectivity and geometry compression performance, respectively. Furthermore, based on the bit plane coding, we develop a progressive transmission method, which improves the qualities of intermediate meshes as well as that of the fully reconstructed mesh, and extend it to the view-dependent transmission method. Experiments on various 3D mesh models show that the proposed algorithm provides significantly better compression performance than the conventional algorithms, while supporting progressive reconstruction efficiently.     

A Shrink Wrapping Approach to Remeshing Polygonal Surfaces

Due to their simplicity and flexibility, polygonal meshes are about to become the standard representation for surface geometry in computer graphics applications. Some algorithms in the context of multiresolution representation and modeling can be performed much more efficiently and robustly if the underlying surface tesselations have the special subdivision connectivity. In this paper, we propose a new algorithm for converting a given unstructured triangle mesh into one having subdivision connectivity. The basic idea is to simulate the shrink wrapping process by adapting the deformable surface technique known from image processing. The resulting algorithm generates subdivision connectivity meshes whose base meshes only have a very small number of triangles. The iterative optimization process that distributes the mesh vertices over the given surface geometry guarantees low local distortion of the triangular faces. We show several examples and applications including the progressive transmission of subdivision surfaces.     

The progressive mesh compression based on meaningful segmentation

Nowadays, both mesh meaningful segmentation (also called shape decomposition) and progressive compression are fundamental important problems, and some compression algorithms have been developed with the help of patch-type segmentation. However, little attention has been paid to the effective combination of mesh compression and meaningful segmentation. In this paper, to accomplish both adaptive selective accessibility and a reasonable compression ratio, we break down the original mesh into meaningful parts and encode each part by an efficient compression algorithm. In our method, the segmentation of a model is obtained by a new feature-based decomposition algorithm, which makes use of the salient feature contours to parse the object. Moreover, the progressive compression is an improved degree-driven method, which adapts a multi-granularity quantization method in geometry encoding to obtain a higher compression ratio. We provide evidence that the proposed combination can be beneficial in many applications, such as view-dependent rendering and streaming of large meshes in a compressed form.     

Using sequential NETGEN as a component for a parallel mesh generator

A parallel tetrahedral mesh generator is developed using the existing sequential NETGEN mesh generator. Mesh generation algorithms developed decompose the geometry into multiple sub-geometries sequentially on a master node and then mesh each sub-geometry in parallel on multiple processors. Two methods are implemented. The first decomposes the geometry and produces conforming surface sub-meshes from which volume meshes can be generated in parallel. A second refinement based method also makes use of the CAD geometry information. A scalable mesh migration algorithm that utilizes “owner updates” rule is implemented. Results show that using the refinement based method, a mesh with a billion elements can be generated in about a minute.     

Segmentation of temporal mesh sequences into rigidly moving components

In this paper is considered the segmentation of meshes into rigid components given temporal sequences of deforming meshes. We propose a fully automatic approach that identifies model parts that consistently move rigidly over time. This approach can handle meshes independently reconstructed at each time instant. It allows therefore for sequences of meshes with varying connectivities as well as varying topology. It incrementally adapts, merges and splits segments along a sequence based on the coherence of motion information within each segment. In order to provide tools for the evaluation of the approach, we also introduce new criteria to quantify a mesh segmentation. Results on both synthetic and real data as well as comparisons are provided in the paper.     

Content-based retrieval of logo and trademarks in unconstrained color image databases using Color Edge Gradient Co-occurrence Histograms

In this paper, we present an algorithm that extends the Color Edge Co-occurrence Histogram (CECH) object detection scheme on compound color objects, for the retrieval of logos and trademarks in unconstrained color image databases. We introduce more accurate information to the CECH, by virtue of incorporating color edge detection using vector order statistics. This produces a more accurate representation of edges in color images, as compared to the simple color pixel difference classification of edges seen with the CECH. Our proposed method is thus reliant on edge gradient information, and so we call it the Color Edge Gradient Co-occurrence Histogram (CEGCH). We also introduce a color quantization method based in the hue–saturation–value (HSV) color space, illustrating that it is a more suitable scheme of quantization for image retrieval, compared to the color quantization scheme introduced with the CECH. Experimental results demonstrate that the CEGCH and the HSV color quantization scheme is insensitive to scaling, rotation, and partial deformations, and outperforms the use of the CECH in image retrieval, with higher precision and recall. We also perform experiments on a closely related algorithm based on the Color Co-occurrence Histogram (CCH) and demonstrate that our algorithm is also superior in comparison, with higher precision and recall.     

基于几何特征的自适应三维模型数字水印算法

针对三维三角网格模型提出一种稳健的数字水印算法.首先将三维三角网格模型进行仿射变换,以获得模型的旋转不变性和缩放不变性;然后将各顶点邻域内顶点位置的平均差值作为掩蔽因子确定水印嵌入的强度,使得嵌入的水印具有不可见性.实验结果表明:该算法简单,对几何变换、简化、随机噪声和剪切攻击具有较好的鲁棒性.     

Variational tetrahedral mesh generation from discrete volume data

In this paper, we propose a novel tetrahedral mesh generation algorithm, which takes volumic data (voxels) as an input. Our algorithm performs a clustering of the original voxels within a variational framework. A vertex replaces each cluster and the set of created vertices is triangulated in order to obtain a tetrahedral mesh, taking into account both the accuracy of the representation and the elements quality. The resulting meshes exhibit good elements quality with respect to minimal dihedral angle and tetrahedra form factor. Experimental results show that the generated meshes are well suited for Finite Element Simulations.     

一种保留特征的网格简化和压缩递进传输方法

针对数字博物馆中三维藏品网络传输及传输过程中藏品特征保留的需要,提出了一种保留拓扑及纹理特征的网格简化方法,在三角形折叠简化算法的基础之上,通过引入边界三角形和色异三角形等概念,对误差矩阵的计算和误差控制方法进行了改进,保留了原始模型的几何边界和纹理属性等特征信息;并结合递进网格和压缩编码,构造了基于八叉树编码的递进网格文件,从而实现了基于网络的三维模型递进传输系统.     

三角网格特征边识别的一种有效方法

三角网格特征边识别在数字几何处理和计算机辅助制造(CAM)的模具加工中都有 着广泛的应用,该文指出了近年来有关网格特征边识别算法的各种弊端及原因,给出了一种鲁 棒的网格特征边识别新算法。该算法以网格特征点的识别为基础,能够识别以往算法常遗漏的 一些二面法向夹角比较小的网格边,增强了对C1 不连续网格边的识别能力。众多数值例子支 持了这个结论。