一种新的边折叠网格模型简化算法

在边折叠简化方法的基础上,提出一种用体积变化的平方作为误差度量的三角网格简化算法。算法中引入三角形法向约束因子的概念,并把它嵌入到边折叠误差矩阵中;能够自适应地分配简化网格的疏密,保持更多的模型几何特征。实验表明,该算法简化误差低,模型视觉质量高,简化效果较好。     

体积平方度量下的特征保持网格简化方法

提出了一种基于体积平方度量的三角形折叠网格简化新方法.新方法通过极小化误差目标函数简化三角形网格.简化误差定义为三角形简化后产生的网格模型平方体积变化,并以三角形几何形状因子和法向因子作为约束.简化误差的表示形式为一个二次目标函数,因此,每次简化后三角形网格的新顶点是一个线性问题的解.与目前简化效率最好的QEM方法相比,新方法不增加算法复杂度.如果被简化的三角形是强特征三角形,则用其高斯曲率最大的顶点作为新顶点,以保持原始模型的细节特征;对于非强特征三角形,新顶点用极小化折叠误差确定.对于边界三角形,新顶点的位置由不同于内部三角形的方法进行计算,保持了网格的边界特征.最后用实例说明新方法的有效性.     

基于特征保留简化的视点相关递进网格方法

人的视觉系统通常对模型的高曲率变化区域、尖角、边界等几何特格外敏感.本文在三角形折叠简化算法的基础上引入三角形的曲率因子,并将其加入到误差测量中,简化模型不仅保留了重要的几何特征,还根据模型表面的曲率变化合理的分配三角面片.本文还给出了一种基于三角形折叠的视点相关递进网格(VDMP)的构造方法.     

一种边折叠三角网格简化算法

针对目前自动网格简化算法在大规模简化时往往丢失模型重要几何特征的问题,该文提出了一种改进的边折叠三角网格简化算法。在Garland算法基础上引入三角形重要度概念,并加入到误差测度中,使得二次误差测度不仅能够度量距离偏差,而且能够反映模型局部表面几何变化。实验结果表明新的算法在保持二次误差测度快速特点的同时,使得简化模型在较低分辨率下能够保持更多的重要几何特征,有效地降低了视觉失真。     

多尺度非均匀渐进网格压缩编码研究

在边折叠网格简化算法的基础上,提出一种多尺度非均匀渐进网格简化算法。该算法不仅简化速度快,而且克服了传统算法在简化模型中网格分布均匀、无法突出模型重要特征的不足之处。该算法在模型的折叠、拐角、凹凸等表达特征的地方,采用的三角形网格面积较小、数量较多;而在平坦等不突出模型特征区域的三角形网格面积较大、数量较少。在简化程度较大的情况下仍然能够保持原始网格的几何特征和视觉特征。由于采用了渐进式多尺度的编码方式,再通过流式传输技术,就可以使采用这种算法生成的模型文件高效、方便地以渐进方式在网络上进行传输。     

一种改进的基于三角形折叠的模型简化算法

本文基于三角形折叠的网格简化算法,提出了一种改进的算法。算法计算三角形顶点到相关平均平面的距离的最大值,结合三角形的面积、表面属性和预设特征给出三角形权值,确定折叠次序;并能够用累进网格实现连续的层次细节模型。该算法实现简单,运算速度快,而且能够有效保持模型预设的重要特征。     

一种三角形折叠网格模型简化的改进算法

目前提出的网格简化算法中,三角形折叠简化方法是一种主要的简化方法,在网格压缩、多细节层次模型生成、递进网格构造中得到了广泛地应用。提出一种基于三角形折叠的网格模型简化改进算法,在基于三角形折叠的基础上,在计算三角形折叠误差代价时引入局部区域面积度量参数,有效控制简化模型的三角形折叠顺序。实验表明,采用该文算法简化后的模型更逼近原始模型。     

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。     

结合局部区域特征的自适应简化率网格简化算法

现有的网格简化算法通常要求人为给定模型整体简化率或者设置几何、颜色、纹理等属性的约束,如何合理地设置这些阈值对没有经验的用户来说比较困难.文中结合监督学习的方法,构建一个多层感知机模型来实现局部区域自适应简化率的预测.该感知机模型能根据网格模型不同区域的局部几何特性,提取出相应的特征,并根据这些特征进行分类.不同的分类对应着不同的简化率,从而在简化网格时根据分类对不同区域设置不同的法线偏差阈值,实现自适应简化率的网格简化算法.为证明该算法的效果,实验中选择不同种类和复杂程度的三维网格模型进行了简化,并与基于QEM能量函数的简化算法进行了整体简化率和简化后的视觉效果的实验对比,结果表明,相对于传统整体简化算法,这种基于局部区域特征设置自适应简化终止条件阈值的简化算法,能有效地根据几何特性对网格进行自适应简化,在保持模型细节的同时,提高了网格的整体简化率.     

