水平集网格简化算法在遗址场景中的应用

将水平集方法引入到三维模型网格简化中,构造符号距离函数,函数的零集定义为初始曲面;引入一个能量泛涵,通过对其极小化诱导出一个水平集形式的二阶几何偏微分方程,从而将网格简化过程转化为隐式模型的体素扩散过程。该方法目前已经用于文化遗产数字化的大场景和文物的模型简化中。对水平集网格简化算法和现常用的基于点对收缩的网格简化算法在视觉质量和几何误差方面做了比较和分析,实验表明该方法适用于任意拓扑形状的网格模型,使得模型大规模简化后,在保持较低误差的同时,仍然能够保持相当多的重要几何特征和较好的整体视觉效果。     

基于逆 Loop 细分的半正则网格简化算法

摘 要：三维网格简化是在保留目标物体几何形状信息的前提下尽量减小精细化三维模型 中的点数和面数的一种操作,对提高三维网格数据的存取和网络传输速度、编辑和渲染效率具 有十分重要的作用。针对大多网格简化算法在简化过程中未考虑网格拓扑结构与视觉质量的问 题,提出了一种基于逆 Loop 细分的半正则网格简化算法。首先根据邻域质心偏移量进行特征 点检测,随后随机选取种子三角形,以边扩展方式获取正则区域并执行逆 Loop 细分进行简化。 最后,以向内分割方式进行边缘拼接,获取最终的简化模型。与经典算法在公开数据集上进行 实验对比,结果表明,该算法能够在简化的同时有效地保持网格特征,尽可能保留与原始网格 一致的规则的拓扑结构,并且在视觉质量上优于边折叠以及聚类简化算法。     

可减少模型简化误差的边折叠简化算法及应用

基于三角形网格边折叠简化思想，提出一种基于边顶点重要度简化算法，简化算法能有效保持模型局部特征，减小简化模型和原始模型之间的误差；采用一种改进的三角形网格数据结构，利用二叉树对顶点重要度进行快速排序并记录三角形合并关系，得到所需分辨率下的近似网格模型。数据结构具有层次清楚、操作简单、可扩充性等特点，能有效支持多分辨率简化与快速可视化。     

Efficient and robust 3D line drawings using difference-of-Gaussian

Line drawings are widely used for sketches, animations, and technical illustrations because they are effective and easy to draw. The existing computer-generated lines, such as suggestive contours, apparent ridges, and demarcating curves, adopt the two-pass framework: in the first pass, certain geometric features or properties are extracted or computed in the object space; then in the second pass, the line drawings are rendered by iterating each polygonal face or edge. It is known these approaches are very sensitive to the mesh quality, and usually require appropriate preprocessing operations (e.g. smoothing, remeshing, etc.) to the input meshes. This paper presents a simple yet robust approach to generate view-dependent line drawings for 3D models. Inspired by the image edge detector, we compute the difference-of-Gaussian of illumination on the 3D model. With moderate assumption, we show all the expensive computations can be done in the pre-computing stage. Our method naturally integrates object- and image-spaces in that we compute the geometric features in the object space and then adopt a simple fragment shader to render the lines in the image space. As a result, our algorithm is more efficient than the existing object-space approaches, since the lines are generated in a single pass without iterating the mesh edges/faces. Furthermore, our method is more flexible and robust than the existing algorithms in that it does not require the preprocessing on the input 3D models. Finally, the difference-of-Gaussian operator can be extended to the anisotropic setting guided by local geometric features. The promising experimental results on a wide range of real-world models demonstrate the effectiveness and robustness of our method.     

自适应三角网格模型重新布点算法的研究

在对任意拓扑三角网格模型进行自动三边界区域划分的基础上，提出一种适应的三角网格模型重新布点算法，该算法首先根据三边界区域划分的结果，构造初始网格模型具有最低分辨率的基础网格模型，然后利用协调映射技术，对网格模型进行重新采样，从而不断对基础网格模型进行细化，算法的特点是可以根据不同的精度自动在曲面的大曲率处重新采样得到较多的点，而在曲面的小曲率处则重新采样得到较少的点，该算法可以用于三角网模型的自适应简化和优化，文中的应用实例表明，该算法可以保证在满足指定精度要求的条件下，得到更合理的三角网格模型，取得理想的效果。     

基于圆形参数域和重要性采样的三维模型网格重建

给出了一个基于参数化和重要性采样的网格重建算法.算法搜索一条切线将三维模型表面切分成一片碟形表面,并将其参数化到二维单位圆中.根据模型的曲率信息和参数化的扭曲度生成一张控制图.利用蓝噪声采样算法对用控制图调制后的采样密度采样得到离散采样点.通过对采样点进行平面三角化并将其映射回三维空间实现了三维网格重建.实验证明,该方法有效地改善了参数化的扭曲度,并能得到具有自适应性的高度规则网格.     

