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基于数学形态学的图像噪声处理

摘 要

本文首先介绍了数学形态学的发展简史及其现状，紧接着详细的阐述了数学形态学在图像处理和分析中的理论基础。并从二值数学形态学出发着重研究了数学形态学的膨胀、腐蚀、开运算、闭运算等各种运算和性质，然后根据已有的运算，接着引入了形态滤波器设计、形态学图像处理的实用算法。由于在图像的获取中存在各种可能的噪声，比如高斯噪声、瑞利噪声、伽马噪声、指数噪声、均匀噪声以及椒盐等噪声，由于这些噪声的普遍存在，因此，利用数学形态学的腐蚀、膨胀、开启、闭合设计出了一种比较理想的（闭和开）形态学滤波器，并且用MATLAB语言编写程序，反复的使用这种开闭、闭开来处理图像中存在的噪声，其效果比较满意。

关键词:数学形态学 图像处理 腐蚀 膨胀 滤波

Studies on Mathematical Morphology

for Image Processing ABSTRACT

In this paper ,we first introduced the brief history and development of mathematical morphology some general theory of mathematical morphology analysis and many experiment results are presented. Later ,from the aspect of morphology of dual value, special emphasis on various operations and properties including dilation, erosion, open operation and close operation etc. In addition, morphology analysis method of the dual value image is also discussed and the practical and improved operations of the morphological image processing such as electric filter design, marginal pattern testing are introduced. As the image of the acquisition in the range of possible noise, such as Gaussian noise, Rayleigh noise, Gamma noise, Uniform noise Salt and Pepper noise and so on. As the prevalence of such noise, so using mathematical morphology of erosion, dilation, opening, closing designed a more ideal (open and closed) morphological filter, And repeated to use opening and closing, closing and opening handle image processing in the noise. It is satisfied with its results. And the simulation results is more satisfactory after the use of MATLAB language programming.

Keyword：mathematical morphology image processing erosion dilation

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目 录

一 绪论 ......................................... 1

1.1 数学形态学发展简史 ............................... 1 1.2 数学形态学与数字图像处理 ......................... 1 1.3 本文的研究内容及安排 ............................. 2

二 数学形态学的基本运算 .......................... 3

2.1 基本概念 ......................................... 3 2.2 二值腐蚀和膨胀 ................................... 3 2.2.1 二值腐蚀运算 ................................... 3 2.2.2 二值膨胀运算 ................................... 4 2.2.3 腐蚀和膨胀的代数性质 ........................... 5 2.3 二值开运算和闭运算 ............................... 6 2.3.1 二值开运算 ..................................... 7 2.3.2 二值闭运算 ..................................... 9 2.4 小结 ............................................ 10

三 使用形态学滤波器处理噪声 ..................... 11

3.1 噪声模型 ........................................ 11 3.1.1 一些重要噪声的概率密度函数 .................... 11 3.1.2 噪声的参数的估计 .............................. 16 3.2 滤波器的设计 .................................... 17 3.3 滤波器对图像噪声的处理 .......................... 19