具有多项式密度分布的直线骨架卷积曲面

给出了一个具有多项式密度分布的直线骨架卷积曲面的解析表达式，并提出了基于控制曲线的密度控制方法，实验结果表明，该方法的自然景物，海生物等光滑物体造型中具有很大的应用价值。     

Warp-based helical implicit primitives

Implicit modeling with skeleton-based primitives has been limited up to now to planar skeleton elements, since no closed-form solution was found for convolution along more complex curves. We show that warping techniques can be adapted to efficiently generate convolution-like implicit primitives of varying radius along helices, a useful 3D skeleton found in a number of natural shapes. Depending on a single parameter of the helix, we warp it onto an arc of circle or onto a line segment. For those latter skeletons closed-form convolutions are known for entire families of kernels. The new warps introduced preserve the circular shape of the normal cross section to the primitive.     

Analytical solutions for sketch-based convolution surface modeling on the GPU

Convolution surfaces are attractive for modeling objects of complex evolving topology. This paper presents some novel analytical convolution solutions for planar polygon skeletons with both finite-support and infinite-support kernel functions. We convert the double integral over a planar polygon into a simple integral along the contour of the polygon based on Green’s theorem, which reduces the computational cost and allows for efficient parallel computation on the GPU. For finite support kernel functions, a skeleton clipping algorithm is presented to compute the valid skeletons. The analytical solutions are integrated into a prototype modeling system on the GPU (Graphics Processing Unit). Our modeling system supports point, polyline and planar polygon skeletons. Complex objects with arbitrary genus can be modeled easily in an interactive way. Resulting convolution surfaces with high quality are rendered with interactive ray casting.     

Efficient polygon decomposition into singular and regular regions via Voronoi diagrams

A new polygon decomposition into regular and singular regions is defined; it is a concept that is useful for skeleton extraction and part analysis of elongated shapes. Polygon regions that are narrow according to the Voronoi diagram of the polygon are extended through the boundary that is adjacent and quasiparallel. Regular regions are the narrow ones surrounded by smooth quasiparallel contour segments, while singular regions are the polygon regions that are not regular. We present an efficient algorithm to calculate the decomposition and make a comparative study with previous algorithms.Received: 21 December 2001, Accepted: 10 January 2003, Published online: 6 June 2003     

线点包容检测算法

提出的算法是先以快速的方法判断线与多边形是否有交点,如有,则求出线与多边形的各个交点,将交点进行排序,将此线按交点顺序分为多段;如果无交点,则此线只有一段。检测各段中点是否位于多边形内,如果位于内部,则此段在内,否则此段在外。以倾斜射线法检测点的包容性,其特点是此射线不与多边形的顶点或边重合,无须作特殊情况的处理,计算区域小,因而计算量小,对自相交多边形及带孔多边形等多类情况同样适用。通过编写程序计算验证表明,此算法简单有效、稳定可靠,适用于多类情况。     

基于凸片段分解的多边形窗口线裁剪算法

将多边形窗口的边顺序地分割成一些片段,使得每个片段都能局部地形成一个凸多边形,称为凸片段,并建立一个二叉树来管理这些凸片段．在裁剪计算时,先根据二叉树快速地找到与被裁剪线段相交的凸片段,再利用高效的凸多边形线裁剪算法对这些凸片段进行裁剪操作．文中算法能有效地降低裁剪计算的时间复杂度,使其在O（logN）～O（N）之间自适应地变化,且大部分情况下时间复杂度小于O（N）．     

Moment-based methods for polygonal approximation of digitized curves

Object shape representation plays an important role in the area of image processing, pattern recognition and computer vision. In the past two decades, many algorithms have been suggested for creating approximated polygons. In this study, two new polygonal approximation methods based on the geometric moments and the orthogonal moments defined in terms of Legendre polynomials are proposed. The difference between the moments defined by the initial contour and those of the approximated polygon is taken as the objective function. Each algorithm provides various polygonal approximation results with different number of line segments for different application situations. For a given error bound, we can determine the optimal polygon with a minimum number of line segments. The procedures are applied to some digital curves and better results are obtained in comparison with some known methods.     

