【摘要】：Hausdorff距離(HD)作為一種相似性度量方法,可以有效地測(cè)量?jī)蓚�(gè)幾何對(duì)象之間的逼近或不匹配程度,已經(jīng)廣泛應(yīng)用在幾何近似、網(wǎng)格簡(jiǎn)化和圖形圖像匹配等領(lǐng)域。對(duì)于離散幾何對(duì)象間的Hausdorff距離,主要應(yīng)用在圖像匹配方面,可根據(jù)Hausdorff距離定義或其改進(jìn)形式直接求解,目前已經(jīng)有比較成熟的應(yīng)用如人臉識(shí)別、車牌識(shí)別、碰撞檢測(cè)等方面。相比于圖像匹配中Hausdorff距離的研究和應(yīng)用,由于計(jì)算高復(fù)雜度和提出方法難以實(shí)現(xiàn),Hausdorff距離在連續(xù)幾何體間的計(jì)算方法和應(yīng)用相對(duì)較少。針對(duì)此問(wèn)題,本文以Hausdorff距離為研究對(duì)象,主要分析了連續(xù)幾何對(duì)象間Hausdorff距離的求解方法及應(yīng)用。本文著重介紹了曲面間Hausdorff距離的求解方法。針對(duì)曲面間Hausdorff距離計(jì)算復(fù)雜度高、相關(guān)計(jì)算方法少的問(wèn)題,提出一種三角面片-包圍盒方法快速計(jì)算參數(shù)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(zhuǎn)化為三角面片集合間的Hausdorff距離。在具體計(jì)算過(guò)程中,輔之以包圍盒技術(shù)對(duì)無(wú)效的三角面片進(jìn)行排除,以提高計(jì)算效率。同時(shí),為進(jìn)一步簡(jiǎn)化兩三角面片間的距離計(jì)算,在誤差可控范圍內(nèi)提出采樣點(diǎn)近似計(jì)算方法。實(shí)驗(yàn)表明,與曲面直接構(gòu)造包圍盒方法相比,本文方法簡(jiǎn)便、易于實(shí)現(xiàn)、排除率高,在不影響計(jì)算結(jié)果的情況下,計(jì)算效率顯著提高,有廣泛的應(yīng)用價(jià)值。在此基礎(chǔ)上,將該方法推廣到曲線到曲面間Hausdorff距離的求解上,并通過(guò)實(shí)驗(yàn)算例證明該方法的有效性和實(shí)用性。另外,本文研究了離散幾何對(duì)象點(diǎn)集和連續(xù)幾何對(duì)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(yīng)用在曲線曲面降階的偏差度量中,利用我們提出的方法對(duì)曲線和曲面降階算例進(jìn)行誤差度量,據(jù)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(xué)位授予單位】：江南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：O186.11;TP391.41

【參考文獻(xiàn)】

相關(guān)期刊論文 前7條

1 林意;薛思騏;郭婷婷;;一種參數(shù)曲線間Hausdorff距離的計(jì)算方法[J];圖學(xué)學(xué)報(bào);2014年05期

2 權(quán)文;王曉丹;甘進(jìn);;圖像匹配中的相似性度量比較與分析[J];航空計(jì)算技術(shù);2008年05期

3 陳學(xué)文,丑武勝,劉靜華,王田苗;基于包圍盒的碰撞檢測(cè)算法研究[J];計(jì)算機(jī)工程與應(yīng)用;2005年05期

4 陳衛(wèi)兵;;幾種圖像相似性度量的匹配性能比較[J];計(jì)算機(jī)應(yīng)用;2010年01期

5 陳小雕;王輝;鄭金生;;基于Hausdorff距離的曲線降階算法[J];杭州電子科技大學(xué)學(xué)報(bào);2012年02期

6 鄧敏;鈕沭聯(lián);李志林;;GIS空間目標(biāo)的廣義Hausdorff距離模型[J];武漢大學(xué)學(xué)報(bào)(信息科學(xué)版);2007年07期

7 王文成;李曉偉;智佳;趙彥發(fā);;基于Hausdorff距離的輪廓線匹配[J];西安郵電學(xué)院學(xué)報(bào);2007年03期

相關(guān)會(huì)議論文 前1條

1 蘇磊;張登福;王世強(qiáng);劉濤;;基于Hausdorff距離的圖像匹配技術(shù)應(yīng)用綜述[A];第八屆全國(guó)信號(hào)與信息處理聯(lián)合學(xué)術(shù)會(huì)議論文集[C];2009年

相關(guān)碩士學(xué)位論文 前4條

1 王琳;基于Hausdorff距離的網(wǎng)格參數(shù)化方法比較[D];大連理工大學(xué);2010年

2 王開磊;基于Hausdorff距離的圖像匹配技術(shù)研究及應(yīng)用開發(fā)[D];華東師范大學(xué);2011年

3 王曉榮;基于AABB包圍盒的碰撞檢測(cè)算法的研究[D];華中師范大學(xué);2007年

4 白彥冰;自由曲線到自由曲線曲面Hausdorff距離近似值的計(jì)算[D];清華大學(xué);2011年

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