Multilevel space-time aggregation for bright field cell microscopy segmentation and tracking
Journal of Biomedical Imaging - Special issue on mathematical methods for images and surfaces
Multigrid and multilevel preconditioners for computational photography
Proceedings of the 2011 SIGGRAPH Asia Conference
A Bootstrap Algebraic Multilevel Method for Markov Chains
SIAM Journal on Scientific Computing
Efficient preconditioning of laplacian matrices for computer graphics
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
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Multigrid solvers proved very efficient for solving massive systems of equations in various fields. These solvers are based on iterative relaxation schemes together with the approximation of the “smooth” error function on a coarser level (grid). We present two efficient multilevel eigensolvers for solving massive eigenvalue problems that emerge in data analysis tasks. The first solver, a version of classical algebraic multigrid (AMG), is applied to eigenproblems arising in clustering, image segmentation, and dimensionality reduction, demonstrating an order of magnitude speedup compared to the popular Lanczos algorithm. The second solver is based on a new, much more accurate interpolation scheme. It enables calculating a large number of eigenvectors very inexpensively.