关节特征约束的3维模型骨架提取算法

根据多分辨率Reeb图（MRG）的原理,提出一种基于关节特征约束的骨架优化算法。它克服了基于曲率约束提取骨架方法中逐点计算顶点的曲率约束轮廓的低效性,通过分析网格顶点的离散高斯曲率,获取模型表面上具有凹陷特性的双曲极值点作为约束点, 进行关节特征区域的有效提取。进而增加关节特性点,优化MRG骨架。实验结果表明,本方法有效地突出了模型的拓扑分支特征以及模型表面的细节,提高了骨架提取的精度和效率。     

交互式轮廓线骨架的提取

为精确抽取自由绘制的二维轮廓线骨架,提出了一种新的自适应骨架提取方法.将用户绘制的轮廓线,采用离散曲率约束,自适应调整步长,提取样点,进行最小二乘法实现样条曲线拟合,有效地突出了曲线形状特征;依据曲线模型的特征点,改进约束化三角剖分方法,高效地重建三角网格的拓扑结构;基于Voronoi图优化提取轮廓线骨架.实验结果表明了该算法的高效性和鲁棒性.     

基于表面及切向属性的点模型骨架提取方法

针对目前在离散点云模型以及低分辨率模型上提取骨架算法存在的局限性,提出一种基于表面及切向属性(attributesofsurfaceandtangency,AST)的新方法.首先给出两个属性定义及其计算方式.然后基于上述属性通过表面光滑收缩和骨架吸引的双重作用达到模型的几何收缩,连接迭代收缩完成后得到的中心点,从而得到模型的骨架.实验表明:该方法得到的骨架能较好地表达原始模型的几何特征和拓扑结构,在缺少连接信息和低分辨率的情况下也能获得较好的骨架提取效果.     

一种MRG骨架树的三维模型检索方法

根据多分辨率Reeb图（MRG）原理,依据测地线函数分割模型,有效地提取反映模型拓扑结构的Reeb图骨架。进而,映射Reeb图为树结构,分析各骨架节点的拓扑属性,并提取其相应区域的离散曲率信息作为局部形状属性。最终,有效结合拓扑和几何形状特征,计算模型的相差度。该方法突出了模型的总体拓扑特征以及模型的表面细节,一系列的实验结果验证了其高效性、鲁棒性。     

基于轮廓线的三维网格曲面绘制

在融合了交互式轮廓绘制与网格造型技术的基础上,提出了一种快速三维网格曲面建模方法.根据绘制轮廓线的特征点分布,进行约束化三角网格剖分,提取二维轮廓线的骨架;选取骨架点和采样点投影到三维空间椭球曲面,并引入二面角原则,优化了空间离散数据点的三角化算法;最后缝合骨架点,获得三维网格曲面表示.实验结果表明了该算法的直观性、高效性.     

基于区域分割的点云骨架提取算法

针对L_1中值骨架提取方法存在迭代次数较多、相邻区域较紧密时骨架易跨越区域等问题,提出一种分区提取骨架的算法。结合点云区域的连通性及局部相关性,采用马尔科夫随机场模型,将给定点云分割成不同区域。在相同标号的区域根据区域大小和点集数自适应地计算不同的初始收缩邻域尺度,用L_1中值不断收缩迭代提取各区域的骨架分支,通过主成分分析及连接角判定骨架连接方式,并根据该连接方式将骨架分支连接成完整的点云骨架。实验结果表明,该算法能够自适应地提取点云骨架,减少点云收缩的迭代次数,保持模型原有的拓扑结构,对于含有区域紧密度不均匀的模型有较好的效果。     

基于非脊点下降算子的多尺度骨架化算法

骨架是目标表示的一种重要方式.提出了一种基于区域标记直接从灰度图像中提取的骨架的新算法.算法对脊点概念作了补充撰述,组合利用了目标的轮廓与区域信息,采用了层次化的处理策略,适用于稳健地提取规则和不规则目标完整的多尺度骨架.所提取的骨架彼此连通、单像素宽并与原始图像拓扑一致.将算法应用于实际图像,检测到了与人视觉感知相一致的目标骨架.     

