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本文为美国普林斯顿大学(作者:Mert Rory Sabuncu)的博士论文,共161页。
本文研究了在图像配准的背景下,不同熵测度(包括熵)的应用。具体地说,我们研究了图像配准中的熵估计问题,并对两种重要的熵估计方法:plug-in估计器和最小熵图进行了理论和实验比较。我们进一步发展了一个基于图论估计器的图像配准框架。在这个框架内,我们解决了一些实际和理论问题,如空间信息的合并、最佳合并的高效和快速搜索以及使用先前对齐的图像对。这些分析给出了适用于不同医学问题的快速、鲁棒、准确的多模态仿射配准算法。其次,研究了非刚性配准问题,提出了一种基于熵的快速非刚性配准算法。最后,我们讨论了一个科学应用,即基于功能反应模式的大脑皮层规范化,并研究了一种基于相关熵测度的算法。
This thesis investigates the employment ofdifferent entropic measures, including R′enyi entropy, in the context of imageregistration. Specifically, we focus on the entropy estimation problem forimage registration and provide theoretical and experimental comparisons of twoimportant entropy estimators: the plug-in estimator and minimal entropicgraphs. We further develop an image registration framework based on thegraph-theoretic estimator. Within this framework, we address practical andtheoretical issues such as the incorporation of spatial information, theefficient and fast search of the optimum alignment, and the employment ofpreviously aligned image pairs. These analyses yield fast, robust and accuratemulti-modal affine registration algorithms applicable to different medicalproblems. Next, we investigate the nonrigid registration problem and provide anovel fast entropy-based nonrigid registration algorithm. Finally, we discuss ascientific application, the normalization of the human cerebral cortex based onpatterns of functional response, and investigate an algorithm that employs acorrelation-based entropic measure.
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