基于数学形态学和小波变换的图像边缘检测的研究

【作者】 孙涛；

【导师】 袁修贵；

【作者基本信息】 中南大学 ， 计算数学， 2010， 硕士

【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。更多还原

【Abstract】 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.更多还原