一种改进的基于特征点求解的骨架提取算法

基于特征点求解和Reeb图思想,实现了一种新的骨架提取算法。首先求取模型特征点集,以特征点为计算依据,根据三角网格中每个顶点与特征点的不同对应关系得到网格分支点,聚合成一系列骨架点,依据骨架点携带的拓扑信息,连接拓扑相邻的骨架点得到模型骨架。采用了改进的特征点提取算法,其时间复杂度由O（n^3）提高到了O（n^2log（n））,实验表明算法能够快速提取骨架,针对一般模型的骨架提取效果令人满意。     

离散曲率约束的三角网格模型拓扑分割算法

针对三角形网格模型简化中保持细节特征的要求,提出了依据离散曲率划分三角网格顶点的特性,并结合区域增长法自适应地确定拓扑分支的优化算法.每个顶点根据其相邻面片顶点的曲率值划分属性区域,并在区域生长过程中重复选择K-ring碟形区域中具有相似属性值的顶点作为种子.为了有效地探索凸凹形状区域,以曲率极值点作为初始点,提出了有效的区域增长及合并的策略,突出了模型的局部特征和拓扑结构.最后通过一系列实验验证了该算法的快捷性.     

基于对称点对序列的带状图骨架化算法研究

文中提出了一种基于离散轮廓的对称点对序列的骨架化算法。首先提出带状图像的对称点对序列的概念,它是通过轮廓离散点的Delaunay三角剖分而获得的,并将这个序列应用于带状图的骨架化算法中。在带状图的交叉区域利用三角剖分对偶图模型对该序列进行归并重构,从而得到交叉区域不畸变的骨架。实验表明,该算法充分利用了带状图的全局和局部信息,产生的骨架准确地反映了带状图像间的拓扑关系。     

Representation and reconstruction of polygons and polyhedra using Hierarchical Extended Gaussian Images

In this paper, two new representation schemes called the Branched Gaussian Image (BGI) and the Hierarchical Extended Gaussian Image (HEGI) are proposed. They can be used for uniquely representing both concave and convex, two-dimensional figures and three-dimensional objects. The representation by the Branched Gaussian Image involves several Gaussian spheres connected by branches where the traversing directions might be different. Examples showing how the use of the BGI enables us to achieve the mapping and inverse mapping of concave polygons and polyhedra uniquely are presented. The Gaussian spheres in the BGI can be organized into a tree-like hierarchical structure known as the Hierarchical Extended Gaussian Image. A general procedure for mapping a polygon or polyhedron to its HEGI representation is described. An approach for reconstructing concave polygons from Branched Gaussian Images is presented. The reconstruction of a concave polyhedron from its Hierarchical Extended Gaussian Images by using an iterative method or a closed-form method for each convex component is also described.     

用高斯·拉普拉斯·过零法计算遥感影像中不同类区域边界位置的精度

高斯·拉普拉斯·过零法是目前计算机图像处理中普遍用来计算遥感影像中不同类区域的边界位置的方法。对该方法计算得到的边界位置的精度作了分析计算，结果表明，边界计算的精度取决于所用的高斯特征尺度σ和实际边界的形状，后者的影响是局地性的。在实际计算中可以忽略掉距离超过４σ的那些边界段的影响。     

On the degree of boundary slip over nonplanar surfaces

The breakdown of the no-slip boundary condition at a fluid–solid interface has been recognized in micro/nanofluidics for many years. However, the relationship between the curvature of the surface and the degree of boundary slip has not been understood sufficiently well. The present study reveals that the degree of slip depends effectively on the surface curvature, which is having an opposing effect over rotating concave and convex surfaces. The results show that as surface curvature increases, the boundary slip becomes negligible over a concave surface, while it becomes increasingly important over a convex surface. In addition, boundary slip formulae are proposed that can accurately predict the boundary slips over convex and concave surfaces. These formulae are found to be in very good agreement with DSMC data for a range of accommodation coefficients and boundary curvatures. The present study then explains the mechanism of the intriguing phenomenon of velocity inversion which has, until the present study, often been mistakenly attributed solely to the effects of boundary curvature.     

