Gabor Wavelets

There is considerable evidence (reviewed in MacLennan 1991) that images in primary visual cortex (V1) are represented in terms of Gabor wavelets, that is, hierarchically arranged, Gaussian-modulated sinusoids (equivalent to the pure states of quantum mechanics). The Gabor-wavelet transform of a two-dimensional visual field generates a four-dimensional field: two of the dimensions are spatial, the other two represent spatial frequency and orientation. To represent this four-dimensional field in two-dimensional cortex, it is necessary to ``slice'' the field, which gives rise to the columns and stripes of striate cortex. The representation is nearly optimal, as defined by the Gabor Uncertainty Principle (a generalization of the Heisenberg Uncertainty Principle to information representation and transmission). Time-varying two-dimensional visual images may be viewed as three-dimensional functions of space-time, and it is possible that time-varying images are represented in vision areas by a three-dimensional Gabor-wavelet transform, which generates a time-varying five-dimensional field (representing two spatial dimensions, spatial frequency, spatial orientation and temporal frequency). The effect is to represent the ``optic flow'' of images in terms spatially fixed, oriented grating patches with moving gratings. (See MacLennan 1991 for more details.) Finally, Pribram provides evidence that Gabor representations are also used for controlling the generation of motor fields (see citations in MacLennan 1997, p. 64).