光线与多边形的快速求交

本文提出了一种新的光线与多边形的快速求交算法，以用于加速光线跟踪过程中的求交计算，这种算法不仅对凸，凹多边形（无论有无内环）都适用，而且无中间数据的存取，无除法等复杂运算，算法简单，便于在一般软硬件环境下的实现。     

允许自由旋转的2个简单多边形匹配算法

为了解决二维不规则排料问题中的匹配问题,提出了一种允许自由旋转条件下,2个无孔洞的简单多边形之间的匹配算法.该算法基于2个多边形可以自由旋转的假设,对它们之间NFP为凹或凸的情况,选择适当的匹配方法,找出一种使得其匹配后空隙尽可能小,同时保证其整体的矩形的规整度也较高的匹配方案;并用匹配空隙的利用率、匹配后整体面积的利用率,以及匹配后整体的矩形规整度等多个指标来衡量匹配的效果.实验选择于ESICUP中的部分代表性的多边形样例与多个算法进行对比实验,结果表明,该算法在任意旋转精度的要求下,均具有运行速度快的特点,可以很好地应用于服装排料等实际问题.     

求平面多边形集凸壳的方法

提出一种计算平面多边形集凸壳的快速算法。将多边形集的凸壳根据极值点划分为右上、左上、左下、右下四段,同时对集合中多边形利用其极值点提取右上、左上、左下、右下四个点列段,凸壳的每一段仅受多边形同一类点列段的影响。根据多边形集合的极值点确定四个矩形区域对四类点列段进行筛选,再按给定规则在矩形区域中进行初始找点,可求出四段凸壳初始点列,它们按顺序可确定一平面多边形,求出到此多边形的凸壳即为所求多边形集的凸壳。算法通过分段、分类、筛选等措施提高了计算效率,并且易于实现,其时间复杂度为O(N)。     

钣金冲孔中直角多边形快速干涉检验算法

针对钣金冲孔中的直角多边形孔的刀具匹配中涉检验提出了一种高效的算法.该算法先对直角多边形的顶点按逆时针方向排序,然后建立起基于空间分区思想的四向辅助图,利用四向辅助图中的规律判断待加工边的可能干涉情况,从而确定刀具的允许最大宽度.算法分析表明:该算法对直角多边形刀具涉检验具有线性的时间复杂度,有效地提高了板材加工中直角多边形孔自动刀具匹配的效率.     

寻求简单多边形凸壳的线性时间算法

本文提出在线性时间内构造简单多边形顶点凸壳的两种算法。第一个算法的基本思想是利用一种技巧对多边形顶点进行筛选，使剩余顶点的角的大小排成递增序，然后用Graham扫描方法删去非凸壳顶点，最后得到多边形凸壳的顶点序列.第二个算法不断删去多边形的凹点及新产生的 凹点，最后得到凸壳顶点序列。这两种算法简单，易于实现，时间复杂性都是O（n)。     

基于斜率的多边形内外点快速判别算法

多边形的内外点判别是图形学的一个基础算法,为了更大限度地降低其算法复杂度和运算量,提出一种基于斜率的点与多边形位置关系的快速判别法。该方法只需计算该点到多边形各顶点的斜率,然后与多边形各顶点的邻边的斜率进行比较,即可对多边形的内外点快速做出判别。该算法无需复杂的点乘、叉乘、求交、三角函数等运算,在判别过程中仅需平均2n次减法运算和n/2次的除法运算,以及一些比较运算,即可对简单n多边形的内外点做出判别。经测试,该算法快速有效。     

基于凸片段分解和格网的点在多边形中的可见边检测

检测点在多边形中的可见边是计算几何中的一种基本计算,文中对此提出一种加速算法.首先对多边形进行凸片段分解,以利用点在凸多边形中可见边的快速计算;然后利用格网结构实现由近及远的计算,避免处理被遮挡的凸片段.该算法可基于格网结构方便地进行并行处理,并可统一处理含空洞和不含空洞的多边形,其预处理时间复杂度为O(n),空间复杂度也是很低的O(n),而检测的时间复杂度在O(logn)～O(n)之间自适应变化,其中n为多边形的边数.     

基于多视图三维重建方法在实验室系统中的应用研究

针对愈渐复杂的实验室系统,采用基于多视图的三维重建方法,实现对实验室系统中设备的结构重建.通过尺度不变特征变换(SIFT)匹配算法进行特征提取和匹配,并利用随机抽样一致性算法(RANSAC)和交叉过滤法降低误匹配率;通过多视图聚簇/基于面片的三维多视角立体视觉算法(CM-VS/PMVS)获取稠密点云;利用PCL泊松曲面重构算法将稠密点云生成多边形网格,得到最终的重建图像.采用真实的实验室设备进行了验证和测试,实验结果表明,该方法可以有效快速地进行实验室设备的三维重建.     

