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。     

基于图分割与Hausdorff距离的多分辨率影像匹配

针对具有复杂场景的航拍图像提出了一种基于图分割理论与Hausdorff距离的多分辨率影像匹配方法。在高斯金字塔图像模型中,低分辨率的图像通过图分割方法,充分考虑图像中的局部和全局的信息,提取到稳定和完整的图像区域边界,并以区域边界作为待匹配的曲线。再通过计算曲线的统计特性作为图像间待匹配特征,并由信号相关的度量方法粗估计出图像间全局仿射变换参数。利用粗估计的参数在高分辨率层次上进一步通过基于Hausdorff距离的匹配方法搜索到精确的变换参数。实验结果表明,该方法在较大变形和强噪音干扰的情况下对复杂场景的图像也能有效地完成匹配。     

B样条曲线与其控制多边形的局部距离上界

在对B样条曲线进行绘制和分析时,一个常用的方法是通过细分控制多边形近似B样条曲线,其中对控制多边形到曲线的距离的上界进行估计是影响细分深度的关键因素.为了获得更紧致的距离上界,从而减小折线近似的数据量,利用控制多边形的二阶差分的模以及前两阶差分之间的夹角,并通过在每一步细分过程中可能发生的最大变化的累加和来估计局部距离...     

基于Hausdorff距离的测井曲线尖峰深度校正

提出了一种基于Hausdorff距离的测井曲线尖峰深度校正方法.先利用极值和变量数列分析法选取合理的尖峰,应用双向Hausdorff距离准确选取相似曲线段位置,再应用单向Hausdorff距离确定最佳匹配尖峰,进而计算尖峰深度校正值.实验表明,该方法能实现快速、精准的尖峰深度校正,为油田的油气层开发提供可靠准确的数据资料.     

距离约束的网格曲面曲线设计方法

针对现有网格曲面曲线设计方法鲁棒性差、收敛慢、适用范围窄等不足,提出一种基于距离约束的新方法.该方法将复杂的流形约束转化为距离约束,并与光滑、插值（逼近）约束共同描述成优化问题.求解时,用切平面逼近局部曲面,并将距离约束松弛成用点到切平面的距离.由于计算距离所用的曲线上的点与其对应的切点相互依赖,采用“整体-局部”交替迭代的策略,并运用Gauss-Newton法的思想控制其收敛行为：整体阶段,通过距离近似将其松弛成凸优化问题求解迭代步长;局部阶段,采用鲁棒高效的投影法将优化后的曲线映射到曲面以更新切平面;最后,利用切割平面法将所有处于松弛状态的折线映射到网格曲面.实验结果表明：该方法与现有方法相比,在效率、鲁棒性、可控性、应用范围等方面均表现出优势.     

一种新的二维开曲线匹配算法研究

在提取碎片轮廓的基础上,提出了一种基于相似变换下的新的尺寸不变为标示符的二维开曲线匹配方法。基本思想是首先以弧长的曲率绝对值的积分方法,通过对轮廓重采样来计算轮廓曲线上的特征点,特征点分曲线为若干段,然后特征段之间的Hausdorff距离来比较两曲线的段的相似性,当Hausdorff距离小于给定的容差时,可认为相应的轮廓是匹配的,实验证明算法更快有效。     

基于正弦级数拟合的行为识别方法

提出了一种基于正弦级数拟合的行为识别方法.该方法利用二值轮廓序列来表示给定的运动图像序列,按照时针顺序计算从轮廓质心到轮廓边界点的距离,将人体轮廓转化为距离曲线,并将这一距离曲线利用正弦级数进行拟合,将距离曲线转化为正弦参数,从而极大地减小了计算量,将行为识别过程转化为曲线参数特征匹配的过程.在特征匹配过程中,通过计算待预测行为与已知类别行为的特征级数距离,对待预测行为中的每一个动作进行分类,最后通过投票决定该行为所属类别.在包含90个不同运动类别的视频数据库上进行留一交叉验证,实验结果表明,提出的方法能够有效地进行人体行为识别.     

