曲线曲面间Hausdorff距离计算及在形状匹配中的研究

发布时间：2018-08-07 08:42

【摘要】：Hausdorff距离(HD)作为一种相似性度量方法,可以有效地测量两个几何对象之间的逼近或不匹配程度,已经广泛应用在几何近似、网格简化和图形图像匹配等领域。对于离散几何对象间的Hausdorff距离,主要应用在图像匹配方面,可根据Hausdorff距离定义或其改进形式直接求解,目前已经有比较成熟的应用如人脸识别、车牌识别、碰撞检测等方面。相比于图像匹配中Hausdorff距离的研究和应用,由于计算高复杂度和提出方法难以实现,Hausdorff距离在连续几何体间的计算方法和应用相对较少。针对此问题,本文以Hausdorff距离为研究对象,主要分析了连续几何对象间Hausdorff距离的求解方法及应用。本文着重介绍了曲面间Hausdorff距离的求解方法。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。同时,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,本文方法简便、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。在此基础上,将该方法推广到曲线到曲面间Hausdorff距离的求解上,并通过实验算例证明该方法的有效性和实用性。另外,本文研究了离散几何对象点集和连续几何对象多边形、曲线曲面基于Hausdorff距离的形状匹配及求解方法,并将Hausdorff距离的相似性度量方法应用在曲线曲面降阶的偏差度量中,利用我们提出的方法对曲线和曲面降阶算例进行误差度量,据此判断降阶方法的有效性。
[Abstract]:As a similarity measure, Hausdorff distance (HD) can effectively measure the degree of approximation or mismatch between two geometric objects. It has been widely used in the fields of geometric approximation, mesh simplification and image matching. The Hausdorff distance between discrete geometric objects is mainly used in image matching, which can be solved directly according to the definition of Hausdorff distance or its improved form. At present, there are some mature applications such as face recognition, license plate recognition, collision detection and so on. Compared with the research and application of Hausdorff distance in image matching, the calculation methods and applications of Hausdorff distance between continuous geometric bodies are relatively few due to the high computational complexity and the difficulty of the proposed method. To solve this problem, this paper takes the Hausdorff distance as the research object, mainly analyzes the solution method and application of the Hausdorff distance between the continuous geometry objects. In this paper, the method of solving the Hausdorff distance between surfaces is introduced. In order to solve the problem of high computational complexity of Hausdorff distance between surfaces and less related calculation methods, a triangular-bounding box method is proposed to calculate the approximate value of Hausdorff distance between parametric surfaces. The set of triangular patches after surface discretization can approach the surface well. With the help of this property, the Hausdorff distance between surfaces is approximately transformed into the Hausdorff distance between the sets of triangular patches. In order to improve the efficiency of calculation, bounding box technique is used to eliminate the invalid triangulation in the process of calculation. At the same time, in order to simplify the calculation of distance between two or three corners, an approximate calculation method of sampling points is put forward in the range of error control. The experimental results show that the proposed method is simple, easy to realize and has high exclusion rate compared with the method of directly constructing bounding box with curved surface. The efficiency of calculation is improved significantly without affecting the result of calculation, and the method has wide application value. On this basis, the method is extended to solve the Hausdorff distance between curves and surfaces, and the effectiveness and practicability of the method are proved by an experimental example. In addition, in this paper, the point set of discrete geometric object and the polygon of continuous geometric object are studied. The shape matching and solving method of curve and surface based on Hausdorff distance is studied, and the similarity measure of Hausdorff distance is applied to the deviation measure of curve and surface reduction. The proposed method is used to measure the error of curve and surface reduction examples and to judge the effectiveness of the method.
【学位授予单位】：江南大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O186.11;TP391.41

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