Matching polygon fragments

Many computer vision systems model objects using polygons. If objects occlude each other or do not appear entirely in view, we need to match a polygon scene fragment with the polygon representation of the model objects. In this paper we present a way to match polygon fragments. Using polygon moments and cross moments we can compute a dissimilarity measure between two fragments. In addition, we also find the coordinate transform that maps one fragment onto the other. These polygon moments can be conputed by using just the end points of the line segments.

If the dissimilarity measure is less than a small number, then we can preliminarily conclude fragments. Otherwise the polygon fragments are dissimilar and are not considered any further. In computing the dissimilarity measure, we will also find a coordinate transform that maps one fragment to another. By using this coordinate transform, we can develop confirmation tests for determining whether the scene polygon fragments really belong to an occluded object.     

基于边界识别的多边形的布尔运算

多边形的布尔运算是图形学的一个重要问题，但目前的算法对线段的属性规定均较复杂，且对某些情况还不是很有效，这是因为没有利用运算的对象、结果都是多边形这一事实。本文试图将多边形的布尔运算建立在多边形识别的基础上，以简化线段的属性规定，使算法更有效，更具有一般性。     

基于轨迹计算的临界多边形求解算法

将多边形滑动碰撞问题转化为顶点和边之间的轨迹线提取问题,从而降低了时间复杂度,并可统一处理边界空腔和内部靠接临界多边形问题．该算法的基本原理是：1）求解多边形顶点相对于另一多边形的轨迹线;2）求解轨迹线集合所形成的外包多边形和内部顺时针环,得到的多边形即为临界多边形．该算法采用基于网格的线段索引方法来加快线段之间的求交计算,进一步提高了临界多边形求解的计算速度．     

Scale Dependency of Image Derivatives for Feature Measurement in Curvilinear Structures

Extraction of image features is a crucial step in many image analysis tasks. In feature extraction methods Gaussian derivative kernels are frequently utilized. Blurring of the image due to convolution with these kernels gives rise to feature measures different from the intended value in the original image. We propose to solve this problem by explicitly modeling the scale dependency of derivatives combined with measurement of derivatives at multiple scales. This approach is illustrated in methods for feature measurement in curvilinear structures. Results in 3D Confocal Images confirm that modelling of scale behavior of derivatives results in improved methods for center line localization in curved line structures and enables curvature and diameter measurement.     

Variational Image Registration Using Inhomogeneous Regularization

We present a generalization of the convolution-based variational image registration approach, in which different regularizers can be implemented by conveniently exchanging the convolution kernel, even if it is nonseparable or nonstationary. Nonseparable kernels pose a challenge because they cannot be efficiently implemented by separate 1D convolutions. We propose to use a low-rank tensor decomposition to efficiently approximate nonseparable convolution. Nonstationary kernels pose an even greater challenge because the convolution kernel depends on, and needs to be evaluated for, every point in the image. We propose to pre-compute the local kernels and efficiently store them in memory using the Tucker tensor decomposition model. In our experiments we use the nonseparable exponential kernel and a nonstationary landmark kernel. The exponential kernel replicates desirable properties of elastic image registration, while the landmark kernel incorporates local prior knowledge about corresponding points in the images. We examine the trade-off between the computational resources needed and the approximation accuracy of the tensor decomposition methods. Furthermore, we obtain very smooth displacement fields even in the presence of large landmark displacements.     

Visualizing 3D flow

We discuss volume line integral convolution (LIC) techniques for effectively visualizing 3D flow, including using visibility-impeding halos and efficient asymmetric filter kernels. Specifically, we suggest techniques for selectively emphasizing critical regions of interest in a flow; facilitating the accurate perception of the 3D depth and orientation of overlapping streamlines; efficiently incorporating an indication of orientation into a flow representation; and conveying additional information about related scalar quantities such as temperature or vorticity over a flow via subtle, continuous line width and color variations     

