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. / PhD thesis

Diffusion tensor imaging provides the ability to study white matter connectivity and integrity noninvasively. The information contained in the diffusion tensors is very complex. Therefore a simple way of dealing with tensors is to compute rotationally invariant scalar quantities. These scalar indices have been used to perform population studies between controls and patients with neurological and psychiatric disorders. Implementing the scalar values may reduce the information contained in the whole tensor. A group analysis using the full tensors may give better estimate of white matter changes that occur in the diseased subjects. For spatial normalization of diffusion tensors, it is necessary to interpolate the tensor representation as well as rotate the diffusion tensors after transformation to keep the tensors consistent with the tissue reorientation. Existing reorientation methods cannot be directly used for higher order diffusion models (e.g. q-ball imaging). A novel technique called gradient rotation is introduced where the rotation is directly applied to the diffusion sensitizing gradients providing a voxel by voxel estimate of the diffusion gradients instead of a volume of by volume estimate. The technique is validated by comparing it with an existing method where the transformation is applied to the resulting diffusion tensors. For better matching of diffusion tensors a novel multichannel registration method is proposed based on a non-parametric diffeomorphic demons algorithm. The channels used for the registration include T1-weighted volume and tensor components. A fractional anisotropy (FA) channel is used for defining the contribution of each channel. Including the anatomical data together with the tensors, allows the registration to accurately match the global brain shape and the underlying white matter architecture simultaneously. Using this multichannel registration framework, 10 healthy controls and 9 patients of schizophrenia were spatially normalized. For the group analysis, the tensors were transformed to log-euclidean space. Linear regression analysis was performed on the transformed tensors. Results show that there is a significant difference in the anisotropy between patients and controls especially in the anterior regions that include genu of the corpus callosum and anterior and superior corona radiata, forceps minor and anterior limb on the internal capsule.

<div>Adolescent collision-sport athletes may be exposed to repetitive head impacts over years of practices and competitions without immediately observable symptoms. Despite the growing concerns, these athletes often continue play while at risk. Concrete objective measurements are desired to inform prompt and effective preventative strategies for this vulnerable population. However, adolescent brains are rapidly developing and the accrual of brain injury is often subtle. Prospective screening with sensitive biomarkers is challenging and requires advanced technologies, rigorous data processing, and the interdisciplinary expertise of engineering, neurobiology, and cognitive sciences.</div><div><br></div><div>To address the challenge, we first developed population-specific brain atlases to facilitate reproducible and meaningful statistical analyses. The atlases better characterized the neuroanatomy of early-to-middle adolescent (ages 13-19) collision-sport athletes, reduced deformation introduced during spatial normalization, and exhibited higher sensitivity in image analysis compared to standardized adult or age-appropriate brain templates. The atlases can be further applied to monitor the neuroanatomical trajectory and can serve as a coordinate reference system to retrospectively harmonize data collected from different sites and imaging acquisition parameters, facilitating group analysis at large scale.</div><div><br></div><div>Next, to assess whether the changes of white matter microstructure can be attributed to repetitive head impacts and are reflected by cognitive performance, we analysed the diffusion tensor imaging (DTI) data of high school men’s football and women's soccer across a single season, with accompanying data from head impact sensors and neurocognitive assessments. Within multiple brain regions, we observed significantly altered DTI metrics, both transiently over a season and chronically with more years of high school experience. For the football players, hits with peak translational acceleration over 37 <i>g</i> were sufficient to alter the distributions of DTI changes, and deficits in white matter microstructure correlated with poorer performance of anti-saccade task at one month post-season, suggesting increased vulnerability for inhibitory control. Monitoring repetitive head impacts thus provides a temporal profile for identifying at-risk individuals during the competitive season, informing prompt interventional strategies, therefore protecting the brain and cognitive health of early-to-middle adolescent collision-sport athletes in the long run.</div>