Compared to the development of visual data acquisition technology and the explosive collection of acquired datasets, computational techniques for knowledge discovery and learning from very large, diverse, heterogeneous visual datasets have only evolved modestly, ultimately impeding the more effective utilization and better understanding. The project aims to bridge the aforementioned gaps and foster a strong research program in geometry-guided knowledge discovery in multimodality visual data, with an emphasis on neuroimaging applications. Specifically, the project focuses on: (1) exploring new tools based on Riemannian geometry for computing geometric structures of 3-manifolds and developing a novel volumetric mapping with geometric flow; (2) developing a rigorous mathematical foundation for semi-supervised data clustering; and (3) extending our approaches on geometric mapping and semi-supervised learning to (high-order) heterogeneous volumetric visual data analysis. Once developed, these novel algorithms are applied to computer assisted diagnosis of various important brain diseases, such as tumors and brain functional disorder. This project can help with identifying disease patterns in human brain, and thus possibly provides both clinical and social benefits to a large sector of the population. Moreover, the project can immediately help to elevate the existing resources and on-going research to a unified, systematic level and strengthen computer science education. The research results will be widely disseminated to both computer science and medical communities through free Web access of the software tools (including source codes), and the set of sample data (including raw neuroimaging data and processed ones such as high-resolution brain surface meshes) via the project Web site (www.cs.wayne.edu/~mdong/NSF_CRI.html).