基于夹边边对的凸多边形间快速相交检测算法

本文在对现有的相交检测算法进行研究的基础上，提出了基于夹边边对的空间平面凸多边形快速相交检测算法，为平面凸多边形间判交问题提供了一致的计算方法，并将算法的应用对象扩展到任意空间平面凸多边形。该算法分为两步：第一步，确定所要检测的两个凸多边形是否都存在相对于另一凸多边形所在平面的夹边边对，如果至少一个凸多多边形中不存在相对于另一凸多边形所在平面的夹边边对，那么立即返回两个多边形不相交；第二步，根据前面计算得到的两个凸多边形中的夹边边对，计算两组边对间对应夹边的符号距离判断两个多边形是否相交     

基于四叉树结构的数字地表模型快速生成算法设计

为了研究数字地表模型的快速生成方法，在总结传统Delaunay三角化算法的基础上，给出了一个基于四叉树结构的数字地表模型快速生成算法的详细设计，该算法的基本思想是首先利用四叉树结构来对离散点进行分割，然后对四叉树叶节点进行Delaunay三角化，再两两合并四叉树节点三角网的凸壳，以快速生成地表表格网模型，该算法是以四叉树为基本单位为实现限定边和限定多边形的快速嵌入，最后给出了算法在不同情况下的测试结果，并对测试结果进行了具体分析，给出了算法的时间效率分析和空间复杂性分析，实测数据结果表明，该算法有着较好的性能，而且也非常稳定，通过实测结果分析和算法的时间效率分析，可以得到算法的时间效率近似为O(nlog(n）），通过算法的空间复杂性分析可以看出，算法可以自动适应不同的点空间分布情况，而且采用四叉树结构也非常有利于限定边和限定多边形的嵌入。     

Partwise cross-parameterization via nonregular convex hull domains

In this paper, we propose a novel partwise framework for cross-parameterization between 3D mesh models. Unlike most existing methods that use regular parameterization domains, our framework uses nonregular approximation domains to build the cross-parameterization. Once the nonregular approximation domains are constructed for 3D models, different (and complex) input shapes are transformed into similar (and simple) shapes, thus facilitating the cross-parameterization process. Specifically, a novel nonregular domain, the convex hull, is adopted to build shape correspondence. We first construct convex hulls for each part of the segmented model, and then adopt our convex-hull cross-parameterization method to generate compatible meshes. Our method exploits properties of the convex hull, e.g., good approximation ability and linear convex representation for interior vertices. After building an initial cross-parameterization via convex-hull domains, we use compatible remeshing algorithms to achieve an accurate approximation of the target geometry and to ensure a complete surface matching. Experimental results show that the compatible meshes constructed are well suited for shape blending and other geometric applications.     

深度特征融合的非刚性三维形状局部匹配

针对海量、异构三维形状匹配与智能检索技术的需求,提出了一种基于级联卷积神经网络(F-PointCNN)深度特征融合的三维形状局部匹配方法.首先,采用特征袋模型,提出几何图像表示方法,该几何图像不仅能够有效区分同类异构的非刚性三维模型,而且能够揭示大尺度不完整三维模型的结构相似性.其次,构建级联卷积神经网络学习框架F-PointCNN,其中,BoF-CNN从几何图像中学习深度全局特征,建立融合局部特征与全局特征的点特征表示;进而对Point-CNN进行点特征的细化与提纯,生成具有丰富信息的深度融合特征,有效提高形状特征的区分性与鲁棒性.最终,通过交叉矩阵度量方法高效实现非刚性三维模型的局部形状匹配.在公开的非刚性三维模型数据库的实验结果表明,该方法提取的特征在大尺度变换的形状分类及局部形状匹配中具有更强的识别力与更高的匹配精度.     

耳廓点云形状特征匹配的路径跟随算法

路径跟随算法结合凸松弛方法与凹松弛方法,通过跟随凸凹问题的解路径,近似地求解图匹配问题,具有较高的匹配精度.将路径跟随算法用于耳廓特征图的匹配问题:首先,基于PCA方法构造耳廓点云的显著性关键点集合;然后,采用乘积型参数域上的单值二次曲面方法拟合关键点邻域内的点集,并将曲面的局部形状特征定义为耳廓的局部形状相似测度;第三,对关键点集合进行Delaunay三角剖分,得到关键点集合在三维空间内的拓扑结构图,并定义关键点图的整体结构差异测度;最后,记耳廓关键点图的组合差异测度为关键点图的整体结构差异测度与关键点上的局部形状相似测度的线性组合,并基于路径跟随算法快速求解关键点图之间的精确匹配.相关实验结果表明:与其他相关算法相比,该算法具有较高的匹配效率和匹配精度.     