Visual saliency guided textured model simplification

Mesh geometry can be used to model both object shape and details. If texture maps are involved, it is common to let mesh geometry mainly model object shapes and let the texture maps model the most object details, optimising data size and complexity of an object. To support efficient object rendering and transmission, model simplification can be applied to reduce the modelling data. However, existing methods do not well consider how object features are jointly represented by mesh geometry and texture maps, having problems in identifying and preserving important features for simplified objects. To address this, we propose a visual saliency detection method for simplifying textured 3D models. We produce good simplification results by jointly processing mesh geometry and texture map to produce a unified saliency map for identifying visually important object features. Results show that our method offers a better object rendering quality than existing methods.     

Semi-regular Quadrilateral-only Remeshing from Simplified Base Domains

Semi-regular meshes describe surface models that exhibit a structural regularity that facilitates many geometric processing algorithms. We introduce a technique to construct semi-regular, quad-only meshes from input surface meshes of arbitrary polygonal type and genus. The algorithm generates a quad-only model through subdivision of the input polygons, then simplifies to a base domain that is homeomorphic to the original mesh. During the simplification, a novel hierarchical mapping method, keyframe mapping , stores specific levels-of-detail to guide the mapping of the original vertices to the base domain. The algorithm implements a scheme for refinement with adaptive resampling of the base domain and backward projects to the original surface. As a byproduct of the remeshing scheme, a surface parameterization is associated with the remesh vertices to facilitate subsequent geometric processing, i.e. texture mapping, subdivision surfaces and spline-based modeling.     

基于强制约束的非均匀网格简化算法

在工程中通常采用三角形网格描述几何物体,但是网格模型的大数据量成为后续处理的瓶颈,因此三角形网格模型的简化成为了多个领域中的研究热点。文章针对逆向工程中的特殊简化要求,提出了一种强制约束下的非均匀网格简化算法。对于工程应用实例的简化计算,可以得到与原始网格拓扑一致的非均匀简化网格,表明了所提出简化算法的有效性。     

High quality surface remeshing with equilateral triangle grid

This study proposes a robust and efficient 3D surface remeshing algorithm for mesh quality optimization. Instead of the global mesh relaxation method proposed in the previous study conducted on remeshing, this study proposes an equilateral triangle grid-resampling scheme for achieving mesh optimization more efficiently. In order to improve the feasibility of resampling by directly using an equilateral triangle grid, the surface structure of the original model is correctly extracted by an automatic surface segmentation technique before the resampling step is executed. Results of this study show that the proposed remeshing algorithm can automatically and substantially improve the quality of triangulation, as well as automatically preserve shape features under an acceptable level of measurement error in the shape approximation, which is suitable for a mesh with a specific topology.     

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.     

一种基于速度的移动对象轨迹简化算法

目前对移动对象轨迹简化问题分为离线简化和在线简化。以往的简化方法中许多依赖轨迹的几何特性,而针对移动对象的速度这一重要特征没有足够的关注。本文基于速度研究移动对象轨迹的离线简化新方法,提出了移动对象轨迹离线简化的动态规划算法、基于广度优先搜索的轨迹简化算法及其优化算法、时间复杂度更低的近似算法。并通过大量实验验证本文提出的算法比基于方向的简化算法和基于位置的简化算法具有更好的简化效率。     

Shape‐adaptive 3‐D mesh simplification based on local optimality measurement

Mesh simplification is the process of reducing the number of triangles in a mesh representation of object surface. For a given level of detail or error tolerance, the conventional mesh simplification algorithms maximize the edge length globally, without explicitly considering local object shape. In this paper, we present a shape‐adaptive mesh simplification algorithm that locally maximizes edge length, depending on local shape. The proposed algorithm achieves shape‐adaptive simplification by iteratively maximizing edges between vertices, based on comparison with the ‘optimal’ edge lengths derived from local directional curvatures for a given error tolerance. Edge‐based processing facilitates the local shape adaptation and preserves sharp features. Experimental results demonstrate the efficacy of the proposed algorithm, by showing good visual quality and extremely small approximation error. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

