基于三角形分解和重构的平面多边形变形方法

为解决较复杂的不同拓扑结构的二维形状渐变问题,提出一种基于三角形分解和重构的平面多边形变形方法.该方法将图形多层分解为三角形,保留分解过程中的各层边角信息;然后通过线性插值各层边长比例及角度,并结合刚性变换方法重构中间多边形的细节和框架,以达到变形的目的.该方法适用于任意点数的多边形,具有一般性.实验结果表明,文中方法能很好地解决变形序列中的萎缩问题,并且对较复杂的狭长图形也能避免自交现象,变形效果自然.     

基于骨架提取特征的可控渐变算法

提出了一种基于视觉特征的渐变算法,通过图像骨架确立特征点,进而对图形进行同构特征分解。采用可控制子多边形边角插值,通过轮廓多边形渐变控制子多边形渐变,用户也可以通过控制轮廓插值交互控制渐变过程。实验表明：该算法简单有效,渐变过程自然合理。     

Multiresolution Mean Shift Clustering Algorithm for Shape Interpolation

In this paper, we solve the problem of 3D shape interpolation with significant pose variation. For an ideal 3D shape interpolation, especially the articulated model, the shape should follow the movement of the underlying articulated structure and be transformed in a way that is as rigid as possible. Given input shapes with compatible connectivity, we propose a novel multiresolution mean shift (MMS) clustering algorithm to automatically extract their near-rigid components. Then, by building the hierarchical relationship among extracted components, we compute a common articulated structure for these input shapes. With the aid of this articulated structure, we solve the shape interpolation by combining 1) a global pose interpolation of near-rigid components from the source shape to the target shape with 2) a local gradient field interpolation for each pair of components, followed by solving a Poisson equation in order to reconstruct an interpolated shape. As a result, an aesthetically pleasing shape interpolation can be generated, with even the poses of shapes varying significantly. In contrast to a recent state-of-the-art work (Kilian et al., 2007), the proposed approach can achieve comparable or even better results and have better computational efficiency as well.     

Light field morphing using 2D features

We present a 2D feature-based technique for morphing 3D objects represented by light fields. Existing light field morphing methods require the user to specify corresponding 3D feature elements to guide morph computation. Since slight errors in 3D specification can lead to significant morphing artifacts, we propose a scheme based on 2D feature elements that is less sensitive to imprecise marking of features. First, 2D features are specified by the user in a number of key views in the source and target light fields. Then the two light fields are warped view by view as guided by the corresponding 2D features. Finally, the two warped light fields are blended together to yield the desired light field morph. Two key issues in light field morphing are feature specification and warping of light field rays. For feature specification, we introduce a user interface for delineating 2D features in key views of a light field, which are automatically interpolated to other views. For ray warping, we describe a 2D technique that accounts for visibility changes and present a comparison to the ideal morphing of light fields. Light field morphing based on 2D features makes it simple to incorporate previous image morphing techniques such as nonuniform blending, as well as to morph between an image and a light field.     

圆弧路径法，一种新的多边形变形方法

二维形状变形技术在二维角色动画、模式匹配、几何造型、虚拟现实、工业模拟、科学计算可视化等领域有着重要的应用。本文提出了一种顶点路径圆弧法的二维形状变形新方法。该算法通过控制关键帧多边形顶点按照一条特殊的圆弧曲线路径进行运动，实现二维形状变形。通过许多实例的测试表明，该算法效果良好：不仅可以保持首末关键帧形状的共同特征，而且中间插值形状变化自然平滑。同时，我们的方法易于用户交互控制；容易推广到高维情形；计算量较小、能达到系统实时的要求。     

基于简化多边形类正切空间表示的图形渐变算法

采用多边形简化的方法提取出包含源图形主要特征点的多边形.在简化多边形的类正切空间表示下,利用图形对应边在渐变过程中所掠过面积总和最小这一特征构造相似度量函数,由动态规划算法求解实现初始和目标简化多边形之间的顶点对应,再进一步建立源图形顶点之间的整体对应,最后通过插值边和角的方法实现图形渐变.实验结果表明:该算法简单有效,对应效果自然、合理.     

