基于小波变换的图像分割的研究

摘要

近年来，对图像分割的研究一直是图像技术研究的焦点。图像分割是一种很重要的图像分析技术，它的目的是把图像分为具有各种特性的区域并把感兴趣的部分提取出来。它融合了多个学科的成果，并且成功应用于工业、农业、医学、军事等领域，得到了广泛的应用。

图像分割是一个经典的问题，实现方法有很多种，但是至今仍没有一种通用的解决方法。经过研究发现，区分真正的噪声和边缘是图像分割的难题之一，然而小波变换则可以解决这一问题，小波变换是一种时--频两域的分析工具。本文则基于小波变换对图像分割技术进行研究，主要介绍了小波阈值分割方法。文中通过直方图、建立模型等手段对这两种方法做出具体的讨论，并利用Matlab分别对两种方法进行仿真，并得到了有效的结果。根据仿真结果我们可以看出不同分割方法的不同分割效果，从而更好地理解这些方法。

关键词：图像分割；小波变换；阈值；

Abstract

In recent years, the study of image segmentation has been the focus of imaging technology. Image segmentation is an important image analysis, its purpose is to take the various characteristics part out of the image. It combines the results of multiple disciplines, and successfully applied to such fields as industry, agriculture, medicine, military, and a wide range of applications.

There are many ways to achieve image segmentation, but could not find a common solution. After the study found that the distinction between real noise and the edge of one of the difficult problem of image segmentation, wavelet transform can solve this problem, wavelet transform is a time - frequency domain analysis tools. In this paper, image segmentation technique based on wavelet transform to study the two wavelet segmentation method, the wavelet thresholding segmentation method. Histogram, the establishment of model and other means to make a specific discussion of these two approaches, and use the Matlab simulation, and the effective results of the two methods, respectively. According to the results of the simulation we can see the different segmentation results of different segmentation methods, in order to better understand these methods.

Key words：Image; Wavelet transform; Threshold

目录

摘要 .................................................................................................................... I Abstract ..................................................................................................................II 1 绪论 .. (1)

1.1 空域图像分割 (1)

1.2 频域图像分割 (2)

1.3 小波域图像分割 (3)

1.3.1 图像分割的描述 (3)

1.3.2 图像分割的发展及现状 (4)

1.3.3 基于适当最优准则实现图像的分割方法 (5)

1.3.4 基于小波变换的图像分割方法 (6)

1.4 本文的组织结构 (7)

2 小波变换理论 (7)

2.1 小波理论 (7)

2.2 小波变换 (8)

2.2.1 小波变换的概述 (8)

2.2.2 正交小波基的种类 (8)

2.2.3 多分辨率分析 (10)

2.2.4 连续小波变换 (11)

2.2.5 离散小波变换 (11)

2.2.6 小波离散图像的描述 (12)

3 图像分割中的小波阈值法 (14)

3.1 小波阈值法的原理 (14)

3.2 图像直方图的多分辨率分析 (15)

3.3 阈值分割算法 (16)

3.4 实验仿真 (16)

4 结论与展望 (18)

4.1 论文的总结 (18)

4.2 论文的展望 (18)

致谢 (20)