A Frequency-Domain Approach to Watermarking 3D Shapes

This paper presents a robust watermarking algorithm with informed detection for 3D polygonal meshes. The algorithm is based on our previous algorithm [ 22 ] that employs mesh‐spectral analysis to modify mesh shapes in their transformed domain. This paper presents extensions to our previous algorithm so that (1) much larger meshes can be watermarked within a reasonable time, and that (2) the watermark is robust against connectivity alteration (e.g., mesh simplification), and that (3) the watermark is robust against attacks that combine similarity transformation with such other attacks as cropping, mesh simplification, and smoothing. Experiment showed that our new watermarks are resistant against mesh simplification and remeshing combined with resection, similarity transformation, and other operations..     

基于三维网格物体的鲁棒性盲水印方案

提出了一种基于3D网格物体的鲁棒性盲水印方案。先将3D物体模型转换到仿射不变空间,然后把顶点坐标转换到球面坐标,利用球面坐标来嵌入水印。由于在仿射不变空间下,3D物体模型不受平移、旋转和比例变换的影响,故该水印方案对于此类变化具有很强的鲁棒性。试验结果也证明了这一点,且该水印具有良好的不可见性。     

A robust feature-preserving semi-regular remeshing method for?triangular meshes

Benefited from the hierarchical representations, 3D models generated by semi-regular remeshing algorithms based on either global parameterization or normal displacement have more advantages for digital geometry processing applications than the ones produced from traditional isotropic remeshing algorithms. Nevertheless, while original models have sharp features or multiple self-intersecting surfaces, it is still a challenge for previous algorithms to produce a semi-regular mesh with sharp features preservation as well as high mesh regularity. Therefore, this study proposes a robust semi-regular remeshing algorithm that uses a two-step surface segmentation scheme to build the high quality base mesh, as well as the regional relationship between the original surface and subdivision domain surface. Using the regional relationship, the proposed algorithm substantially enhances the accuracy and robustness of the backward projection process of subdivision vertices based on normal displacement. Furthermore, the mesh regularity of remeshed models is improved by the quadric mesh relaxation scheme. The experimental results demonstrate the capabilities of the proposed algorithm’s semi-regular remeshing to preserve geometric features and have good triangle aspect ratio.     

一种大规模地形模型的视相关简化算法

提出了一种基于点删除的视相关简化算法。首先依据视锥准则、背离面准则和屏幕投影误差对原始网格进行可见性预处理，再对预处理后的网格依据顶点重要度大小进行点删除简化。重要度以顶点到平均平面的距离表示，在计算过程中，采用了距离加权的办法，从而进一步加强了视相关简化效果。实验表明，算法具有较高的绘制速度，并且绘制帧速率基本独立于模型的复杂度。     

Out-of-Core remeshing of large polygonal meshes

We propose an out-of-core method for creating semi-regular surface representations from large input surface meshes. Our approach is based on a streaming implementation of the MAPS remesher of Lee et al. [18]. Our remeshing procedure consists of two stages. First, a simplification process is used to obtain the base domain. During simplification, we maintain the mapping information between the input and the simplified meshes. The second stage of remeshing uses the mapping information to produce samples of the output semi-regular mesh. The out-of-core operation of our method is enabled by the synchronous streaming of a simplified mesh and the mapping information stored at the original vertices. The synchronicity of two streaming buffers is maintained using a specially designed write strategy for each buffer. Experimental results demonstrate the remeshing performance of the proposed method, as well as other applications that use the created mapping between the simplified and the original surface representations.     

Reducing complexity in polygonal meshes with view-based saliency

Salient features in 3D meshes such as small high-curvature details in the middle of largely flat regions are easily ignored by most mesh simplification methods. Nevertheless, these features can be perceived by human observers as perceptually important in CAD models. Recently, mesh saliency has been introduced to identify those visually interesting regions. In this paper, we apply view-based mesh saliency to a purely visual method for surface simplification from two approaches. In the first one, we propose a new simplification error metric that considers polygonal saliency. In the second approach, we use viewpoint saliency as a weighting factor of the quality of a viewpoint in the simplification algorithm. Our results show that saliency can improve the preservation of small but visually significant surfaces even in visual algorithms for surface simplification. However, this comes at a price, because logically some other low-saliency regions in the mesh are simplified further.