物体变形的广义形态变换方法

将广义形态变换理论用于非刚体运动的描述和内插，通过对非刚体的凸剖分把非刚体的运动分解为非刚体的变形与子凸集的旋转，提出物体近似骨架的概念；通过近似骨架实现子凸集匹配，实现了任意非同拓扑结构(包括有孔及凹多面体)物体的变形．广义形态变换具有基于体元的变形方法和基于边界形状的变形方法的优点，同时克服了它们的缺点．实验表明，该方法变形物体边界光滑、定位精度高、计算速度快，可应用于CAD、虚拟现实和生物医学工程。     

一种全局优化的多边形变形方法及应用

通过对多边形的凸部分,并建立２种不同多边形的凸子集映射,提出了一种全新的基于凸多边形的全局优化方法,解决了任意非同拓扑结构（包括有孔及凸边形）的变形问题。理论上证明了此方法的正确性,讨论了不同凸剖分对变形的影响。实验证明此方法变形效果自然、质量好、速度快、自动化程度高,并可用于汉字的合成与二维动画关键帧的内插。     

基于Delaunay三角剖分密度度量的聚类算法

针对K-means聚类算法无法正确识别非凸形状簇的缺陷,提出一种基于Delaunay三角剖分密度度量的聚类方法,利用Delaunay三角剖分图的最近性、邻接性等优良特性来反映数据自身特点并进行密度度量,同时以混沌优化方法实现聚类目标函数的全局优化,达到全局最小解。实验结果证明,基于Delaunay三角剖分密度度量方式的聚类算法能发现任意非凸形状簇。     

汉字字形的凸剖分变形及合成

文中提出了一种全新的基于凸多边形变形的汉字字形自动生成方法. 通过对字体的凸剖分,把字体分解成若干个子凸多边形,并经过全局优化迭代建立两种不同字体的子凸多边形间的匹配关系,计算两匹配子凸多边形的形态和,再进行合并,则得到合成后的字体.理论上证明了此方法的正确性,讨论了不同剖分对生成字形的影响,可解决不同构字体间的合成问题,通过不同的结构元的形态变换,实现不同字体的衍生.实验证明此方法生成的汉字字形多,质量好,自动化程度高,并可用于三维字体生成.     

约束三角剖分在雨量等值线的应用

雨量等值线在水文、防汛领域应用广泛,Delaunay三角剖分具有空外接圆和最大的最小角度两个良好性质,对于非规则分布的离散点数据进行三角剖分内插是生成等值线的最常用的算法,但实际应用中往往都不是凸壳进行三角化,而是有限定边(或限定点)对三角剖分进行约束。该文在标准Delaunay三角剖分基础上,分析了逐点插入法的基本原理,基于此提出了一种解决有限定边的约束三角网格剖分生成等值线的方法,给出了限定边进行三角剖分的算法,同时对边界采用网格加密和邻域内插算子进行边界附件插值,提高等值线的边界拟合精度,并在雨量等值线生成中得到较好应用。     

约束三角剖分在雨量等值线的应用

雨量等值线在水文、防汛领域应用广泛,Delaunay三角剖分具有空外接圆和最大的最小角度两个良好性质,对于非规则分布的离散点数据进行三角剖分内插是生成等值线的最常用的算法,但实际应用中往往都术是凸壳进行三角化,而是有限定边（或限定点）对三角剖分进行约束。该文在标准Delaunay三角剖分基础上,分析了逐点插入法的基本原理,基于此提出了一种解决有限定边的约束三角网格剖分生成等值线的方法,给出了限定边进行三角剖分的算法,同时对边界采用网格加密和邻域内插算子进行边界附件插值,提高等值线的边界拟合精度,并在雨量等值线生成中得到较好应用。     

基于弦内角余切参数的三角剖分算法

为提高三角剖分质量和优化速度，提出了基于弦内角余切参数的三角剖分优化算法，三角剖分优化问题实质上是凸四边形的对角线选择问题，在两个三角形组成的凸四边形中，将弦内角映射成弦内角的余切值，经过证明弦内角余切值与弦内角具有等价的三角剖分优化特性，因此三角剖分局部优化转化为余切参数的判别问题。理论分析与实践证明。该方法实现起来容易，且映射参数计算简洁方便。弦内角余切参数方法避免了传统方法所必需的角度、半径距离计算，明显地提高了计算速度。     

用空间形状优化标准完成散乱数据的三角剖分

本文提出了一种三维散乱数据三角剖分时的空间形状优化标准，它可以保证三角剖分的空间形状变化均匀，具有保凸性，并且基于此三角剖分上的插值曲面比较光顺。     

基于弦内角映射参数的多边形三角剖分快速优化

为提高三角剖分质量及其优化的速度，提出了基于弦内角映射参数的三角剖分优化算法，三角剖分优化问题实质是凸四边形的对角线选择问题，在两个三角形组成的凸四边形中，将弦内角映射成两三角形公共边中垂线上的映射参数值，经过证明映射参数与弦内角具有等价的三角剖分优化判别特性，因此三角剖分局部优化转化为映射参数的判别问题。理论分析与实践表明，该方法实现非常容易，且映射参数计算简洁方便、快捷可靠，弦内角映射参数判别方法避免了传统方法所必需的角度、半径距离计算，明显地提高了计算效率。     

基于变分的图像恢复算法及收敛性

提出了一种保持边缘的正则化图像恢复算法,该方法可有效地用于求解线性逆问题的 非凸优化过程.通过对正则化函数及相应泛函性质的理论分析,得出了使泛函达到最小的正则 化函数表达式;引入一个与原非凸泛函相应的二元泛函,将非凸优化问题转化为本质上的凸优 化问题,采用松弛迭代算法获得非凸优化问题的局部极小解;证明了所提出的算法是全局收敛 的.通过实验验证了算法的有效性.     

