Dimension reduction, generalized deformable models and the development of occularity and orientation

It has been proposed that the spatial organization of cells in the visual cortex satisfies an abstract optimization criterion based on a smooth mapping criterion. The authors apply this criterion to the development of occularity and show that it can be expressed in terms of a generalized deformable model. From this model one can derive two alternative algorithms, one based on elastic nets and the other on Hebb rules. This shows a surprising mathematical relation between the elastic net model of G.J. Goodhill and D. Willshaw (1990) and the Hebbian models of K.D. Miller et al. (1989) and Tanaka (1990), even though their biophysical mechanisms are very different. Applying the same techniques to the development of orientation shows mathematically that a variant of the dimension reduction criterion of R. Durbin and G. Mitchison (1990) can be closely approximated by an elastic net. Computer simulations of the present algorithms give good agreement with experimental data. >