Many large-scale cross-sectional and longitudinal imaging studies have been or are being widely conducted to better understand the progress of neurodegenerative and neuropsychiatric disorders or normal brain development. This project will analyze imaging, behavioral, and clinical data from two large neuroimaging studies of schizophrenia and autism. The primary goal of this project is to develop new statistical tools and to evaluate these statistical tools for analysis of imaging data (e.g., diffusion tensor, deformation tensor, medial shape representation) in curved space, in combination with behavioral and clinical information in Euclidean space obtained from both cross-sectional and longitudinal studies. As these tools are developed, they will be evaluated and refined, and the efficacy of the tools developed under this grant will be tested by both simulated datasets and the two datasets including a longitudinal MRI study of schizophrenia and a longitudinal MRI study of autism, respectively. Moreover, the companion software for all developed statistical tools, once validated, will be disseminated to imaging researchers through http://www.nitrc.org/. This analysis software will provide much needed imaging tools for analyzing complex, correlated imaging data in biomedical, behavioral, and social sciences.