一种快速计算参数曲面间Hausdorff距离近似值的方法

针对曲面间Hausdorff距离计算复杂度高、相关计算方法少的问题,提出一种三角面片-包围盒方法快速计算参数曲面间Hausdorff距离的近似值。曲面离散化后的三角面片集合可以较好地逼近曲面,借助这一特性,将曲面间的Hausdorff距离近似转化为三角面片集合间的Hausdorff距离。在具体计算过程中,辅之以包围盒技术对无效的三角面片进行排除,以提高计算效率。为进一步简化两三角面片间的距离计算,在误差可控范围内提出采样点近似计算方法。实验表明,与曲面直接构造包围盒方法相比,该方法简便、易于实现、排除率高,在不影响计算结果的情况下,计算效率显著提高,有广泛的应用价值。     

一种鲁棒型Hausdorff距离图像匹配方法

图像匹配是图像处理的一项关键技术,传统方法受光照、噪声和遮挡的影响,使匹配过程变得困难。为了提高图像匹配的鲁棒性,提出了一种基于方向信息的鲁棒型Hausdorff距离匹配方法。该方法采用方向信息提取图像边缘,通过计算边缘匹配率(edge matching rate,EMR)获得候选匹配区域,然后采用修正后的Hausdorff距离构造相似性测度。实验结果表明,该方法加快了匹配过程,提高了抗噪性能,并能够准确匹配含有遮挡和伪边缘点的图像,从而解决了基于传统Hausdorff距离匹配方法因噪声点、伪边缘点和出格点而造成的误匹配问题。     

一种改进的Hausdorff距离地图匹配方法

目前的地图匹配算法分为在线和离线匹配两类。针对离线地图匹配中Marchal算法精度较低的问题,提出了一种改进的Housdorff距离匹配算法,利用航线方向角与Housdorff距离对Marchal匹配算法进行了改进。通过仿真试验的定性定量分析,新算法可以较好地纠正矢量数据不完整时产生的错误结果,很大程度上提高了匹配的准确性,可以为导航系统以及规划部门提供保障服务。     

一种基于Hausdorff距离的图像匹配算法

在图像匹配过程中,经常有目标图像被遮掩、有缺损的情形,使识别过程较为困难。文章在提取边缘特征点的基础上,用部分Hausdorff距离的均值对图像进行相似性度量。仿真实验结果表明,对上述提到的小目标识别效果良好,速度也较快。     

一种基于Hausdorff距离的车牌字符识别算法

提出了一种基于Hausdorff距离的车牌字符识别算法，即先对待识别的字符图像进行细化，然后用改进的Hausdorff距离进行匹配识别。     

Bezier曲线间最近距离的计算方法

针对Bezier曲线间最近距离计算问题,提出一种简捷、可靠的计算方法．该方法以Bernstein多项式算术运算为工具,建立Bezier曲线间最近距离的计算模型;然后充分利用Bezier曲面的凸包性质和de Casteljau分割算法进行求解．该方法几何意义明确,能有效地避免迭代初始值的选择和非线性方程组的求解,并可进一步推广应用于计算Bezier曲线／曲面间的最近距离．实验结果表明,该方法简捷、可靠且容易实现,与Newton-Raphson方法的融合可进一步提高该方法的运行速度．     

一种改进的Hausdorff距离模板匹配算法

检测和提取图像中的目标图像是图像处理和模式识别等领域里非常活跃的问题.因为Hausdorff距离对于目标遮挡、图像噪声和图像晃动等情况具有较好的鲁棒性,因此使用Hausdorff距离进行图像匹配是较常用的方法之一.为了降低此算法的计算复杂度,提高匹配效率,提出了一种能够从待匹配图像中高效匹配出模板图像的改进算法.将文中提出的改进算法分别应用到一幅图像和视频序列图像中,实验结果证明了该算法的高效性.     

