摘要信息论是人们在长期通信实践活动中，由通信技术与概率论、随机过程、数理统计等学科相结合而逐步发展起来的一门新兴交叉学科。

而熵是信息论中事件出现概率的不确定性的量度，能有效反映事件包含的信息。

随着科学技术，特别是信息技术的迅猛发展，信息理论在通信领域中发挥了越来越重要的作用，由于信息理论解决问题的思路和方法独特、新颖和有效，信息论已渗透到其他科学领域。

随着计算机技术和数学理论的不断发展，人工智能、神经网络、遗传算法、模糊理论的不断完善，信息理论的应用越来越广泛。

在图像处理研究中，信息熵也越来越受到关注。

为了寻找快速有效的图像处理方法，信息理论越来越多地渗透到图像处理技术中。

本文通过进一步探讨概论率中熵的概念，分析其在图像处理中的应用，通过概念的分析理解，详细讨论其在图像处理的各个方面：如图像分割、图像配准、人脸识别，特征检测等的应用。

本文介绍了信息熵在图像处理中的应用，总结了一些基于熵的基本概念，互信息的定义。

并给出了信息熵在图像处理特别是图像分割和图像配准中的应用，最后实现了信息熵在图像配准中的方法。

关键词：信息熵，互信息，图像分割，图像配准AbstractInformation theory is a new interdisciplinary subject developed in people long-term communication practice, combining with communication technology, theory of probability, stochastic processes, and mathematical statistics. Entropy is a measure of the uncertainty the probability of the occurrence of the event in the information theory, it can effectively reflect the information event contains. With the development of science and technology, especially the rapid development of information technology, information theory has played a more and more important role in the communication field, because the ideas and methods to solve the problem of information theory is unique, novel and effective, information theory has penetrated into other areas of science. With the development of computer technology and mathematical theory, continuous improvement of artificial intelligence, neural network, genetic algorithm, fuzzy theory, there are more and more extensive applications of information theory. In the research of image processing, the information entropy has attracted more and more attention. Inorder to find the fast and effective image processing method, information theory is used more and more frequently in the image processing technology. In this paper, through the further discussion onconcept of entropy, analyzes its application in image processing, such asimage segmentation, image registration, face recognition, feature detection etc.This paper introduces the application of information entropy inimage processing, summarizes some basic concepts based on the definition of entropy, mutual information. And the information entropyof image processing especially for image segmentation and image registration. Finally realize the information entropy in image registration.Keywords：I nformation entropy, Mutual information, Image segmentation,Image registration目录摘要.......................................................................................................................... ...... ABSTRACT .........................................................................................................................目录.............................................................................................................................1 引言...................................................................................................................................1.1信息熵的概念.............................................................................................................1.2信息熵的基本性质及证明.........................................................................................1.2.1 单峰性..................................................................................................................1.2.2 对称性..................................................................................................................1.2.4 展开性..................................................................................................................1.2.5 确定性.................................................................................................................. 2基于熵的互信息理论 .......................................................................................................2.1 互信息的概述............................................................................................................2.2 互信息的定义............................................................................................................2.3 熵与互信息的关系....................................................................................................3 信息熵在图像分割中的应用...........................................................................................3.1图像分割的基本概念 ...............................................................................................3.1.1图像分割的研究现状 ..........................................................................................3.1.2 图像分割的方法..................................................................................................3.2 基于改进粒子群优化的模糊熵煤尘图像分割.........................................................3.2.1 基本粒子群算法..................................................................................................3.2.2 改进粒子群优化算法..........................................................................................3.2.3 Morlet变异 ..........................................................................................................3.2.4改建粒子群优化的图像分割方法.......................................................................3.2.5 实验结果及分析..................................................................................................3.3 一种新信息熵的定义及其在图像分割中的应用 ....................................................3.3.1香农熵的概念及性质..........................................................................................3.3.2一种信息熵的定义及证明..................................................................................3.3.3信息熵计算复杂性分析......................................................................................3.3.4二维信息熵阈值法..............................................................................................3.3.5二维信息熵阈值法的复杂性分析......................................................................3.3.6 结论及分析.........................................................................................................4 信息熵在图像配准中的应用...........................................................................................4.2基于互信息的图像配准.............................................................................................4.3P OWELL算法 ..............................................................................................................4.4变换.............................................................................................................................4.4.1平移变换...............................................................................................................4.4.2旋转变换...............................................................................................................4.5基于互信息的图像配准的设计与实现.....................................................................4.5.1总体设计思路和图像配准实现 .........................................................................4.5.2直方图 ...................................................................................................................4.5.3联合直方图...........................................................................................................4.5.4灰度级差值技术 ...................................................................................................4.4.5优化搜索办法级结论 .......................................................................................... 5结语...............................................................................................................................致谢...............................................................................................................................参考文献...........................................................................................................................1 引言1.1.信息熵的概念1948年，美国科学家香农(C．E．Shannon)发表了一篇著名的论文《通信的数学理论》。