發(fā)布時間：2018-08-07 08:42

【摘要】：Hausdorff距離(HD)作為一種相似性度量方法,可以有效地測量兩個幾何對象之間的逼近或不匹配程度,已經廣泛應用在幾何近似、網格簡化和圖形圖像匹配等領域。對于離散幾何對象間的Hausdorff距離,主要應用在圖像匹配方面,可根據Hausdorff距離定義或其改進形式直接求解,目前已經有比較成熟的應用如人臉識別、車牌識別、碰撞檢測等方面。相比于圖像匹配中Hausdorff距離的研究和應用,由于計算高復雜度和提出方法難以實現,Hausdorff距離在連續(xù)幾何體間的計算方法和應用相對較少。針對此問題,本文以Hausdorff距離為研究對象,主要分析了連續(xù)幾何對象間Hausdorff距離的求解方法及應用。本文著重介紹了曲面間Hausdorff距離的求解方法。針對曲面間Hausdorff距離計算復雜度高、相關計算方法少的問題,提出一種三角面片-包圍盒方法快速計算參數曲面間Hausdorff距離的近似值。曲面離散化后的三角面片集合可以較好地逼近曲面,借助這一特性,將曲面間的Hausdorff距離近似轉化為三角面片集合間的Hausdorff距離。在具體計算過程中,輔之以包圍盒技術對無效的三角面片進行排除,以提高計算效率。同時,為進一步簡化兩三角面片間的距離計算,在誤差可控范圍內提出采樣點近似計算方法。實驗表明,與曲面直接構造包圍盒方法相比,本文方法簡便、易于實現、排除率高,在不影響計算結果的情況下,計算效率顯著提高,有廣泛的應用價值。在此基礎上,將該方法推廣到曲線到曲面間Hausdorff距離的求解上,并通過實驗算例證明該方法的有效性和實用性。另外,本文研究了離散幾何對象點集和連續(xù)幾何對象多邊形、曲線曲面基于Hausdorff距離的形狀匹配及求解方法,并將Hausdorff距離的相似性度量方法應用在曲線曲面降階的偏差度量中,利用我們提出的方法對曲線和曲面降階算例進行誤差度量,據此判斷降階方法的有效性。
[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.
【學位授予單位】：江南大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O186.11;TP391.41

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本文編號：2169498