A multigrid approach to visual cortex mapping


  • David Herschel Smith




Multigrid, cortex, optimisation


Standard unconstrained optimisation methods, utilising conjugate gradient and limited memory reduced Hessian search direction updates, are implemented in a multigrid mode on an objective function minimisation model of visual cortex mapping. The multigrid operations, executed on a hierarchy of four grids, easily outpace fine grid iterations, and penetrate deeper into the objective function. References
  • W. H. Bosking et al., Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex, The Journal of Neuroscience 17, 6 p2112--2127 (1997). http://www.jneurosci.org/cgi/content/abstract/17/6/2112
  • W. L. Briggs, A Multigrid Tutorial, SIAM, Philadelphia (1988).
  • R. H. Byrd et al., Representations of quasi-Newton matrices and their use in limited memory methods, Mathematical Programming 63, 4 p129--156 (1994). doi:10.1007/BF01582063
  • M. A. Carreira--Perpinan, R. J. Lister and G. J. Goodhill, A computational model for the development of multiple maps in primary visual cortex, Cerebral Cortex 15, 8 p1222--1233 (2005). doi:10.1093/cercor/bhi004
  • T. Dreyer et al., Multigrid optimization in applications, J. Comp. Appl. Math. 120 p67--84 (2000). doi:10.1016/S0377-0427(00)00304-6
  • R. Durbin and G. Mitchison, A dimension reduction framework for understanding cortical maps, Nature 343, p644--647 (1990). doi:10.1038/343644a0
  • R. Fletcher, Practical Methods of Optimization, Wiley (1987).
  • S. Fulton et al., Multigrid methods for elliptic problems: A review, Monthly Weather Review 114 p943--959 (1986). doi:10.1175/1520-0493(1986)114<0943:MMFEPA>2.0.CO;2
  • J. Gilbert and J. Nocedal, Global convergence properties of conjugate gradient methods for optimization, SIAM J. Opt. 2, 1 p21--42 (1992). doi:10.1137/0802003
  • Numerical recipes online, http://www.nr.com.
  • Octave numerical computation software http://www.octave.org.
  • D. H. Smith, Visual cortex mapping by conjugate gradients, ANZIAM J. 50 (CTAC2008) pC75--C89, (2008). http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/1373
  • F. Wolf and T. Geisel, Spontaneous pinwheel annihilation during visual development, Nature 395, 3 p73--78 (1998). doi:10.1038/25736





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