基于曲面拟合的三角形网格简化

针对有限元网格简化问题,将边折叠和三角形折叠算法相结合,提出一种基于曲面拟合的网格简化方法。根据节点离散度识别网格特征,对具有不同特征的部位采用不同的简化策略从而实现自适应变密度网格简化。按长高比最优原则对合并后的节点进行预测,运用曲面拟合技术最终确定合并后的节点,达到优化网格和保持网格特征的目的。实验结果证明,该方法能在保证网格质量的前提下有效简化网格模型,提高CAE分析速度,最多可缩短75%的计算时间。     

基于三角网下的仿射不变几何约束的图像匹配算法研究

针对当前图像匹配方法在进行图像匹配时,主要通过度量特征向量之间的距离来完成图像匹配,导致算法鲁棒性差、误配率较高及效率较低等不足,本文提出了基于三角网下的仿射不变几何约束的图像匹配算法。首先,在尺度空间上通过Hessian矩阵对特征点进行检测,利用子块的三角特征与对角特征对SUR机制进行改进,用以生成新的特征描述子,并通过定义阀值评估策略,对图像特征点匹配,从而生成了初始匹配点;然后,引入 三角网,对初始匹配点进行聚类,以获取匹配三角形,将三角形以外的无效特征点剔除。最后,引入仿射不变几何约束,对匹配三角形进行细化,通过细化的匹配三角形获取最终的匹配特征点,有效剔除误配点,进一步提高配准精度。仿真结果表明,与当前图像匹配算法相比,本文算法具有更好的鲁棒性,且其具有更佳的匹配精度与效率,有效剔除了误配点。     

多分辨率三维建筑群建模与实时绘制技术

将纹理特征分析技术引入到多边形网格建模中,提出一种基于高程特征值进行曲面细分的算法以构建多分辨率虚拟建筑群模型。该算法给出一种三角边与纹理特征曲线相交的三角面分裂方法构造自适应细分三角网格。通过设计细分三角网格的二叉树数据结构和开发测试程序进行测试,表明该算法具有自适应网格速度快和保持几何特征较好的特点,可以满足在PC机上实现三维建筑群的大范围建模和实时交互显示要求。     

基于凸凹性的网格细分综合优化

实际工程中希望表示物体的三角形网格形状优良,同时拓扑逼近真实曲面。但是对非均匀离散点云重建得到的网格进行优化时,这两个标准常常是相互矛盾的。该文针对在实际工程中遇见的这个问题,提出一种结合全局特征以及局部特性的细分算法。该算法避免了一般细分方法对凹区域处理出现的折叠现象,可以获取三角形形状和空间拓扑的综合优化解。最后通过对于工程应用实例的细分计算,得到了与原始网格拓扑一致,但更逼近真实曲面的细分优化网格,表明了所提出简化算法的有效性。     

点与三角形位置关系对三角网格拓扑的影响

逐点添加、局部优化的Watson算法和局部变换法是生成大规模离散点集Delaunay三角网格的常用方法。点与三角形位置关系判别和三角形外接圆包含点的测试分别是局部变换法和Watson算法正确生成Delaunay三角网格的重要环节。计算误差会导致点与三角形位置关系以及三角形外接圆包含点的错误判别,从而生成几何拓扑关系不正确的三角网格。采用相对位置坐标可以提高面积坐标和外接圆圆心、半径的计算精度。以等高线地图采集的地形数据为例,用改进的算法生成了包含393252个离散点的Delaunay三角网格。     

Object tracking using the Gabor wavelet transform and the golden section algorithm

The paper presents an object tracking method for object-based video processing which uses a two-dimensional (2D) Gabor wavelet transform (GWT) and a 2D golden section algorithm. An object in the current frame is modeled by local features from a number of the selected feature points, and the global placement of these feature points. The feature points are stochastically selected based on the energy of their GWT coefficients. Points with higher energy have a higher probability of being selected since they are visually more important. The amplitudes of the GWT coefficients of a feature point are then used as the local feature. The global placement of the feature points is determined by a 2D mesh whose feature is the area of the triangles formed by the feature points. In this way, a local feature is represented by a GWT coefficient amplitude vector, and a global feature is represented by a triangle area vector. One advantage of the 2D mesh is that the direction of its triangle area vector is invariant to affine transform. Consequently, the similarity between two local features or two global features can be defined as a function of the angle and the length ratio between two vectors, and the overall similarity between two objects is a weighted sum of the local and global similarities. In order to find the corresponding object in the next frame, the 2D golden section algorithm is employed. Our results show that the method is robust to object deformation and supports object tracking in noisy video sequences.     

