The rapid development in acquiring multi-modal neuroimaging data provides exciting new opportunities to systematically characterize human brain structure, its relationship to cognition and behavior, and the contributions of genetic and environmental factors to individual differences in brain circuitry. To optimally use such rich multi-modal data, there is an urgent need for powerful computational frameworks to integrate and analyze multi-source data. The current practice usually combines available data features from different sources without considering the intrinsic geometry and biology structure relationship between data sources. Shape analysis based approach may serve as a bridge for a general and integrative approach to multi-model data fusion and analysis. Although numerous studies have been devoted to imaging data registration research, limited progress has been made to integrate different modality data with some physically nature and geometrically intrinsic structures. This proposal focuses on investigating and developing computational algorithms on harmonic map with prescribed Riemannian metric, and on producing theoretically sound and practically efficient solutions for general multi-modal data fusion and analysis problems. The work outlined in this proposal will have applications in a number of research fields, including (1) Shape Analysis, neuroimaging and medical imaging in general. The proposed research unifies and connects a variety of computational geometry techniques and tackles a few open problems making it an ideal framework for teaching concepts in shape analysis as well as providing students a broader context in which various components may fit together. The algorithms and tools developed in this project will have a direct impact on neuroimaging research. It may enable discovery of multi-modal imaging biomarkers for some neurodegenerative disease, such as Alzheimer's disease. Harmonic maps and their related methods have applications in many other fields, including medical imaging, computer vision, machine learning, computer graphics, and geometric modeling. The PI will make the software tools accessible to the society. This project will facilitate the development of new courses and laboratory infrastructure for neuroimaging research. It also provides a unique opportunity for students from computer science to learn neuroscience more efficiently. The funding will allow continuation of ongoing efforts to actively recruit and advise students from under-represented groups.
An integrated research and education plan is outlined in this project to investigate and develop computational theorems and algorithms. The first goal is to develop a method to compute the harmonic map under a designed Riemannian metric between general surfaces. One key novelty is that the new method formulates multi-source information with a Riemannian metric and thus the multi-source fusion problem is converted to compute a surface harmonic map which is adapted to any designed Riemannian metric on the target surface. Next, a variational formulation that optimizes the diffeomorphic harmonic map via adjusting the Riemannian metric will be developed. The harmonic map guarantees that it has the global minimum deformation. It will be a practical way to optimize diffeomorphisms between surfaces and provide the flexibility to introduce general objective functions defined by other data sources. In addition, an algorithm for volumetric harmonic maps under a designed Riemannian metric and a set of novel multivariate geometry statistics for multi-source data analysis will be implemented. The framework explores multi-source data fusion with intrinsic geometry structures and the multivariate statistics may provide more sensitive, reliable and accessible brain imaging biomarkers for neuroimaging analysis. The anticipated outcomes of this research project are: (1) new computational algorithms on harmonic maps with significant applications in various fields, such as medical imaging, computer vision, machine learning, computer graphics and geometric modeling; (2) a practical software package with a rigorous mathematical foundation to analyze multi-modal data and produce sensitive and comprehensive multivariate imaging statistics. It will be tested on a large public neuroimaging dataset and evaluated by various classification tasks.