Approach to Nonrigid Body Metamorphosis UsingGeneralized Morph-translation

An approach of morphing by decomposing two objects into sets of individual convex sub objects respectively and contructing the mapping between two sets is presented The Minkvski addition of two convex sub-objects according to their mapping ralationship is calculated, then all the Minkovski additions are combined to obtain the final result. Nonrigid body motion can be divided into nonrigid body metamorphosis and rigid body rotation A novel method for describing nonrigid body motion based on generalized morph-translation is proposed. This method can solve the metamorphosis problem of two non-homotopic objects. Experiments show tha this method can generate natural, high quality metamorphosis results with simple computation. This method can also be used in interpolation between two keyframes in 2D and 3D computer animation automatically.     

基于形态学的新的汉字字形自动生成方法

电子印刷,桌面出版,艺术,广告等领域对不同风格汉字的需求,迫切需求一种自动的汉字字形生成方法。传统方法只适用于两种字形相关不大的字体进行合成,并且需人干预,本文通过对字体的凸剖分,并建立两种不同字体的子凸集映射,提出了一种全新的基于形态变换的汉字形自动生成方法,     

Polyhedral Objects Metamorphosis Using Convex Decomposition and Morphology

A new technique is presented for computing continuous shape transformations between polyhedral objects. The polyhedron shape transformations can be divided into polyhedron metamorphosis and bi-directional local rigid body rotation transformation. By decomposing two objects into sets of individual convex sub-objects respectively, and establishing the matching between two subsets, the approach can solve the metamorphosis problem of two non-homotopic objects (including concave objects and holey objects). Compared with other methods, this metamorphosis algorithm can be executed automatically for arbitrary polyhedrons and no need user interaction. The user has the ability to choose an automatic matching or to select interactively pairs of corresponding matching convex subsets to obtain special effects. Experiments show that this method can generate natural, high-fidelity, eye-pleasing metamorphosis results with simple computation.     

一个加权剖分简单多边形为凸多边形的算法

本文提出了可以为简单多边形中的可视点对建立一种权函数，这种权函数容易计算，可以反映在点时间加入剖分线时获得剖分在形态质量方面的性质，因此可以用来引导剖分，描述了一个利用这种权函数加权剖分简单多边形凸多边形的算法来实现步骤，讨论了所建立算法的生质，结果表明算法既能够使剖分得到凸多边形数目较少，又能够使得的部分有较好的形态质量，因此有很好的实用性。     

Shape blending using the star-skeleton representation

Shape blending, the metamorphosis of one shape into another, is a central problem in two-dimensional computer animation. In spite of impressive uses of morphing in film and video productions, the problem is far from solved. In particular, shape blending still requires considerable manual effort. By decomposing two polygons into equivalent star-shaped pieces and a connecting skeleton, the paper presents a blending method which can represent polygon interiors, not just boundaries, and generate high-quality results with minimal user intervention     

Recognition and inspection of two-dimensional industrial parts using subpolygons

A model-based scene analysis for the recognition of imperfect and possibly occluded two-dimensional (2D) industrial parts is described. The means of recognition leads reliably to the correct association of the sides making up the unknown object to those of the model. Both the scene polygon and the model are divided into pairs of complementary subpolygons. This is done by a cutting line drawn parallel and close to a selected side. The subpolygons from the object are compared to all possible subpolygons from the model. Invariant moments are used in the analysis. A matching process using clusters of mutually consistent features is used to hypothesize the identity of the object. Examples are given to illustrate the method.     

Matching point features under small nonrigid motion

This paper describes a method for matching point features between images of objects that have undergone small nonrigid motion. Feature points are assumed to be available and, given a properly extracted set of feature points, a robust matching is established under the condition that the local nonrigid motion of each point is restricted to a circle of radius δ, where δ is not too large. This is in contrast to other techniques for point matching which assume either rigid motion or nonrigid motion of a known kind. The point matching problem is viewed in terms of weighted bipartite graph matching. In order to account for the possibility that the feature selector can be imprecise, we incorporate a greedy matching strategy with the weighted graph matching algorithm. Our algorithm is robust and insensitive to noise and missing features. The resulting matching can be used with image warping or other techniques for nonrigid motion analysis, image subtraction, etc. We present our experimental results on sequences of mammograms, images of a deformable clay object and satellite cloud images. In the first two cases we provide quantitative comparison with known ground truth.