一种基于特征点识别的曲线离散化方法

提出了曲线局部特征点的概念，并根据平行线原理给出了一种快速求取特征点的算法。通过对局部特征点进行优化，得到所需的局部特征点集，实现了曲线的离散。该方法在离散过程中充分考虑了离散精度误差与逼近弦长对后续三角化质量的影响。实验结果表明，由这些特征点组成的多边形可较好地逼近曲线，算法效率较高。     

A new feature-preserving mesh-smoothing algorithm

We present a novel mesh denoising and smoothing method in this paper. Our approach starts by estimating the principal curvatures and mesh saliency value for each vertex. Then, we calculate the uniform principal curvature of each vertex based on the weighted average of local principal curvatures. After that, we use the weighted bi-quadratic Bézier surface to fit the neighborhood of each vertex using the least-square method and obtain the new vertex position by adjusting the parameters of the fitting surface. Experiments show that our smoothing method preserves the geometric feature of the original mesh model efficiently. Our approach also prevents the volume shrinkage of the input mesh and obtains smooth boundaries for non-closed mesh models.     

Combinatorial manifold mesh reconstruction and optimization from unorganized points with arbitrary topology

In this paper, a novel approach is proposed to reliably reconstruct the geometric shape of a physically existing object based on unorganized point cloud sampled from its boundary surface. The proposed approach is composed of two steps. In the first step, triangle mesh structure is reconstructed as a continuous manifold surface by imposing explicit relationship among the discrete data points. For efficient reconstruction, a growing procedure is employed to build the 2-manifold directly without intermediate 3D representation. Local and global topological operations with ensured completeness and soundness are defined to incrementally construct the 2-manifold with arbitrary topology. In addition, a novel criterion is proposed to control the growing process for ensured geometric integrity and automatic boundary detection with a non-metric threshold. The reconstructed manifold surface captures the object topology with the built-in combinatorial structure and approximates the object geometry to the first order. In the second step, new methods are proposed to efficiently obtain reliable curvature estimation for both the object surface and the reconstructed mesh surface. The combinatorial structure of the triangle mesh is then optimized by changing its local topology to minimize the curvature difference between the two surfaces. The optimized triangle mesh achieves second order approximation to the object geometry and can serve as a basis for many applications including virtual reality, computer vision, and reverse engineering.     

Geometry seam carving

We present a novel approach to feature-aware mesh deformation. Previous mesh editing methods are based on an elastic deformation model and thus tend to uniformly distribute the distortion in a least-squares sense over the entire deformation region. Recent results from image resizing, however, show that discrete local modifications such as deleting or adding connected seams of image pixels in regions with low saliency lead to far superior preservation of local features compared to uniform scaling — the image retargeting analog to least-squares mesh deformation. Hence, we propose a discrete mesh editing scheme that combines elastic as well as plastic deformation (in regions with little geometric detail) by transferring the concept of seam carving from image retargeting to the mesh deformation scenario. A geometry seam consists of a connected strip of triangles within the mesh’s deformation region. By collapsing or splitting the interior edges of this strip, we perform a deletion or insertion operation that is equivalent to image seam carving and can be interpreted as a local plastic deformation. We use a feature measure to rate the geometric saliency of each triangle in the mesh and a well-adjusted distortion measure to determine where the current mesh distortion asks for plastic deformations, i.e., for deletion or insertion of geometry seams. Precomputing a fixed set of low-saliency seams in the deformation region allows us to perform fast seam deletion and insertion operations in a predetermined order such that the local mesh modifications are properly restored when a mesh editing operation is (partially) undone. Geometry seam carving hence enables the deformation of a given mesh in a way that causes stronger distortion in homogeneous mesh regions while salient features are preserved much better.     

Skeleton-based Variational Mesh Deformations

In this paper, a new free-form shape deformation approach is proposed. We combine a skeleton-based mesh deformation technique with discrete differential coordinates in order to create natural-looking global shape deformations. Given a triangle mesh, we first extract a skeletal mesh, a two-sided Voronoibased approximation of the medial axis. Next the skeletal mesh is modified by free-form deformations. Then a desired global shape deformation is obtained by reconstructing the shape corresponding to the deformed skeletal mesh. The reconstruction is based on using discrete differential coordinates. Our method preserves fine geometric details and original shape thickness because of using discrete differential coordinates and skeleton-based deformations. We also develop a new mesh evolution technique which allow us to eliminate possible global and local self-intersections of the deformed mesh while preserving fine geometric details. Finally, we present a multi-resolution version of our approach in order to simplify and accelerate the deformation process. In addition, interesting links between the proposed free-form shape deformation technique and classical and modern results in the differential geometry of sphere congruences are established and discussed.