A Unified Information Theoretic Framework for Pair- and Group-wise Registration of Medical Images
The field of medical image analysis has been rapidly growing for the past two decades. Besides a significant growth in computational power, scanner performance, and storage facilities, this acceleration is partially due to an unprecedented increase in the amount of data sets accessible for researchers. Medical experts traditionally rely on manual comparisons of images, but the abundance of information now available makes this task increasingly difficult. Such a challenge prompts for more automation in processing the images.In order to carry out any sort of comparison among multiple medical images, onefrequently needs to identify the proper correspondence between them. This step allows us to follow the changes that happen to anatomy throughout a time interval, to identify differences between individuals, or to acquire complementary information from different data modalities. Registration achieves such a correspondence. In this dissertation we focus on the unified analysis and characterization of statistical registration approaches.We formulate and interpret a select group of pair-wise registration methods in the context of a unified statistical and information theoretic framework. This clarifies the implicit assumptions of each method and yields a better understanding of their relative strengths and weaknesses. This guides us to a new registration algorithm that incorporates the advantages of the previously described methods. Next we extend the unified formulation with analysis of the group-wise registration algorithms that align a population as opposed to pairs of data sets. Finally, we present our group-wise registration framework, stochastic congealing. The algorithm runs in a simultaneous fashion, with every member of the population approaching the central tendency of the collection at the same time. It eliminates the need for selecting a particular referenceframe a priori, resulting in a non-biased estimate of a digital template. Our algorithm adopts an information theoretic objective function which is optimized via a gradientbased stochastic approximation process embedded in a multi-resolution setting. We demonstrate the accuracy and performance characteristics of stochastic congealing via experiments on both synthetic and real images.