Representation of local geometry in the visual system
- 964 Downloads
It is shown that a convolution with certain reasonable receptive field (RF) profiles yields the exact partial derivatives of the retinal illuminance blurred to a specified degree. Arbitrary concatenations of such RF profiles yield again similar ones of higher order and for a greater degree of blurring.
By replacing the illuminance with its third order jet extension we obtain position dependent geometries. It is shown how such a representation can function as the substrate for “point processors” computing geometrical features such as edge curvature. We obtain a clear dichotomy between local and multilocal visual routines. The terms of the truncated Taylor series representing the jets are partial derivatives whose corresponding RF profiles closely mimic the well known units in the primary visual cortex. Hence this description provides a novel means to understand and classify these units.
Taking the receptive field outputs as the basic input data one may devise visual routines that compute geometric features on the basis of standard differential geometry exploiting the equivalence with the local jets (partial derivatives with respect to the space coordinates).
Unable to display preview. Download preview PDF.
- Abramowitz M, Stegun IA (1964) Handbook of mathematical functions. Dover, New YorkGoogle Scholar
- Arnold VI, Gusein-Zade SM, Varchenko AN (1985) Singularities of differential maps. Birkhäuser, BostonGoogle Scholar
- Campbell DT, Robson JG (1968) Application of Fourier analysis to the visibility of gratings. J Physiol 197:551–566Google Scholar
- Cartan E (1943) Les surfaces qui admettent une seconde forme fondamentale donnée. Bull Sci Math 67:8–32Google Scholar
- Babor D (1946) Theory of communication. J IEE 93:429–459Google Scholar
- Hartmann G (1982) Recursive features of circular receptive fields. Biol Cybern 43:199–208Google Scholar
- Hubel D, Wiesel T (1977) Functional architecture of Macaque monkey visual cortex. Proc R Soc (London) B 198:1–59Google Scholar
- Koenderink JJ, Doorn AJ van (1984) The structure of images. Biol Cybern 50:363–370Google Scholar
- Koenderink JJ, Doorn AJ van (1986) Dynamic shape. Biol Cybern 53:383–396Google Scholar
- Poston T, Stewart I (1978) Catastrophy theory and its applications. Pitman, LondonGoogle Scholar
- Sekuler R, Blake R (1985) Perception. A.A. Knopf, New YorkGoogle Scholar