综合曲率约束的在线网格模型分割方法研究

针对现有三角网格模型块分割方法普遍存在计算复杂度高,无法体现工程意义,综合效果不理想,不满足Web环境下高效快速分割等问题,提出一种面向Web环境的简单高效的三角网格模型分割方法。根据高斯曲率和平均曲率特性划分出网格模型的凹区域,在凹区域中依据最小负曲率阈值提取凹特征区域,结合区域中心特征线提取方法以及边界线闭合和优化算法构造出闭合分割线,通过分割线将三角网格模型分割成有意义的分块。依托开源数字几何处理软件MeshLabJS,运用WebGL的几何处理及图形渲染功能,在普林斯顿标准数据集和COSEG形状数据集上进行算法测试,验证所提方法能够在Web环境下快速、高效、有意义地分割三维模型。     

基于高斯平滑的自适应角点检测

文中算法首先在曲线尺度空间中通过高斯平滑以消除噪声；然后再基于自适应弯曲度计算和角点筛选准则确定角点，该算法不需要预先输入参数，具有较好的抗干扰性，实现简单有效。     

Mesh segmentation driven by Gaussian curvature

Mesh parameterization is a fundamental problem in computer graphics as it allows for texture mapping and facilitates many mesh processing tasks. Although there exists a variety of good parameterization methods for meshes that are topologically equivalent to a disk, the segmentation into nicely parameterizable charts of higher genus meshes has been studied less. In this paper we propose a new segmentation method for the generation of charts that can be flattened efficiently. The integrated Gaussian curvature is used to measure the developability of a chart, and a robust and simple scheme is proposed to integrate the Gaussian curvature. The segmentation approach evenly distributes Gaussian curvature over the charts and automatically ensures a disklike topology of each chart. For numerical stability, we use an area on the Gauss map to represent Gaussian curvature. The resulting parameterization shows that charts generated in this way have less distortion compared to charts generated by other methods.     

Sign of Gaussian curvature from curve orientation in photometricspace

We compute the sign of Gaussian curvature using a purely geometric definition. Consider a point p on a smooth surface S and a closed curve γ on S which encloses p. The image of γ on the unit normal Gaussian sphere is a new curve β. The Gaussian curvature at p is defined as the ratio of the area enclosed by γ over the area enclosed by β as γ contracts to p. The sign of Gaussian curvature at p is determined by the relative orientations of the closed curves γ and β. We directly compute the relative orientation of two such curves from intensity data. We employ three unknown illumination conditions to create a photometric scatter plot. This plot is in one-to-one correspondence with the subset of the unit Gaussian sphere containing the mutually illuminated surface normal. This permits direct computation of the sign of Gaussian curvature without the recovery of surface normals. Our method is albedo invariant. We assume diffuse reflectance, but the nature of the diffuse reflectance can be general and unknown. Error analysis on simulated images shows the accuracy of our technique. We also demonstrate the performance of this methodology on empirical data     

Directable Weathering of Concave Rock Using Curvature Estimation

We address the problem of directable weathering of exposed concave rock for use in computer-generated animation or games. Previous weathering models that admit concave surfaces are computationally inefficient and difficult to control. In nature, the spheroidal and cavernous weathering rates depend on the surface curvature. Spheroidal weathering is fastest in areas with large positive mean curvature and cavernous weathering is fastest in areas with large negative mean curvature. We simulate both processes using an approximation of mean curvature on a voxel grid. Both weathering rates are also influenced by rock durability. The user controls rock durability by editing a durability graph before and during weathering simulation. Simulations of rockfall and colluvium deposition further improve realism. The profile of the final weathered rock matches the shape of the durability graph up to the effects of weathering and colluvium deposition. We demonstrate the top-down directability and visual plausibility of the resulting model through a series of screenshots and rendered images. The results include the weathering of a cube into a sphere and of a sheltered inside corner into a cavern as predicted by the underlying geomorphological models.