基于二元混合有理插值的形状渐变方法

为实现多个多边形间的平滑自然渐变,提出基于二元混合向量值有理插值的非线性二维形状渐变方法。将多个多边形的顶点坐标作为平面域上的向量,利用二元Newton-Thiele型向量连分式建立有理插值曲面,通过对插值曲面进行重采样得到一系列渐变中间多边形。实验结果表明,该方法具有计算精度高、适应性强、易于编程实现的特点。     

基于多层次特征结构的二维形状渐变

二维形状渐变在二维角色动画、模式匹配、几何造型中有着重要的应用.已有方法大多根据边长、角度、面积等局部几何属性来完成形状之间的最佳对应和渐变,忽略了形状的内在特征结构.为此,提出一种基于多层次特征结构的二维形状渐变方法,首先将源形状和目标形状分解为若干个视觉显著性特征,并通过一种用户启发式的半自动方法建立2个形状的特征对应关系;然后根据形状的特征信息构建源形状和目标形状的多层次特征结构,分别表示形状特征的整体位置和朝向、形状特征的局部朝向和形状特征的局部细节;最后组合不同特征层次上的插值结果,重构出中间形状.在源形状到目标形状的渐变过程中,针对不同层次上的特征信息分别使用近似保刚性插值、边角插值以及弹性线性插值方法进行过渡.实验结果表明,该方法简单高效,有效地避免了形状的内部扭曲,保持了形状的局部特征,可产生自然、光滑且视觉真实的形状渐变序列.     

Multiresolution morphing for planar curves

We present a multiresolution morphing algorithm using ``as-rigid-as-possible' shape interpolation combined with an angle-length based multiresolution decomposition of simple 2D piecewise curves. This novel multiresolution representation is defined intrinsically and has the advantage that the details' orientation follows any deformation naturally. The multiresolution morphing algorithm consists of transforming separately the coarse and detail coefficients of the multiresolution decomposition. Thus all LoD (level of detail) applications like LoD display, compression, LoD editing etc. can be applied directly to all morphs without any extra computation. Furthermore, the algorithm can robustly morph between very large size polygons with many local details as illustrated in numerous figures. The intermediate morphs behave natural and least-distorting due to the particular intrinsic multiresolution representation.     

Data‐Driven Shape Interpolation and Morphing Editing

Shape interpolation has many applications in computer graphics such as morphing for computer animation. In this paper, we propose a novel data‐driven mesh interpolation method. We adapt patch‐based linear rotational invariant coordinates to effectively represent deformations of models in a shape collection, and utilize this information to guide the synthesis of interpolated shapes. Unlike previous data‐driven approaches, we use a rotation/translation invariant representation which defines the plausible deformations in a global continuous space. By effectively exploiting the knowledge in the shape space, our method produces realistic interpolation results at interactive rates, outperforming state‐of‐the‐art methods for challenging cases. We further propose a novel approach to interactive editing of shape morphing according to the shape distribution. The user can explore the morphing path and select example models intuitively and adjust the path with simple interactions to edit the morphing sequences. This provides a useful tool to allow users to generate desired morphing with little effort. We demonstrate the effectiveness of our approach using various examples.     

CR-Morph: Controllable Rigid Morphing for 2D Animation

This paper presents a rigidity-preserving morphing technique that blends a pair of 2D shapes in a controllable manner. The morphing is controllable in two aspects:1) motion dynamics in the interpolation sequences can be effectively enhanced through an intuitive skeleton control and 2) not only the boundaries but also the interior features of the source and target shapes are precisely aligned during the morphing. We introduce a new compatible triangulation algorithm to decompose the source and target shapes into isomorphic triangles. Moreover, a robust and motion-controllable rigiditypreserving transformation scheme is proposed to blend the compatible triangulations, ultimately leading to a morphing sequence which is appearance-preserving and with the desired motion dynamics. Our approach constitutes a powerful and easy-to-use morphing tool for two-dimensional animation. We demonstrate its versatility, effectiveness and visual accuracy through a variety of examples and comparisons to prior work.     

