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Center for Nonlinear Studies |
Multigrid Eigensolvers for Image Segmentation Andrew Knyazev Dept Math. and Stat. Sci., UC Denver Image segmentation can be performed using eigenvectors of corresponding graph Laplacians. We give an intuitive mechanical interpretation of the process using vibration modes of mass-spring systems in a thought experiment, where masses correspond to the pixels and springs stiffness is determined by a similarity between the pixels. The ultimate goal is to find methods with linear complexity, i.e. with computational costs that scale linearly with with the number of the pixels. Multigrid approaches are natural for image segmentation, where different image resolution scales are easily available. We numerically analyze our eigensolver PETSc-BLOPEX with Hypre algebraic multigrid preconditioning for megapixel image segmentation on parallel computers. E.g., we bipartition a 24 megapixel image in seconds on IBM BlueGene/L. References: A. V. Knyazev, I. Lashuk, M. E. Argentati, and E. Ovchinnikov, Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) in hypre and PETSc. SIAM J. Sci. Comp. 25: 2224-2239, 2007.
Host: Anna Matsekh