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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。
本文研究了图像配准背景下不同熵测度的应用,包括Renyi熵。具体来说,我们专注于图像配准的熵估计问题,并提供了两个重要的熵估计理论和实验比较:plug-in估计和最小熵图。我们进一步发展了一个基于图论估计的图像配准框架。在这个框架内,我们讨论了实际和理论问题,如空间信息的合并、有效和快速的最佳对齐搜索,以及预先对齐的图像对使用。这些分析产生了适用于不同医学问题的快速、鲁棒和精确的多模态仿射配准算法。接下来,我们研究了非刚性配准问题,提出了一种新的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标准化,并研究了一种基于相关熵测度的算法。
This thesis investigates the employment of different entropic measures,including R ́enyi entropy, in the context of image registration. Specifically, we focus on the entropyestimation problem for image registration and provide theoretical andexperimental comparisons of two important entropy estimators: the plug-inestimator and minimal entropic graphs. We further develop an image registrationframework based on the graph-theoretic estimator. Within this framework, weaddress practical and theoretical issues such as the incorporation of spatial information,the efficient and fast search of the optimum alignment, and the employment ofpreviously aligned image pairs. These analyses yield fast, robust and accurate multi-modalaffine registration algorithms applicable to different medical problems. Next,we investigate the nonrigid registration problem and provide a novel fast entropy-basednonrigid registration algorithm. Finally, we discuss a scientific application,the normalization of the human cerebral cortex based on patterns of functionalresponse, and investigate an algorithm that employs a correlation-basedentropic measure.
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