本文为美国科罗拉多大学（作者：Katherine AnneBachman）的硕士论文，共126页。

本研究以离散互信息为基础，以平面、二维影像为例，运用不同的搜索策略验证了该理论的应用。图像配准是在图像数据之间寻找最佳几何变换的过程。虽然它在很多领域都有应用，但本文所研究的是医学图像配准。医学图像配准有着广泛的应用前景，但其重点是放射线成像。互信息是由单个重叠图像的熵之和与组合图像的联合熵之差给出的，是由于对另一个图像的了解而减少对一个图像不确定性的度量。它不假设两幅图像的函数形式或图像强度之间的关系。除了在通信和计算机视觉中有应用外，互信息被证明是可靠的，并产生了目前正在使用的全自动配准算法。

本论文的结构如下。第一章概述了医学图像配准，并在此背景下提出了基于互信息的医学图像配准研究课题。第二章论述了离散互信息的理论和数学及其在信息论中的起源。第三章介绍了该理论在图像配准中的应用。第四章介绍了基于互信息的图像配准在放射成像中的应用——数字重建射线照片（DRRs）和电子束图像（EPIs）的配准。附录包括与理解本文所述材料相关但不重要的信息。由于概率论是信息论的一个重要组成部分，因此，在附录中简要介绍了离散概率论，作为读者的快速参考。附录和整个论文正文都提供了示例。

This study regards discrete mutual information and demonstratesthe use of the theory with an example of radiological image registration within-plane, two dimensional images, using various search strategies. Imageregistration is the process of finding an optimal geometric transformation betweencorresponding image data. Although it has applications in many fields, the onethat is addressed in this thesis is medical image registration. Medical imageregistration has a wide range of potential applications, but the emphasis is onradiological imaging. Mutual information, which is given by the differencebetween the sum of the entropies of individual overlapping images and the jointentropy of the combined images, is a measure of the reduction in uncertaintyabout one image due to knowledge of the other. It makes no assumption of thefunctional form or relationship between image intensities in the two images. Inaddition to having application in communication and computer vision, mutualinformation has proven robust and has resulted in fully automated registrationalgorithms that are currently in use. The thesis is organized as follows.Chapter 1 gives a broad overview of medical image registration as the contextin which to present the subject of mutual information-based medical imageregistration. Chapter 2 regards the theory and mathematics of discrete mutualinformation and its origin in information theory. Chapter 3 looks at theimplementation of the theory applied to image registration in general. Chapter4 looks at an application of mutual information-based image registration inradiological imaging - registration of Digitally Reconstructed Radiographs(DRRs) and Electronic Portal Images (EPIs). The Appendix includes informationthat is relevant, but not critical, to the understanding of the material presentedin this thesis. Because probability theory is a major part of information theoryand, consequently, mutual information theory, a brief overview of discrete probabilitytheory is included in the Appendix as a quick reference. Examples are providedin the Appendix as well as throughout the body of the thesis.

1 医学图像配准回顾

2 信息论

3 应用于图像配准的信息论

4 基于互信息的数字化重建射线照片与电子束图像配准

5 结论

附录A 离散概率论概述

附录B 凸特性

附录C 对数转换

附录D 样本输出

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