Mathematical description of the responses of simple cortical cells*

Abstract

On the basis of measured receptive field profiles and spatial frequency tuning characteristics of simple cortical cells, it can be concluded that the representation of an image in the visual cortex must involve both spatial and spatial frequency variables. In a scheme due to Gabor, an image is represented in terms of localized symmetrical and antisymmetrical elementary signals. Both measured receptive fields and measured spatial frequency tuning curves conform closely to the functional form of Gabor elementary signals. It is argued that the visual cortex representation corresponds closely to the Gabor scheme owing to its advantages in treating the subsequent problem of pattern recognition.

Biological image motion processing: A review

“…3(B)]. This orthogonal basis set of receptive fields has been suggested for the visual cortex by Marcelja (1980) and corresponding single unit evidence for the existence of orthogonal sine and cosine cells has been reported by Pollen and Ronner (1979). This is a reasonable assumption because an orthogonally configured array of such channels optimally codes visual information with the smallest number of channels.…”

“…each sensitive to both the spatial position of the retinal image and also to different spatial frequency ranges (Blakemore and Campbell. 1969;Campbell cl a[.. 1969: Wilson and Bergen, 1979: Marcelja. 1980).…”

“…Alternatively, the same image motion can be equivalently expressed in the frequency domain where L(Er, Fy, Fr) is the Fourier transform of L(x,y, I). Because it appears that the early processing of visual information involves a simultaneous and rather efficient encoding of both position and spatial frequency (Campbell et al, 1969;DeValois et al, 1982;Marcelja, 1980), it is also useful to think of image motion in spatio-temporal frequency terms.…”

Variation in visual acuity within pigmented, and between pigmented and albino rat strains

“…Sinusoidal grating acuity was measured specifically because the receptive fields of neurons in primary visual cortex are spatial frequency and orientation tuned, and a sinusoid presents a single spatial frequency. In addition, any complex visual stimulus can be decomposed into component sine waves and the mammalian visual system displays many of the functional features of Fourier analysis [15].…”

Motion detection, noise reduction, texture suppression, and contour enhancement by spatiotemporal Gabor filters with surround inhibition

“…Computational models were developed aiming at simulating the function of these neurons for understanding and predicting their responses to more complex visual stimuli. The spatial summation properties of simple cells were modeled by linear filters followed by half-wave rectification (Movshon et al 1978b;Andrews and Pollen 1979;Glezer et al 1980;Kulikowski and Bishop 1981) and Gabor functions proved to be particularly well suited for this purpose (Marcelja 1980;Daugman 1985;Jones and Palmer 1987). Complex cells needed more intricate modeling, which included linear filtering, half-wave rectification and subsequent local spatial summation, or quadrature pair summation of linear filter responses (Movshon et al 1978a;Spitzer and Hochstein 1985;Morrone and Burr 1988;Petkov and Kruizinga 1997;Kruizinga and Petkov 1999;Grigorescu et al 2002, Grigorescu et al 2003.…”