1. A quantitative, general purpose method was developed for measuring the responses of visual neurons to stimuli distributed with high resolution over the two-dimensional (2D) spatial frequency domain. The stimuli consisted of drifting sinusoidal gratings of nonsaturating contrasts whose spatial frequency and orientation were drawn in random order from a 16 X 16 array of coordinates covering each neuron's responsive area. This method was applied to a population of 36 simple cells in area 17 of cat. 2. The response of each simple cell to drifting sinusoidal gratings appeared as a rectified sinusoidal modulation of the spike frequency. The degree of rectification varied from cell to cell, but for each cell, the form of the response was constant irrespective of stimulus spatial frequency, orientation, or contrast. The amplitude of the average response at the stimulus temporal frequency was used as the response metric at all spectral coordinates. Variations in this amplitude over two spectral dimensions forms a surface that we call the 2D spectral response profile. 3. For each cell, the 2D spectral response profile was localized to a limited region of the complete 2D spatial frequency domain. In bidirectionally responsive cells, there were two lobes in the surface disposed with mirror symmetry about the origin. In all cells, each lobe exhibited a single maximum and the response decayed smoothly in every direction away from the maximum. Isoresponse amplitude contours were elliptical and often, but not always, elongated about an axis of symmetry passing through the origin. 4. We tested the hypothesis that orientation and spatial frequency tuning are independent by forming scaled radial and angular sections through 2D spectral response profiles. In virtually every case polar separability did not obtain, that is, orientation selectivity depended on spatial frequency and vice versa. 5. In contrast, more than half the cells had 2D spectral response profiles that were Cartesian separable. The 2D spectral response profiles of most of the remaining cells were neither polar nor Cartesian separable, because the response profiles were elongated about an axis of symmetry that did not pass through the origin. 6. These results are discussed in terms of the constraints they place on models of the contributions simple cells make toward the neural representation of images.
Watermarking in the space/spatial-frequency domain using two-dimensional Radon-Wigner distribution