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**0**

**7**

Phillip Sheridan *Griffith University*

*Australia*

**Cortical Specification of a Fast Fourier**

Currently, the full extent of the role Fourier analysis plays in biological vision is unclear. Although we have examples of sensory organs that perform Fourier transforms, e.g. the lens of the eye and the cochlear, to date there is no direct empirical evidence for its implementation in cortical architecture. However, there does exist intriguing theoretical evidence that suggests a role for the Fourier transform in a primate's primary visual cortex (area V1) which emerges from recent developments in our knowledge of contextual modulation. This paper proposes a new Fourier transform and a specification of how this transform has a natural implementation in cortical architecture. The significance of this new Fourier transform and its specification in neural circuitry is that it provides a plausible explanation for previously unexplained

The spatial response properties, such as orientation tuning and spatial frequency tuning, of neurons in area V1 have been known for some time (Schiller et al., 1976). For a while, it was generally accepted that these tuning functions of receptive fields are largely context-independent (De Valois et al., 1979). However, later research has demonstrated contextual influences from the region close to the receptive field (Sceniak et al., 2001); (Cavanaugh et al., 2002); (Bair & Movshen, 2004). Moreover, it has been found that this near surround region of a receptive field can modify receptive field responses through suppression (Blakemore & Tobin, 1972) and by cross-orientation facilitation effects (Sillito & Jones, 1996); (Cavanaugh et al., 2002); (Kimura & Ohzawa, 2009). It has also been demonstrated that long-range contextual modulation is as robust a feature of neural function in area V1 as the extensively studied receptive field properties of this area (Lamme, 1995). Since that time, the evidence for long-range contextual modulation continues to grow, e.g. (Zipser et al., 1996);

Concurrent with this research establishing the empirical evidence for contextual modulation has been research aimed at developing functional models of V1 that are consistent with the empirical evidence. In the early 1980's the concept of convolution was employed by David Marr (Marr & Hildreth, 1980) as a model that accounted for considerable observable

**1. Introduction**

1.0.0.1

1.0.0.2

observable properties of the primate vision system.

(Lamme et al., 1998); (Lee et al., 1998).

**Transform Supports a Convolution**

**Model of Visual Perception**