三次Bézier 曲线与圆弧有重合点时的Hausdorff 距离

Hausdorff 距离常用来度量两条曲线的匹配程度,因此,它可以用来度量三次Bézier 曲线与圆弧之间的逼近程度。论文给出了三次Bézier 曲线与圆弧在中点重合时,它们之间的Hausdorff 距离表达式;以及三次Bézier 曲线与圆弧在一般情况重合（除端点外）时的Hausdorff 距离表达式。通过这些表达式可以直接得出三次Bézier 曲线与圆弧之间的Hausdorff 距离。     

一种改进的Hausdorff距离目标跟踪算法

基于机器人视觉平台,对成像目标进行模板提取及边缘检测。针对目标在运动过程中的形变和部分遮挡问题,采用一种改进的Hausdorff距离进行相似度量。提出了一种边缘细化方法及自适应模板尺寸修正策略,减少了边缘特征点,大大降低Hausdorff距离的计算量。基于Hausdorff距离进行模板更新,避免固定模板误差累积问题。实验表明,实时跟踪效果良好,并有效解决了目标部分遮挡问题。     

一种基于Hausdorff距离的运动物体跟踪算法

针对视频处理中运动物体的检测和跟踪问题,提出了一种基于Hausdorff距离的目标跟踪算法。新算法提出首先采用多尺度分水岭变换获取运动物体模型,消除了传统基于分水岭变换算法存在的缺陷;然后使用部分Hausdorff距离实现后续帧中运动物体模型的匹配;最后再次使用多尺度分水岭算法完成运动物体模型的更新。实验表明,该算法可以有效地跟踪多个刚体或非刚体目标。     

Polyline approach for approximating Hausdorff distance between planar free-form curves

This paper presents a practical polyline approach for approximating the Hausdorff distance between planar free-form curves. After the input curves are approximated with polylines using the recursively splitting method, the precise Hausdorff distance between polylines is computed as the approximation of the Hausdorff distance between free-form curves, and the error of the approximation is controllable. The computation of the Hausdorff distance between polylines is based on an incremental algorithm that computes the directed Hausdorff distance from a line segment to a polyline. Furthermore, not every segment on polylines contributes to the final Hausdorff distance. Based on the bound properties of the Hausdorff distance and the continuity of polylines, two pruning strategies are applied in order to prune useless segments. The R-Tree structure is employed as well to accelerate the pruning process. We experimented on Bezier curves, B-Spline curves and NURBS curves respectively with our algorithm, and there are 95% segments pruned on approximating polylines in average. Two comparisons are also presented: One is with an algorithm computing the directed Hausdorff distance on polylines by building Voronoi diagram of segments. The other comparison is with equation solving and pruning methods for computing the Hausdorff distance between free-form curves.     

Error-bounded biarc approximation of planar curves

Presented in this paper is an error-bounded method for approximating a planar parametric curve with a G¹ arc spline made of biarcs. The approximated curve is not restricted in specially bounded shapes of confined degrees, and it does not have to be compatible with non-uniform rational B-splines (NURBS). The main idea of the method is to divide the curve of interest into smaller segments so that each segment can be approximated with a biarc within a specified tolerance. The biarc is obtained by polygonal approximation to the curve segment and single biarc fitting to the polygon. In this process, the Hausdorff distance is used as a criterion for approximation quality. An iterative approach is proposed for fitting an optimized biarc to a given polygon and its two end tangents. The approach is robust and acceptable in computation since the Hausdorff distance between a polygon and its fitted biarc can be computed directly and precisely. The method is simple in concept, provides reasonable accuracy control, and produces the smaller number of biarcs in the resulting arc spline. Some experimental results demonstrate its usefulness and quality.     

