复数域在图像处理中的应用

摘要

图像分割，正如字面上所理解的，对图像信息进行分块，并取得自己所需要的那一块。图像分割是图像分析处理的重要环节。为了能更好的理解与分析，和处理图像，尤其是自己感兴趣的那一块，我们离不开图像分割。它将原始图像，通过目标识别，匹配，提取，测量参数后，找到处理的根本对象所在。

如何在图像中表现出其是否是均匀的、是粗糙的又或者是细致的？为了区分图像，我们引入图像纹理特征，它是图像的本身属性。在灰度的变化过程中，通过统计变化，空间中，图像的纹理特征也发生相应的改变。由此可知，纹理特征是指图像内所含有的，一定区域内的，按一定规律形成的或者周期排列的，小形状区域块。

傅里叶变换，就如同处理信号，把图像从“空域”变为“频域”。在一幅图像中，其细节以及纹理特征信息在频谱图的高频率部分呈现出；低频部分代表了图像的轮廓信息。若我们将一幅精细的图像通过低通滤波器变换，那么图像经过变换后的结果就剩下了轮廓。这与信号处理的基本思想是相通的。我们就可以用滤波器来恢复噪点恰巧位于图像的某个特定“频率”范围内的图像。

本文主要是对图像进行傅里叶变换分析并对比Gabor变换和脊波变换。

关键词：图像处理，傅里叶变换，复数域，纹理特征

ABSTRACT

Image segmentation refers to the image into various characteristics of the region and extract the target of wich we are interest in.The first step to understand and analysis a image is to make a image segment, the need for image object extraction, measurement and it makes the expression of the target feature extraction, parameter measurement of the original image is the foundation of the image analysis and understanding.

Texture refers to the shapes that exist within a certain range of the image,usually is very small,semi-periodic or regular arrangement of the pattern. For same phenomenon, texture is used in image interpretation of meticulous and rough.Texture is one of the main features of image processing and pattern recognition.The texture feature is the image gray level changes,such changes and statistics will be concerned.Image texture features reflect the properties of the image itself,contribute to the distinction between images.

As one-dimensional signal processed,Fourier transform trans the image from the "airspace" to"frequency".For a picture,high-frequency part represents the image detail and texture information;low-frequency part represents the outline of the image information.For example,a fine image processed with a low pass filter,then filtering the result to the rest of the silhouette.This is the basic idea of the signal processing are interlinked.If the image is subject to a noise just in a specific "frequency" range,it can pass through the filter to restore the original image.

This article is mainly for image Fourier transform analysis and process with Matlab. KEY WORDS：Image process, Fourier transform, Complex Unit,texture feature,

目录

摘要............................................................. I ABSTRACT............................................................ II 第一章绪论. (4)

1.1选题背景和意义 (4)

1.2国内外研究现状 (4)

1.3 设计（论文）的主要研究内容及预期目标 (5)

第二章纹理特征 (1)

2.1 纹理 (1)

2.2 基于纹理特征的方法 (2)

2.2.1 信号处理方法 (2)

第三章复数域上的Fourier变换 (3)

3.1 Fourier变换 (3)

3.2 Gabor变换 (4)

3.2.1 Gabor变换定义式 (4)

3.2.2 窗口的宽高关系 (5)

3.2.3离散Gabor变换的一般求法 (5)

3.2.4 Gabor变换的解析理论 (6)

3.2.5 适用条件 (6)

3.2.6 应用 (6)

3.3脊波变换 (7)

3.4 Radon、Fourier和Ridgelet变换的关系 (8)

第四章复数域上的图像处理计算机实践 (9)

4.1 实践环境 (9)

4.2傅里叶变换的MATLAB实践 (9)

4.3 Gabor变换及脊波变换 (9)

第五章总结 (11)

参考文献 (12)

致谢 (13)