III: Small: Multi-modal Neuroimaging Data Fusion and Analysis with Harmonic Maps Under Designed Riemannian Metric III: Small: Multi-modal Neuroimaging Data Fusion and Analysis with Harmonic Maps Under Designed Riemannian Metric Multi-modal Neuroimaging Data Fusion and Analysis with Harmonic Map Under Designed Riemannian Metric Project Summary The fast development in acquiring multi-modal neuroimaging data provide 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 these multi-modal data, there is an urgent need for multi-source data fusion frameworks to integrate and analyze these imaging data. The current practice usually involves nonlinear registration of brain volumetric data. These approaches ignores the folded brain cortical structures and the relationship between brain grey matter and white matter. Surface based approach may serve as a bridge for an integrative and generalized approach for multi-model data fusion and analysis. Although numerous studies have been devoted to surface based research, limited progress has been made to integrate different modality data with intrinsic surface 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-source data fusion and analysis problem. Intellectual Merit. An integrated research and education plan is outlined in this project to investigate and develop computational theorems and algorithms: (1) a method to compute the harmonic map under designed Riemannian metric between general surfaces. One key novelty is that the new method formulates multi-source information with Riemannian metric and thus the multi-source fusion problem is converted to compute harmonic map which is adapted to any designed Riemannian metric on the target surface; (2) a variational formulation that optimizes diffeomorphic harmonic map via adjusting the Riemannian metric. It will be a practical way to optimize diffeomorphisms between surfaces and provide the flexibility to introduce general objective functions defined on other sources; (3) a framework to compute the longitudinal registration of multi-modal data via designed Riemannian metric. The framework exploits freely available spatiotemporal atlas and may provide information about the missing data. This research will be based on the PIs extensive experience in conformal geometry. The anticipated outcomes of this research project are: (1) new computational algorithms on harmonic map with significant applications in various fields, such as computer vision, medical imaging, machine learning, computer graphics and geometric modeling; (2) a practical software package with rigorous mathematical foundation to register multi-modal data with arbitrary underlying topology structures. It will be tested on two datasets and evaluated by some established performance criteria. Broader Impact. The work outlined in this proposal will have applications in a number of research fields, including (1) Shape Analysis: 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. (2) Neuroimaging: 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 Alzheimers disease. (3) Related elds: Harmonic map and its related methods have applications in many other fields, including computer vision, medical imaging, machine learning, computer graphics, and geometric modeling. The PI will make the software tools accessible to the society. (4) Integrated education: This project will facilitate the development of new courses and laboratory infrastructure for computer vision 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.
|Effective start/end date||8/1/14 → 7/31/19|
- National Science Foundation (NSF): $418,114.00
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