基于曲率特征的轮廓匹配方法

首先对轮廓曲线进行多边形近似,然后通过Hermite插值曲线求出多边形各顶点的曲率作为特征,最后以Hausdorff距离为准则进行轮廓线匹配。算法充分利用了轮廓线的几何信息,匹配速度快,准确度高,具有一定的旋转不变性。     

GIS空间目标间距离表达方法及分析

空间目标间的距离是约束和表达空间目标分布关系的一个重要度量指标。如何表达和计算空间目标间的距离将直接影响空间查询、推理和空间分析结果的有效性。经典的欧氏距离只适合于点目标,而简单扩展的最近、最远和质心距离未顾及空间目标的整体形状、位置分布等特征。针对这些传统距离的局限性,学者们基于实际应用问题分别发展了一些较有代表性的距离表达方法,如Hausdorff距离、Hausdorff边界距离、对偶Hausdorff距离、广义Hausdorff距离、Fréchet距离、旋转函数距离以及对称差的面积度量。着重阐述这些距离的表达方法以及适用性,以便于发展更稳健的距离度量方法,更好地解决地理信息科学领域中的实际问题。     

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。     

Curve fitting and optimal interpolation for CNC machining under confined error using quadratic B-splines

In CNC machining, fitting the polyline machining tool path with parametric curves can be used for smooth tool path generation and data compression. In this paper, an optimization problem is solved to find a quadratic B-spline curve whose Hausdorff distance to the given polyline tool path is within a given precision. Furthermore, adopting time parameter for the fitting curve, we combine the usual two stages of tool path generation and optimal velocity planning to derive a one-step solution for the CNC optimal interpolation problem of polyline tool paths. Compared with the traditional decoupled model of curve fitting and velocity planning, experimental results show that our method generates a smoother path with minimal machining time.     

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.     

Computing the Hausdorff distance between two B-spline curves

This paper presents a geometric pruning method for computing the Hausdorff distance between two B-spline curves. It presents a heuristic method for obtaining the one-sided Hausdorff distance in some interval as a lower bound of the Hausdorff distance, which is also possibly the exact Hausdorff distance. Then, an estimation of the upper bound of the Hausdorff distance in an sub-interval is given, which is used to eliminate the sub-intervals whose upper bounds are smaller than the present lower bound. The conditions whether the Hausdorff distance occurs at an end point of the two curves are also provided. These conditions are used to turn the Hausdorff distance computation problem between two curves into a minimum or maximum distance computation problem between a point and a curve, which can be solved well. A pruning technique based on several other elimination criteria is utilized to improve the efficiency of the new method. Numerical examples illustrate the efficiency and the robustness of the new method.     

G1 continuous approximate curves on NURBS surfaces

Curves on surfaces play an important role in computer aided geometric design. In this paper, we present a parabola approximation method based on the cubic reparameterization of rational Bézier surfaces, which generates G¹ continuous approximate curves lying completely on the surfaces by using iso-parameter curves of the reparameterized surfaces. The Hausdorff distance between the approximate curve and the exact curve is controlled under the user-specified tolerance. Examples are given to show the performance of our algorithm.     

基于Hausdorff度量的快速图象匹配算法

借助于计算机形态学的膨胀运算,文章提出了一种基于Hausdorff距离的快速图象匹配算法.Hausdorff距离相似性度量简化为膨胀和累加运算两个步骤,与传统的Hausdorff距离计算方法相比,具有简单、快速的特点.仿真结果验证了所提出算法的有效性.     

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.     

Comparison of Distance Measures for Planar Curves

The Hausdorff distance is a very natural and straightforward distance measure for comparing geometric shapes like curves or other compact sets. Unfortunately, it is not an appropriate distance measure in some cases. For this reason, the Fréchet distance has been investigated for measuring the resemblance of geometric shapes which avoids the drawbacks of the Hausdorff distance. Unfortunately, it is much harder to compute. Here we investigate under which conditions the two distance measures approximately coincide, i.e., the pathological cases for the Hausdorff distance cannot occur. We show that for closed convex curves both distance measures are the same. Furthermore, they are within a constant factor of each other for so-called κ-straight curves, i.e., curves where the arc length between any two points on the curve is at most a constant κ times their Euclidean distance. Therefore, algorithms for computing the Hausdorff distance can be used in these cases to get exact or approximate computations of the Fréchet distance, as well.     

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.