图像点模式匹配的一种凸包序列的图谱方法

利用点集的凸包具有仿射不变性和局部可控性,针对图谱方法难以精确匹配旋转角度较大图像的问题,提出了图像点模式匹配的一种凸包序列的图谱方法,使得匹配在图像旋转角度较大的情形下仍具有稳定性。构建图像特征点集新的图模型（凸包）,利用改进的图谱方法对凸包进行匹配,并减小原始特征点集,迭代上述过程,通过构造凸包序列,自特征点集的外围到内部逐步匹配,得到较精确的匹配对。实现基于凸包序列的图谱方法的图像点模式匹配。实验结果表明,该方法不但能精确匹配旋转角度较小的图像,而且对于旋转角度大的图像以及多光谱图像匹配精度也较高。     

3D model retrieval using principal plane analysis and dynamic programming

Three dimensional models play an important role in many applications; the problem is how to select the appropriate models from a 3D database rapidly and accurately. In recent years, a variety of shape representations, statistical methods, and geometric algorithms have been proposed for matching 3D shapes or models. In this paper, we propose a 3D shape representation scheme based on a combination of principal plane analysis and dynamic programming. The proposed 3D shape representation scheme consists of three steps. First, a 3D model is transformed into a 2D image by projecting the vertices of the model onto its principal plane. Second, the convex hall of the 2D shape of the model is further segmented into multiple disjoint triangles using dynamic programming. Finally, for each triangle, a projection score histogram and moments are extracted as the feature vectors for similarity searching. Experimental results showed the robustness of the proposed scheme, which resists translation, rotation, scaling, noise, and destructive attacks. The proposed 3D model retrieval method performs fairly well in retrieving models having similar characteristics from a database of 3D models.     

一种起始点无关的小波系数形状匹配

小波变换的多分辨率特征使其在计算机视觉中得到广泛的应用,在形状匹配中,小波变换对起始点的依赖制约了小波变换的应用。为了克服小波变换对起始点的依赖,引入Zernike矩,提出一种起始点无关的小波系数形状匹配算法。对输入图像进行预处理后提取目标轮廓,生成具有平移、尺度不变的形状链状表达,并通过小波变换进行多尺度分析。最后计算各个尺度下的各阶Zernike矩,来解决小波变换的起始点问题,实现形状表达的旋转不变性。实验结果表明该算法适用于轮廓较明显的目标,同时具有速度快、精度高、鲁棒性强的优点。     

Continuous Matching via Vector Field Flow

We present a new method for non‐rigid shape matching designed to enforce continuity of the resulting correspondence. Our method is based on the recently proposed functional map representation, which allows efficient manipulation and inference but often fails to provide a continuous point‐to‐point mapping. We address this problem by exploiting the connection between the operator representation of mappings and flows of vector fields. In particular, starting from an arbitrary continuous map between two surfaces we find an optimal flow that makes the final correspondence operator as close as possible to the initial functional map. Our method also helps to address the symmetric ambiguity problem inherent in many intrinsic correspondence methods when matching symmetric shapes. We provide practical and theoretical results showing that our method can be used to obtain an orientation preserving or reversing map starting from a functional map that represents the mixture of the two. We also show how this method can be used to improve the quality of maps produced by existing shape matching methods, and compare the resulting map's continuity with results obtained by other operator‐based techniques.     

Recognition of Bangla compound characters using structural decomposition

In this paper we propose a novel character recognition method for Bangla compound characters. Accurate recognition of compound characters is a difficult problem due to their complex shapes. Our strategy is to decompose a compound character into skeletal segments. The compound character is then recognized by extracting the convex shape primitives and using a template matching scheme. The novelty of our approach lies in the formulation of appropriate rules of character decomposition for segmenting the character skeleton into stroke segments and then grouping them for extraction of meaningful shape components. Our technique is applicable to both printed and handwritten characters. The proposed method performs well for complex-shaped compound characters, which were confusing to the existing methods.     

Dissimilarity between two skeletal trees in a context

Skeletal trees are commonly used in order to express geometric properties of the shape. Accordingly, tree-edit distance is used to compute a dissimilarity between two given shapes. We present a new tree-edit based shape matching method which uses a recent coarse skeleton representation. The coarse skeleton representation allows us to represent both shapes and shape categories in the form of depth-1 trees. Consequently, we can easily integrate the influence of the categories into shape dissimilarity measurements. The new dissimilarity measure gives a better within group versus between group separation, and it mimics the asymmetric nature of human similarity judgements.