图像正交变换方法研究.doc

理工大学学士学位论文I摘摘 要要随着计算机技术的日益发展和不断普及，人类已经进入一个高速发展的信息化时代，作为信息化标志之一的计算机已经在人们的生活中起着不可替代的重要作用，在信息化时代来临以及计算机被广泛应用的今天，图片所包含的信息量是远远大于文字和声音的，所以图像信息在这些被传递的信息中占 90%以上，在数字图像处理中，正交变换因其独特的性质而广泛运用,它是信号处理中最重要的一类变换，这种方法为图像的传输起到了很大的正面作用正交变换是为了有效和快速的对图像进行处理和分析以及将定义在原图像空间的图像以某种形式转换到另外一些空间，并利用这些空间特有的性质更方便的进行加工最后再变回图像空间以得到所需结果目前正交变换被广泛地运用于图像特征提取、图像增强、图像复原、图像压缩和图像识别等领域本文介绍了正交变换的定义,讨论了在数字图像处理中采用正交变换的意义,重点研究了正交变换的标准基,介绍了正交变换的三种方法即傅里叶变换，离散余弦变换和沃尔什，并通过实例，给出图像变换前后效果对比来说明器变换的作用，从而得出不同变换方法对图像处理的影响实验数据结果表明，在正交变换中，沃尔什变换无论在变换时间和图像处理质量上都比离散余弦变换效果更好。

关键词：：数字图像处理；正交变换；标准基图像；离散余弦变换；理工大学学士学位论文IIAbstractAlong with the increasing development of computer technology and popularization, human has entered a rapid development of information age, as one of the symbols of informatization of the computer has been in people life plays an irreplaceable important role, in the image information of the information that is passed by more than 90%, in digital image processing, the orthogonal transformation is widely used due to its unique properties, it is the most important transformation in signal processing. Orthogonal transformation is widely applied to image feature extraction, image enhancement, image restoration, image compression and image recognition and other fields.This paper introduces the definition of orthogonal transformation, discussed the significance of orthogonal transform in digital image processing, and focuses on the standard of orthogonal transformation, orthogonal transformation is introduced three methods of Fourier transform, discrete cosine transform and the wavelet transformation, and through example, image transformation effect before and after contrast, apparatus for transformation is given, which concluded that the influence of different transformation methods for image processing. Experimental data, the results show that in the orthogonal transformation, the wavelet transform both in the transformation time and the quality of image processing is better than the discrete cosine transform.Key words：：digital image processing; orthogonal mapping; standard base image; DCT; 理工大学学士学位论文III目目 录录1 引言.................................................................................................................................11.1 图像正交变换的研究现状................................................................................11.2 图像正交变换的研究意义................................................................................21.3 图像正交变换的研究方向................................................................................31.4 图像正交变换的基本定义................................................................................32 开发环境 Visual C++....................................................................................................52.1 Visual C++ 6.0 介绍..........................................................................................52.2 Visual C++ 6.0 面向对象的有关概念的介绍..................................................62.3 Visual C++开发的介绍.....................................................................................82.4 Visual C++软件平台介绍.................................................................................92.4.1 单文档格式.............................................................................................92.4.2 界面板部分...........................................................................................102.4.3 程序控制部分.......................................................................................102.5 设计中的 MFC 介绍.......................................................................................113 CDIB 类的功能及作用...................................................................................................133.1 与设备无关的位图（DIB）...........................................................................133.2 Cdib 类的建立及构造.....................................................................................153.3 Cdib 类的设计目标.........................................................................................163.4 设计中的 CDib 类...........................................................................................174 图像正交变换方法研究...............................................................................................184.1 信号的正交分解..............................................................................................184.2 正交变换的重要性质......................................................................................184.3 正交变换的分类..............................................................................................194.4 正交变换的标准基..........................................................................................194.4.1 一维 DFT 的标准基.............................................................................194.4.2 二维 DFT..............................................................................................214.4.3 正交变换的标准基图像.......................................................................22理工大学学士学位论文IV4.5 正交变换在图像处理中的应用.....................................。