## Keywords

motion, model, inversive geometry

## Abstract

Velocity encoding in the primate brain can be modelled by a spatiotemporal gradient approach, with neurons characterized as spatio-temporal derivative operators (Johnston et al. 1999). This strategy works well for moving 1D spatial patterns, but it can produce systematic errors, as it can be overly influenced by the direction of the local spatial gradient of the image brightness. For 2D pattern it is possible to develop a similar spatio-temporal approach, in which the system solves a set of over-determined linear equations directly, to provide an estimate for the 2D image motion. However, in this case the matrix one needs to invert is indeterminate for 1D image pattern. This can be accommodated by introducing a constant on the diagonal of the matrix, as is done in ridge regression. However, the constant, however chosen, will introduce different degrees of error at each location due to the variation in the magnitudes of the spatio-temporal derivatives. Here we return to a geometric view of the solution of a system of linear equations through Cramer’s rule and formulate a geometrical strategy which delivers the 2D solution when the image pattern has 2D structure but which defaults automatically to the 1D computation (Johnston et al. 1999), when the image structure is 1D. The model makes the key prediction of the existence of neurons that respond to 2D pattern (plaids) but not 1D pattern (gratings), sometimes referred to as super pattern cells, which do not fit well into current theories of primate motion processing.

## Start Date

16-5-2018 11:35 AM

## End Date

16-5-2018 12:00 PM

#### Included in

A Model of 1D and 2D Motion Processing in the Primate Brain

Velocity encoding in the primate brain can be modelled by a spatiotemporal gradient approach, with neurons characterized as spatio-temporal derivative operators (Johnston et al. 1999). This strategy works well for moving 1D spatial patterns, but it can produce systematic errors, as it can be overly influenced by the direction of the local spatial gradient of the image brightness. For 2D pattern it is possible to develop a similar spatio-temporal approach, in which the system solves a set of over-determined linear equations directly, to provide an estimate for the 2D image motion. However, in this case the matrix one needs to invert is indeterminate for 1D image pattern. This can be accommodated by introducing a constant on the diagonal of the matrix, as is done in ridge regression. However, the constant, however chosen, will introduce different degrees of error at each location due to the variation in the magnitudes of the spatio-temporal derivatives. Here we return to a geometric view of the solution of a system of linear equations through Cramer’s rule and formulate a geometrical strategy which delivers the 2D solution when the image pattern has 2D structure but which defaults automatically to the 1D computation (Johnston et al. 1999), when the image structure is 1D. The model makes the key prediction of the existence of neurons that respond to 2D pattern (plaids) but not 1D pattern (gratings), sometimes referred to as super pattern cells, which do not fit well into current theories of primate motion processing.