Stable Region Correspondences Between Non‐Isometric Shapes

We consider the problem of finding meaningful correspondences between 3D models that are related but not necessarily very similar. When the shapes are quite different, a point‐to‐point map is not always appropriate, so our focus in this paper is a method to build a set of correspondences between shape regions or parts. The proposed approach exploits a variety of feature functions on the shapes and makes use of the key observation that points in matching parts have similar ranks in the sorting of the corresponding feature values. Our algorithm proceeds in two steps. We first build an affinity matrix between points on the two shapes, based on feature rank similarity over many feature functions. We then define a notion of stability of a pair of regions, with respect to this affinity matrix, obtained as a fixed point of a nonlinear operator. Our method yields a family of corresponding maximally stable regions between the two shapes that can be used to define shape parts. We observe that this is an instance of the biclustering problem and that it is related to solving a constrained maximal eigenvalue problem. We provide an algorithm to solve this problem that mimics the power method. We show the robustness of its output to noisy input features as well its convergence properties. The obtained part correspondences are shown to be almost perfect matches in the isometric case, and also semantically appropriate even in non‐isometric cases. We provide numerous examples and applications of this technique, for example to sharpening correspondences in traditional shape matching algorithms.     

与视点对应的视图插补

ＩｍａｇｅＭｏｒｐｈｉｎｇ是产生图象之间插补变换一类被广泛使用的技术,所有的Ｍｏｒｐｈｉｎｇ方法奢阳基于两幅图象之间的象素位置和颜色的内插。现行的Ｍｏｒｐｈｉｎｇ技术不能保证所生成图象的真实性。本文提出的视图插 补技术,使得所生成的插 补图象对应于某个视点,且不需要知识源图象所对应的摄像朵矩阵,因此计算简单。     

Interpolating Polyhedral Models Using Intrinsic Shape Parameters

Metamorphosis, or morphing, is the gradual transformation of one shape into another. It generally consists of two subproblems: the correspondence problem and the interpolation problem. This paper presents a solution to the interpolation problem of transforming one polyhedral model into another. It is an extension of the intrinsic shape interpolation scheme (T. W. Sederberg, P. Gao, G. Wang and H. Mu, ‘2-D shape blending: an intrinsic solution to the vertex path problem, SIGGRAPH '93, pp. 15–18.) for 2D polygons. Rather than considering a polyhedron as a set of independent points or faces, our solution treats a polyhedron as a graph representing the interrelations between faces. Intrinsic shape parameters, such as dihedral angles and edge lengths that interrelate the vertices and faces in the two graphs, are used for interpolation. This approach produces more satisfactory results than the linear or cubic curve paths would, and is translation and rotation invariant. © 1997 by John Wiley & Sons, Ltd.     

基于边角插值法的图形渐变避免自交算法研究

提出了一种新的算法,该算法根据图形渐变序列中出现的局部自交点,先判断出这些点的位置并计算出自交区域所占整个图形面积的比例,根据设定的阈值,采用合理的微调整算法,在尽可能保持源图形形态的基础上,将自交点剔除,达到渐变序列中图形全部为简单多边形的目的。结果表明提出的算法能够很好地将图形渐变中的自交点剔除,实现比单独采用边角插值法更理想的图形渐变效果。     

