边缘检测论文：边缘检测 各向异性扩散方程 数学形态学 小波变换 去噪.doc

边缘检测论文：边缘检测 各向异性扩散方程 数学形态学 小波变换 去噪【中文摘要】边缘是图像的基本特征之一,边缘检测是图像分割、目标识别、区域形状提取等图像处理领域十分重要的基础。图像边缘检测已拥有很长的研究历史,提出的方法也有很多种,但各有其优缺点,没有一种普适性方法。关键在于边缘和噪声都处于图像的高频区域,在去噪的同时,不可避免的会去除图像的细节,所以,在当前边缘检测仍是图像研究的热点和难点。因此,改进已有的方法,或根据要求设计新的方法已成为现在边缘检测研究的主要方向。本文共分五章,第一章介绍了图像边缘检测的意义和研究现状；第二章首先介绍了图像预处理方法,提出一种基于16向的各向异性扩散方程的滤波方法,其次介绍了经典的边缘检测算法,提出了一种基于改进Sobel算子和Canny算子融合的边缘检测方法,并对各种方法的结果进行了比较；第三章介绍了形态学边缘检测的基本理论和传统的边缘检测算子,构造出一种新的形态学边缘检测算子,并与扩散方程结合,从多方位多结构的角度进行边缘检测；第四章介绍了小波变换的基本理论和小波极大值边缘检测方法,并将扩散方程与构造的形态学算子和小波变换进行结合,来检测边缘,通过试验对所提方法结果进行了比较；最后,在本文的第五章进行了总结,并对未来的研究进行了展望。【英文摘要】Edge is an important feature of the image, edge detection is a digital image segmentation, object recognition, shape extraction region, and is very important foundation for the field of image analysis.The research on edge detection has a long history, and there have been lots of methods proposed for it. But all of the methods for edge detection still have some drawbacks and advantages. It is hard to propose a general method of edge detection applied to all images. Because, It is crucial that edge and noise are in the high frequency region of image. And It is inevitable that the image details will be removed, when de-noising. Therefore, edge detection is still a hot and difficult currently. So the main research orientation of edge detection is to make improvements to existing methods or to find new methods for edge detection with requirements.The paper is organized as following five parts. Chapter one gives an introduction of the significance and development of the field of edge detection. In chapter two, firstly, it gives an introduction of the preprocessing method, and a new method based on anistropic diffusion equation is proposed. Then it introduces classical edge detection algorithm, and proposes a new fusion edge detection method based on the improved Sobel operator and Canny operator, and gives edge detection results of these methods and offers some relative analysis and comparison. The chapter three offers the basic theory of morphological edge detection and traditional edge detection operators. Meanwhile, a new morphological detection operator is constructed and combined with the diffusion equation, which is detecting edge from the perspective of multi-dimensional and more structure. In the chapter four, at first, it gives an introduction of the basic theory of wavelet transformation and edge detection method of maximum value of wavelet. Then, it is combined with anistropic diffusion equation and morphological operators, and detecting edge, and comparing with the proposed method by experiment results. At last, the paper ends with a conclusion and some further research plans mentioned in chapter five.【关键词】边缘检测 各向异性扩散方程 数学形态学 小波变换 去噪【英文关键词】edge detection anisotropic diffusion equations de-noising mathematical morphology wavelet transformation【目录】基于数学形态学和小波变换的图像边缘检测的研究摘要3-4ABSTRACT4第一章 绪论8-121.1 引言8-91.2 图像边缘检测发展现状及研究意义9-111.2.1 课题的选题意义和研究价值9-101.2.2 本课题国内外研究现状和发展动态101.2.3 本文的研究内容及创新点10-111.3 本章小结11-12第二章 图像边缘检测方法12-312.1 图像滤波预处理12-212.1.1 空间域滤波13-142.1.2 频率域滤波14-162.1.3 基于各向异性扩散方程滤波16-202.1.4 图像预处理结果与分析20-212.2 一阶微分边缘检测算子21-232.2.1 Robert算子21-222.2.2 Sobel算子222.2.3 Prewitt算子22-232.3 二阶过零点边缘检测算子23-262.3.1 LOG算子24-252.3.2 Canny算子25-262.4 改进Sobel算子和Canny算子融合算法26-272.4.1 改进Sobel算子262.4.2 边缘融合算法26-272.5 试验结果与分析27-302.6 本章小结30-31第三章 形态学边缘检测算法31-453.1 灰度形态学基本运算与性质31-333.1.1 形态学基本运算31-333.1.2 灰度形态学运算的基本性质333.2 数学形态学边缘检测算法33-363.2.1 经典的数学形态学边缘检测算法343.2.2 新构造的数学形态学边缘检测算法34-353.2.3 多结构多方位的数学形态学边缘检测算法35-363.3 基于16向的各向异性扩散与多结构多方位的形态学边缘检测算法363.4 实验结果与分析36-443.4.1 经典的数学形态学边缘检测结果与分析37-393.4.2 新构造的数学形态学边缘检测结果与分析39-423.4.3 多结构多方位的数学形态学边缘检测结果与分析42-433.4.4 基于16向的各向异性扩散与多结构多方位形态学的边缘检测结果与分析43-443.5 本章小结44-45第四章 基于小波变换的边缘检测算法45-594.1 小波变换的基本理论46-494.1.1 一维小波变换46-474.1.2 多分辨率分析47-484.1.3 二维小波变换及分解48-494.2 小波模极大值边缘检测49-514.3 小波与形态学结合的边缘检测算法51-524.4 各向异性扩散方程与小波变换结合的边缘检测算法52-534.5 实验结果与分析53-584.5.1 小波极大值边缘检测实验结果与分析53-554.5.2 小波与形态学结合的边缘检测实验结果与