| This dissertation addresses two of the main components in intensity-based two-dimensional and three-dimensional multimodal biomedical image registration: (1) The similarity measure, which indicates the closeness of the match between the images, and (2) The optimization approach to find the highest value of the similarity measure. Feature-based, statistical, and information-theoretic approaches have been used as similarity metrics. The latter have been shown to be robust and accurate, and are increasingly popular in many registration applications. These measures are largely based on the Shannon-Boltzmann-Gibbs definition of entropy. This dissertation proposes using information measures based on generalized entropies, including the Renyi, Havrada-Charvat-Tsallis, and R-norm measures, in addition to the Shannon measure. These entropies, of which the Shannon entropy is a special case, have properties that facilitate accurate registration.; Optimization of the similarity metric is the second focus of this dissertation. Traditionally, local techniques, such as Powell's direction set method and gradient-based methods, have been used. However, computing the derivative of the multidimensional similarity metric function is difficult and computationally expensive, and Powell's method is susceptible to entrapment in local extrema. Studies have recently appeared showing that local optimization, by itself, is often not sufficient for registration, and suggesting the use of simulated annealing, genetic algorithms, or evolutionary strategies for similarity metric optimization. The current work demonstrates that other global optimization methods, such as particle swarm optimization, may also be applied to registration. These methods have been adapted specifically for multimodal biomedical image registration.; The dissertation is divided into nine chapters. Chapter One provides an overview of image registration and describes the fundamental issues that must be addressed in registration. Chapter Two presents common similarity metrics, with emphasis on information-theoretic measures. The concept of entropy is also developed from its original physical context. Chapter Three presents the concept of generalized entropies and the derivation of similarity measures from these measures. Their properties, as they relate to registration, are discussed. In Chapter Four, the main local and global optimization paradigms for registration are presented, and new registration optimization adaptations, including the tabu search and particle swarm optimization, are proposed. Chapter Five discusses the materials and methods used in the experimental part of this work. Chapter Six presents the results of experiments to demonstrate the validity of using the proposed similarity measures, as well as comparing them with traditional similarity metrics. In Chapter Seven, the results of the proposed optimization approaches, as well as comparisons with other local and global techniques, are presented. In Chapter Eight, the results are discussed, and the relationship between similarity metrics and the methods needed to optimize these metrics is explored. Chapter Nine summarizes the dissertation, and indicates avenues for future work and improvements. Biomedical image registration is an expanding field in which there is still much room for further discoveries, and in which the potential for clinical and research benefits are just beginning to be realized. |