Visual salience guided feature-aware shape simplification

In the area of 3D digital engineering and 3D digital geometry processing, shape simplification is an important task to reduce their requirement of large memory and high time complexity. By incorporating the content-aware visual salience measure of a polygonal mesh into simplification operation, a novel feature-aware shape simplification approach is presented in this paper. Owing to the robust extraction of relief heights on 3D highly detailed meshes, our visual salience measure is defined by a center-surround operator on Gaussian-weighted relief heights in a scale-dependent manner. Guided by our visual salience map, the feature-aware shape simplification algorithm can be performed by weighting the high-dimensional feature space quadric error metric of vertex pair contractions with the weight map derived from our visual salience map. The weighted quadric error metric is calculated in a six-dimensional feature space by combining the position and normal information of mesh vertices. Experimental results demonstrate that our visual salience guided shape simplification scheme can adaptively and effectively re-sample the underlying models in a feature-aware manner, which can account for the visually salient features of the complex shapes and thus yield better visual fidelity.     

Metamorphosis of 3D polyhedral models using progressive connectivity transformations

Three-dimensional (3D) metamorphosis is a powerful technique to produce a 3D shape transformation between two or more existing models. We propose a novel 3D morphing technique that avoids creating a merged embedding that contains the faces, edges, and vertices of two given embeddings. This novel 3D morphing technique dynamically adds or removes vertices to gradually transform the connectivity of 3D polyhedrons from a source model into a target model and simultaneously creates the intermediate shapes. In addition, a priority control function provides the animators with control of arising or dissolving of input models' features in a morphing sequence. This is a useful tool to control a morphing sequence more easily and flexibly. Several examples of aesthetically pleasing morphs are demonstrated using the proposed method.     

基于增量式迭代变换的蜡染图形渐变算法

针对蜡染图形创新, 提出一种基于增量式迭代变换法的图形渐变方法, 即在不受特征点集对应的约束下, 实现两个平面图形之间自然、平滑渐变。该方法采用迭代渐变的思想, 对图形进行矢量预处理, 并分别在源矢量图形和目标矢量图形上采样一组几何特征点, 通过等分弧长对应的规则把两个图形进行权重归中, 对采样的节点求全局最小二乘进行特征匹配与映射, 再通过增量式迭代变换法得到一系列渐变中间图形。计算机仿真结果表明, 此算法能够较好地实现非特征对应的图形渐变, 达到过渡自然、平滑的目的。     

多特征融合的图像自动变形

目的 图像变形算法中特征基元提取和匹配方式大部分都是采用人机交互的方式进行,并且在遮挡区域变形时出现较多的鬼影和模糊现象,使得针对同一场景图像变形实现繁琐且效果不佳,针对这些问题提出一种基于多特征融合的自动图像变形算法。方法 该算法提取多种图像特征信息（如Surf特征算子、Harris算子、Canny算子等）并进行多特征融合匹配,得到一个分布适当且对应关系正确的三角网格,再结合图像变形,实现自动图像插值。结果 实验结果显示,自动的提取特征基元有效地减少了人工操作,而多特征融合匹配有效地抑制了图像变形时边缘或遮挡区域鬼影的产生。结论 提出的融合匹配方法,将不同的特征信息有效地融合匹配从而改善了图像变形算法。通过对多组实验结果进行问卷调查,91%的参与者认为该算法有效地改进图像变形结果。     

Structure Preserving Manipulation and Interpolation for Multi‐element 2D Shapes

This paper presents a method that generates natural and intuitive deformations via direct manipulation and smooth interpolation for multi‐element 2D shapes. Observing that the structural relationships between different parts of a multi‐element 2D shape are important for capturing its feature semantics, we introduce a simple structure called a feature frame to represent such relationships. A constrained optimization is solved for shape manipulation to find optimal deformed shapes under user‐specified handle constraints. Based on the feature frame, local feature preservation and structural relationship maintenance are directly encoded into the objective function. Beyond deforming a given multi‐element 2D shape into a new one at each key frame, our method can automatically generate a sequence of natural intermediate deformations by interpolating the shapes between the key frames. The method is computationally efficient, allowing real‐time manipulation and interpolation, as well as generating natural and visually plausible results.