摘要图像的边缘是图像中灰度变化较大的地方，是图像的最基础的特征。边缘检测在图像处理以及计算机视觉中发挥着非常重要的作用，主要应用于图像分割、遥感、医学图像分析、自动识别目标等领域。边缘检测也是分析和处理图像中最根本的内容之一，而且到现在仍然没有得到圆满的解决。78256

本论文基于matlab7。0,研究数学形态学的图像边缘检测方法。文中先对几种常用的线性图像边缘检测方法做了一些介绍，给出了实验仿真结果，并且讨论了这几种算法对于加躁图像的处理效果。然后详细的介绍了几种形态学基本算法，分析了各个算法拥有的特点。

本文详细的研究了基于形态学的图像边缘检测方法。先分析了传统的形态学边缘检测方法拥有的特点以及存在的不足，然后根据形态学运算的特性，对已有的形态学边缘检测算子做了较大的改进。接着，用改进后的形态学边缘检测算子对不同的图片做了仿真，并将结果与传统的非形态学边缘检测算子进行了对比。最终证明了改进后的形态学边缘检测算子拥有较好的检测效果以及良好的抗噪性，可以适用于不同的场景。

毕业论文关键词： 图像处理；matlab；边缘检测；数学形态学

Abstract The edge of the image is the place where grayscale changes greatly and it is the most basic characteristic of the image。 Edge detection plays a very important role in image processing and computer vision, which is mainly used in areas such as image segmentation, remote sensing, medical image analysis and automatic target recognition。 Edge detection is the most basic content in analysing and processing images, and has not been resolved satisfactorily yet。

This paper studies the image edge detection method of mathematical morphology through matlab 7。0。 The paper has rough introduction about several frequently used linear image edge detection methods, gives out xperimental simulation results and discusses about the treatment effects of these methods on noised images。 Then, the paper introduces some basic algorithms about morphology in details and analyses the characteristics of each algorithms。 

This paper studies the methods of image edge detection based on morphology。 First, it analyzes the characteristics and existing problems of traditional Morphological edge detection method。 Then , it improves the existing morphological edge detection operator greatly according to the characteristics of morphological operation。 After that, it completes the simulation for different images with the improved morphological edge detection operator and the results are compared with the traditional Non - morphological edge detection operator。 Finally, it proves that the improved morphological edge detection operator has a better detection effects and good anti-noise property, which can be applied to different scenarios。

Keywords: Image processing; Matlab;Edge detection;Mathematical morphology

目  录

第一章 绪论 1

1。1课题研究背景及意义 1

1。2 图像边缘检测技术的研究现状 2

1。2。1 经典算子 2

1。2。2 最优算子 2

1。2。3 基于形态学的边缘检测方法 3

第二章 传统的线性图像边缘检测算法 5

2。1 基于一阶导数的边缘检测算子 5

2。1。1 Roberts算子 7

2。1。2 Sobel算子 8

2。2 二阶的微分边缘检测算子