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1、 哈尔滨工程大学本科生毕业论文图像边缘检测与修复技术研究院 (系) 名 称：理学院专 业 名 称：数学与应用数学学 生 姓 名：徐毅 指 导 教 师：邓廷权 教授2010 年 6 月哈尔滨工程大学本科生毕业论文摘要数字图像处理被广泛应用于生物医学、材料、遥感、通信、交通管理、军事侦察、文档处理和工业自动化等众多领域。数字图像边缘检测是图像分割、目标识别和形状提取等图像分析领域十分重要的基础，是图像识别中提取图像特征的一个重要方法。边缘中包含图像中目标有价值的边界信息，这些信息可以用于图像理解和分析。通过边缘检测可以极大地降低后续图像分析和处理的数据量。本文对边缘检测理论和算法作了深入的研究，在
2、具体分析传统的边缘检测算法的基础上，重点研究了 Canny 算子。通过引进高斯函数计算局部梯度对传统 Canny 算子进行了改进。经过边缘检测得到的边缘图，通常会出现不同程度边缘断裂的现象。本文提出了一种基于路径形态学的断裂边缘修复技术。综合考虑等照度线曲率、梯度值、边缘端点前进方向等条件，通过对三个条件加权来定义邻接关系，以确定后继，构建形态学闭算子，对边缘图进行路径闭运算，完成对断裂边缘的连接。该算法能有效修复图像断裂边缘，同时能很好的控制断裂边缘的错误连接，为后续的图像处理提供了准确的信息。关键词：图像预处理；边缘检测；路径形态学；边缘连接ABSTRACTDigital image pr
3、ocessing is widely applied in many fields such as biomedicine, material, remote sensing, communication, traffic control, military reconnaissance, document processing, and industry automation. Digital image edge detections play important roles in image analysis and segmentation, interested objects re
4、cognition and shape extraction, It is also an important method in image feature extraction for image recognition. Edge of image includes valuable boundary information in images, which can be used in image understanding and analysisMoreover, the data dimension of an image will be, to a large degree,
5、reduced through edge detection in image analysis and processing.The thesis focuses on thorough research upon theory and algorithms of edge detection. On the basis of detail analysis of various kinds of traditional edge detection methods, the Canny edge detector is paid attention to. The traditional
6、Canny edge detector is improved and meliorated by introducing local gradient of image with the help of Gaussian function.The edge image obtained by an edge detection algorithm, in general, will suffer from edge crack or breaking in various degrees. In the article, a new technique of restoring breaki
7、ng edges is proposed on the basis of path morphology. Based on the comprehensive analysis upon curvature of isolux line, gradient value and edge endpoints, adjacency relationship of edge points is defined according to weighting such three conditions and the subsequential edge points are determined.
8、A morphological closing operator is established and the path closing operation of edge image is implemented so as to arrive at links of edge crack or breaking.The edge crack or breaking can be effectively repaired by the proposed method. Meanwhile, errors of edge linking can be controlled and accura
9、te Information will be provided in subsequent image processing.Keywords: image preprocessing; edge detection; path morphology; edge linking哈尔滨工程大学本科生毕业论文目录第 1 章 绪论 11.1 选题的意义 11.2 数字图像边缘定义 21.3 国内外研究现状 31.3.1 边缘检测的研究现状 31.3.2 边缘连接的研究现状 61.3.3 数学形态学 81.4 论文的主要工作和成果 101.5 论文的内容安排 11第 2 章 图像预处理 122.1 空间滤波基础 122.2 平滑空间滤波器 132.2.1 平滑线性滤波器 142.2.2 统计排序滤波器 152.3 实验仿真 172.4 本章小结 18第 3 章 边缘检测 193.1经典边 缘检测算法 193.1.1 基于一阶导数极大值的边缘检测 203.1.2 基于二阶导数过零点的边缘检测 233.2 Canny 边缘检测算法 253.2.1 Canny 算子的边缘检测基理 253.2.2 改进的 Canny 边缘检测算子 283.3 实验仿真结果及比较 303.4 本章小结 32哈尔滨工程大学本科生毕业论文第 4 章数学形态 学基本理论