一种基于Delaunay三角化的笔划分割算法

字符笔划在字符识别等领域中存在广泛的应用。针对字符图形的骨架化及笔划提取,本文提出了一种基于动态约束Delaunay三角剖分的算法。该方法首先通过对字符的轮廓多边形进行三角剖分,生成一系列具有拓扑关系的三角形,再根据三角形的三种类型生成各三角形骨架,并连接为整个字符的骨架。然后定义了骨架的平滑度函数及分支长度阈值,消除了畸变分支,并根据得到的骨架进行笔划分割。实验结果表明,该算法具有快速稳定的特点且鲁棒性较好。     

基于骨架的断层间复杂轮廓线的三角片曲面重构

提出了一个基于轮廓线骨架点的三角片曲面重构的算法,首先对散乱骨架点进行拓扑连接,得到一个由骨架点构成的多边形,然后分析骨架多边形得到所需的特征骨架点,进而得到断层间轮廓线的相似特征部分,把断层间轮廓线分割为相对应的简单曲线段,最后,重构的曲面由这些分段重构的子曲面拼接而成。     

Finding the best conic approximation to the convolution curve of two compatible conics based on Hausdorff distance

We consider the convolution of two compatible conic segments. First, we find an exact parametric expression for the convolution curve, which is not rational in general, and then we find the conic approximation to the convolution curve with the minimum error. The error is expressed as a Hausdorff distance which measures the square of the maximal collinear normal distance between the approximation and the exact convolution curve. For this purpose, we identify the necessary and sufficient conditions for the conic approximation to have the minimum Haudorff distance from the convolution curve. Then we use an iterative process to generate a sequence of weights for the rational quadratic Bézier curves which we use to represent conic approximations. This sequence converges to the weight of the rational quadratic Bézier curve with the minimum Hausdorff distance, within a given tolerance. We verify our method with several examples.     

Polygon Inflation for Animated Models: a Method for the Extrusion of Arbitrary Polygon Meshes

A method for the extrusion of arbitrary polygon meshes is introduced. This method can be applied to model a large class of complex 3-D closed surfaces. It consists of defining a (typically small) set of connected polygons in 3-D that form a skeleton of the final object, and assigning extrusion distances to all polygons. The two sides of a polygon may have different extrusion distances. An automatic extrusion algorithm constructs a closed 3-D polygon mesh around the skeleton, making use of the indicated extrusion distances. We call this process inflating the polygons of the skeleton. Unlike traditional extrusion, the method works for non-planar skeleton configurations, and it also supports branching skeleton structures (i.e. edges with more than two incident polygons). © 1997 by John Wiley & Sons, Ltd.     

基于网格与R-树空间索引的矢量线图任意简单多边形窗口裁剪算法

针对大规模矢量线与大量裁剪窗口同时出现的线裁剪算法存在的三个主要问题,减少线段求交次数、简化交点出入属性计算以及无交点矢量线的取舍,本文提出了一种基于双空间索引的大规模线图任意多边形裁剪算法。算法根据裁剪多边形的边分别建立R-树索引和均匀Cell索引,应用两种索引各自的优点大幅减少被裁剪线段与裁剪多边形上线段的求交次数。在此基础上,基于均匀网格索引,提出局部射线法,简化交点出入属性计算和无交点矢量线的取舍。本文在传统算法基础上提出三点改进:首先提出基于两种空间索引模型进行线段求交计算,保证算法在理论上具有较低的时间复杂度;其次,在射线法和网格索引基础上提出局部射线法,使得判断每个交点出入属性的时间复杂度为O(1)～ O(n~(1/2)),与参考文献中的算法相比,此方法的优点是避免判断多边形上顶点的方向;最后,算法中裁剪多边形可以是包含任意多个洞的任意简单多边形,克服传统算法中对裁剪多边形的特定约束条件。     

Implicit Brushes for Stylized Line‐based Rendering

We introduce a new technique called Implicit Brushes to render animated 3D scenes with stylized lines in realtime with temporal coherence. An Implicit Brush is defined at a given pixel by the convolution of a brush footprint along a feature skeleton; the skeleton itself is obtained by locating surface features in the pixel neighborhood. Features are identified via image‐space fitting techniques that not only extract their location, but also their profile, which permits to distinguish between sharp and smooth features. Profile parameters are then mapped to stylistic parameters such as brush orientation, size or opacity to give rise to a wide range of line‐based styles.