Papers that reference this paper.

A hexagonal orthogonal-oriented pyramid as a model of image representation in visual cortex

Andrew B. Watson & A. J. Ahumada Jr. (1989) IEEE Transactions on Biomedical Engineering 36(1), 97-106.

Acrobat Version

Abstract

Retinal ganglion cells represent the visual image with a spatial code, in which each cell conveys information about a small region in the image. In contrast, cells of primary visual cortex employ a hybrid space-frequency code in which each cell conveys information about a region that is local in space, spatial frequency, and orientation. Despite the presumeable importance of this transformation, we lack any comprehensive notion of how it occurs. Here we describe a mathematical model for this transformation. The hexagonal orthogonal-oriented quadrature pyramid (HOP) transform, which operates on a hexagonal input lattice, employs basis functions that are orthogonal, self-similar, and localized in space, spatial frequency, orientation, and phase. The basis functions, which are generated from seven basic types through a recursive process, form an image code of the pyramid type. The seven basis functions, six bandpass and one low-pass, occupy a point and a hexagon of six nearest neighbors on a hexagonal sample lattice. The six bandpass functions consist of three with even symmetry, and three with odd symmetry. The three even kernels are rotations of 0 deg, 60 deg, and 120 deg of a common kernel; likewise for the three odd kernels. At the lowest level the inputs are image samples. At each higher level, the input lattice is provided by the low-pass coefficients computed at the previous level. At each level, the output is subsampled in such a way as to yield a new hexagonal lattice with a spacing the square root of seven larger than the previous level, so that the number of coefficients is reduced by a factor of seven at each level. In the biological model, the input lattice is the retinal ganglion cell array. The resulting scheme provides a compact, efficient code of the image and generates receptive fields that resemble those of the primary visual cortex.