CCB / Math-VIGRE Summer graduate student research fellowships -- Summer 2008
Together with
Math/VIGRE support, CCB is sponsoring annual Summer Research Fellowships for graduate students. In 2008, the following 4 projects were selected that address some of the
main mathematical and computational challenges tackled by CCB researchers.
Quantitative Comparisons of Narrow-Band and Mesh-based Algorithms for Computing the Laplace-Beltrami Spectrum
- GSR: Wenhua Gao
- Summary: In this project we will perform quantitative comparisons of a narrow-band approach of computing the Laplace-Beltrami spectrum, which we developed recently, with the conventional algorithm using triangular meshes. Because the narrow-band approach is based on regular grids, we believe it will perform better numerically. More specifically, we will first study the conditional number of the eigenvalue problem that is formed by the two different approaches. After that, we will study the robustness of the two different approaches with respect to small perturbations to the geometry of the surface.
Graph matching techniques for the analysis cortical folding patterns
- GSR: Alvin Wong
- Summary: The folding pattern of the cortical surfaces is an intriguing and important topic in analyzing brain morphometry. Based on previous work of computing Hamilton-Hacobi skeletons on cortical surfaces, we investigate the analysis of cortical folding patterns via graph matching. We will first study the construction of attributed graphs based on the skeletal representation of the sucal/gyral regions. After that, graph matching algorithm will be designed to extract the major sulci/gyri from the cortical surface.
Application of eigenfunctions of Laplacian_Beltrami operator to shape analysis
- GSR: Rongjie Lai
- Summary: This project will study how to use eigenfunctions of Laplacian-Beltrami operator on shapes to study shapes themselves. Mathematically, all of eigenfunctions of a given shape form a basis of the L^2 function space of the given shape, and if we know the L^2 function space of a given shapes, we should know the information of the given shape. Moreover, the big advantage of eigenfunctions is that all of them are intrinsic, i.e. rotation and translation invariant. We already know how to get the eigenfunctions of a given shape -- our goal this summer is to find out how to use these eigenfunctions to study the intrinsic geometric information of the shape.
Spherical deconvolution techniques for diffusion image reconstruction
- GSR: Wenye Ma
- Summary: With the promise of resolving crossing fibers in the white matter of human brains, high angular resolution diffusion imaging (HARDI) is becoming an important research topic in brain mapping. In this project, we will study spherical deconvolution techniques to reconstruct fiber orientation density (FOD) functions from noisy and sparse HARDI data. More specifically, we will investigate and extend L1 regularization techniques to the problem of spherical deconvolution and compare with existing algorithms in terms of resolution and efficiency.
- Private HARDI Project Page