基于分支特征点的景象匹配算法

由于传统Hausdorff距离算法对减少非零均值高斯噪声的干扰不明显,且匹配精度不能满足惯导的要求,因而提出了一种改进的算法分支点的加权Hausdorff离（Weiighted Hausdorff Distance,WHD）算法,并给出了权值的求取公式。方法能有效匹配被非高斯噪声污染的图像,提高景象匹配的精度和速度,增强算法的鲁棒性。并对提出的WHD算法与部分的平均距离算法（PMHD）分别作仿真实验进行比较,证明了前者算法的实用性和有效性。     

Linear One-Sided Stability of MAT for Weakly Injective Domain

Medial axis transform (MAT) is very sensitive to noise, in the sense that, even if a shape is perturbed only slightly, the Hausdorff distance between the MATs of the original shape and the perturbed one may be large. But it turns out that MAT is stable, if we view this phenomenon with the one-sided Hausdorff distance, rather than with the two-sided Hausdorff distance. In this paper, we show that, if the original domain is weakly injective, which means that the MAT of the domain has no end point which is the center of an inscribed circle osculating the boundary at only one point, the one-sided Hausdorff distance of the original domain's MAT with respect to that of the perturbed one is bounded linearly with the Hausdorff distance of the perturbation. We also show by example that the linearity of this bound cannot be achieved for the domains which are not weakly injective. In particular, these results apply to the domains with sharp corners, which were excluded in the past. One consequence of these results is that we can clarify theoretically the notion of extracting the essential part of the MAT, which is the heart of the existing pruning methods.     

豪斯道夫微积分和分数阶微积分模型的分形分析

清晰解读豪斯道夫微积分和分数阶微积分阶数的分形维意义,并比较这2种微积分建模方法的区别与联系.这是首次清晰定量地导出分数阶微积分的分形几何基础.提供豪斯道夫导数模型描述历史依赖过程的几何解释,即初始时刻依赖性问题,并与分数阶导数模型对比.基于本文作者的早期工作,详细描述非欧几里得距离的豪斯道夫分形距离定义——豪斯道夫导数扩散方程的基本解就是基于该豪斯道夫分形距离.该基本解实质上就是目前广泛使用的伸展高斯分布和伸展指数衰减统计模型.     

有理参数曲线的近似恰当化

有理参数曲线的恰当性是曲线的基本性质,虽然其在有理系数情况下已经有完备的结果,但在工程和CAGD应用中常常得到带误差浮点系数的有理表示形式.为此,讨论了这类有误差的有理参数曲线,定义了近似非恰当参数形式和近似非恰当指数,并通过半代数系统计算近似非恰当指数;在给出近似非恰当指数的同时,得到近似最大公因子.最后基于最小二乘法给出近似参数有理变换表示,计算出曲线恰当的近似有理参数表示.     

一种基于Hausdorff距离的图像配准算法

首先检测两幅图像中的角点,然后自适应地提取基准特征模板,再利用改进的基于特征强度响应空间的Hausdorff距离对基准模板进行初始匹配,最后通过区域相关法进行优化.算法不要求特征间的一一对应,也无需距离变换,实验证明这是一种快速有效的图像配准算法.     

基于几何约束的三次代数曲线插值

尽管三次参数曲线在曲线曲面造型中扮演着主要角色,但是计算几何专家也一直没有放弃对三次代数曲线的性质及应用进行研究。该文首先综述了近年来有关三次代数曲线研究的最新进展,对各主要方法的优缺点进行了客观的评价。然后提出了一种基于几何约束的三次代数曲线的插值方法,该方法守完全通过几何量如控制顶点、切线和曲率来控制三次代数曲线的形状,使得对三次代数曲线的编辑与对三次B－样条曲线的编辑一样灵活方便。该文提出的代数曲线的结构有两种,一种是插值平面上四点及两端点切线的三次代数曲线;另一种是插值两端点、两切线及两曲率的三次代数曲线。在第二种情况下对曲率的情况进行了详细的分类。并且从理论上对曲线的连续性及保凸性进行了严格的证明。     

Line segment Hausdorff distance on face matching

A novel concept of line segment Hausdorff distance is proposed in this paper. Researchers apply Hausdorff distance to measure the similarity of two point sets. It is extended here to match two sets of line segments. The new approach has the advantage to incorporate structural and spatial information to compute the similarity. The added information can conceptually provide more and better distinctive capability for recognition. This would strengthen and enhance the matching process of similar objects such as faces. The proposed technique has been applied online segments generated from the edge maps of faces with encouraging result that supports the concept experimentally. The results also implicate that line segments could provide sufficient information for face recognition. This might imply a new way for face coding and recognition.