PROJECT SUMMARY / ABSTRACT As of 2015 there were 940 million people with some degree of visual impairment in the world. Visual impairments generate considerable economic burden for the society. The World Health Organization estimates that 80% of visual impairments are either preventable or curable with treatment. Noninvasive imaging techniques have been used extensively by eye specialists for diagnosis and treatment of visual disorders and imaging is one of the priorities in the six core program areas of the National Eye Institute. As a noninvasive high spatial resolution technique for measuring brain activities, functional magnetic resonance imaging (fMRI) has provided a wealth of data on visual cortical organizations. Although numerous studies have been devoted to discovering and validating different retinotopic maps in the human visual system, limited progress has been made in developing software tools that fully consider the intrinsic geometrical features of the underlying cortical structures, enforce diffeomorphic mapping when constructing retinotopic maps and atlases, and integrate both individual and population statistics for more robust data analysis. In preliminary work, we have developed a complete and invertible description of retinotopic maps (U.S. Patent Application Nos. 16/230,284 and 63/004,721, supported by NSF collaborative research awards DMS-1413417 and DMS-1412722). This project will continue developing and applying novel quasiconformal geometry and hierarchical Bayesian modeling (HBM) algorithms to retinotopy data obtained from the Human Connectome Project (HCP), the largest high resolution retinotopy dataset to date. We hypothesize that, by combining Beltrami smoothing, quasiconformal mapping and HBM, the proposed approach will reduce manual annotation work and maximize the statistical power of retinotopic mapping techniques. The project aims to: (1) Develop computational methods to effectively smooth retinotopic maps across multiple visual areas based on Beltrami smoothing. With Beltrami descriptions, the proposed method will simultaneously smooth eccentricity and polar angle retinotopy data in V1, V2 and V3, while preserving the underlying topological continuity; (2) Develop computational methods to effectively register retinotopic maps of multiple visual areas across subjects with quasiconformal mapping. Unlike previous work that relied on either structural MRI (sMRI) or fMRI data only, the proposed method will simultaneously register both sMRI and fMRI data from multiple visual areas across subjects and ensure diffeomorphism; (3) Develop an HBM of the retinotopic maps to capture the hierarchy at both the individual and group levels. The proposed HBM will help overcome measurement noise, reveal both population properties and individual differences, and offer unprecedented accuracy on retinotopic map analysis; (4) Develop and disseminate software tools and atlases of human retinotopic maps. The developed open-source softw...