【作者】 吕科；

【导师】 周明全；

【作者基本信息】 西北大学 ， 计算机软件与理论， 2003， 博士

【摘要】 轮廓曲线匹配是计算机视觉、图象分析和模式识别中的一个重要问题，在文字识别、物体运动跟踪、基于内容的图像检索和医疗诊断等众多领域都有十分广泛的应用。本文是在完成“国家自然科学基金项目”和“国家863高技术项目”的过程中，主要针对物体轮廓曲线匹配方法及相关的关键技术开展的研究工作，研究成果已成功应用于计算机辅助文物复原系统当中。主要工作在以下几个方面： 1．对于轮廓曲线的特性、复原目标、过程模型作了论述，完成了物体数字化采用的方法、数字化物体的存储、具有3D边缘保持的网格简化、轮廓曲线提取、轮廓曲线的光顺滤波、曲线的重采样等轮廓曲线匹配中所要用到的相关方法。 2．研究了2D轮廓曲线的匹配方法，给出了一种新的基于连续曲率概念推广的的多边形周期性离散曲率函数。周期性离散曲率函数具有和原有曲率相似的位移、旋转、缩放等特性，为提高匹配的准确度，利用高斯函数进行平滑处理，取得了较好的结果，同时该方法具有直观、速度快等优点，在2D轮廓曲线的匹配中，具有实用可靠的用途。 3．依据样条曲线的基本理论，研究了基于B样条的轮廓曲线的匹配方法，给出了由轮廓曲线不变量曲率和挠率构造的相似不变量的选取以及基于相似矩阵的匹配算法，并对该算法的时间复杂度作了估计，同时，将多尺度技术引入到物体轮廓的匹配问题中。 4．讨论了基于Hash矢量和Fourier变换的轮廓曲线匹配方法，在匹配中不要求一段轮廓线与另外一段轮廓线完全匹配，而是把它们分成很多子段，再用这些子段来进行匹配。提出了用于判断曲线段匹配的的判别方法，并对所给的方法做了严密的数学证明。 5．给出了计算机辅助文物复原系统的主要功能，文物碎片数据库的管理方法，碎片的复原流程以及基本的数据结构类型。更多还原

【Abstract】 The best matching of two curves is the central important problem in the fields of computer vision, image analysis and pattern recognition, which also can be applied in many other fields, such as character recognition, object recognition, image retrieval and diagnose. This paper aims at the research of curve matching approach and some corresponding techniques, and the application in reconstruction of archaeological fragments. The research work can be organized in the following aspects.1. An important application of shape matching technique is the reconstruction of archaeological fragments.Conceming this application, a series of processing algorithms is presented. An efficient algorithm of fragment digital, mesh simplification, extracting mesh outlines is presented, and the mesh simplification algorithm with features of 3D edge preservation by applying edge operations, In order to reduce the difference, smooth, filter and resample are applied on the original information.2. We introduced a new polygon periodic discrete curvature function based on curve continue curvature concept in 2D contour matching, the periodic discrete curvature has local, rotation and translation invariant. Applying efficient techniques to find the proper matching substrings, we also applied the hashing technique to find long matching substrings.3. According to the spline theory we presented a shape matching algorithm based on the similarity matrix of curvature and torsion values of 3D curve, we reduced the 3-D curve matching task into a 1-D string matching problem, which makes the matching more veracious and can be used on the 2D or 3D curve matching. In order to reduce the cost of matching, we used multiple scale technique.4. We presented a novel method of searching for similar fragments of 3D curves, with this method, a hash vector is associated with each fixed-length fragments of 3D sherd. Each vector consists of low frequence component of Fourier-Like spectrum for the distance between profile curve and the centroid. Then we can analyze the similarity of two fragments by evaluating the difference between hash vectors. The novel aspect of the method is that the following property is proved theoretically: if the distance between two fragments of curve is small, the distance between the hash vectors is small.5. In the process of reassembly of fragments, we provided virtual display and edit technique to afford convenience for user and ensure the result.In the end of the paper, we give a conclusion and tell the possible range of the curve matching methods.This research is supported by the National Natural Science Foundation of China and the National High Technology Development 863 program of China.更多还原