A parallel stream model of cat area 18 cells for processing luminance and contrast-envelope stimuli. Cat area 18 cells show similar orientation and spatial frequency selectivity to luminance stimuli (left) and contrast-envelope stimuli (right). Luminance stimuli are thought to be processed through a conventional linear RF (left). The contrast-envelope stimuli are processed with filter-rectify-filter circuits (right), in which fine texture elements (carrier) are extracted at first-stage filters and second-stage filters sum the rectified outputs of the first-stage filters to extract the contrast envelope.
Spatial frequency tunings of two neurons for luminance stimuli and the carrier of contrast-envelope stimuli. Open circles and solid squares indicate the mean discharge rates when the spatial frequency of luminance stimuli and the carrier spatial frequency of the contrast-envelope stimuli were varied, respectively. The spatial frequency of the envelope of the contrast-envelope stimuli was fixed near the optimal values for the luminance stimuli (0.08 c/deg for the neuron in A, 0.24 c/deg for the neuron in B). Solid curves indicate Gaussian functions fitted to the data points. The optimal spatial frequency and bandwidth at half-height were obtained from the fitted curves. Note that these neurons are narrowly tuned to the carrier spatial frequency. Carrier bandwidths of the neurons in A and B are 1.10 and 0.66 octaves, respectively. Note also that the response range for the two stimuli did not overlap (we confirmed, during initial manual searches, that luminance stimuli with spatial frequencies above the highest one tested in computer-controlled measurements did not evoke responses). Error bars indicate the SEM. Horizontal lines below the tuning curves indicate the spontaneous discharge rates. Because the two tuning curves were measured separately, the spontaneous discharge rates are not necessarily the same.
Interocular phase tunings of area 18 neurons for contrast-envelope stimuli. A–C, Data for a pair of neurons recorded simultaneously from different electrodes. A, B, PSTHs for monocular (left, first row; right, second row), null (third row), and interocular (bottom 12 rows) phase stimuli of the two neurons. The discharge rates and stimulus duration (4 s) are indicated at the bottom rows. C, Mean discharge rates are shown against the interocular phase, which is linearly related to binocular disparity of stimuli. Response amplitudes computed from PSTHs shown in A and B are indicated by open squares and filled circles, respectively. Data are fitted with sinusoidal curves. Error bars indicate SE. Left- and right-eye monocular responses are indicated by triangles at the left and right margins, respectively (open triangle, neuron in A; filled triangle, neuron in B). Horizontal lines near the phase axis indicate the spontaneous firing rate. The spatial frequency of the envelope and carrier was 0.13 and 1.35 c/deg, respectively, whereas their orientations were both 65°. The envelope was drifted at 2 Hz for these cells and all other neurons in this study. The carrier was stationary for these neurons. D–F, Data for another pair of simultaneously recorded cells (from different electrodes), shown in the same format as for the first pair. In F, data for the neuron shown in D (open squares) are scaled up by a factor of 8 for comparison and plotted in gray, together with the original curve and data near the horizontal axis. The spatial frequencies of the envelope and the carrier were 0.08 and 1.15 c/deg, whereas their orientations were 60 and 120°, respectively. The carrier was stationary for these neurons. G, Distribution of modulation depth of the disparity-tuning curves. Modulation depth is defined as the ratio of the amplitude of F1 to that of the F0 component of the tuning curves (see Materials and Methods). The mean modulation ratio and its SD were 0.35 and 0.29, respectively (n = 70). Filled bars indicate a subset of neurons for which significant modulations by the interocular phase were observed (n = 25). H, Distribution of differences of optimal interocular phases for simultaneously recorded cells (n = 10). L, Left; R, right; sp/s, spikes per second.
Insensitivity of envelope-responsive neurons to the carrier interocular phase. A–C, Responses of three neurons are shown as a function of the carrier interocular phase (varied in 30° steps over one cycle), whereas the interocular envelope phase was fixed at the optimal value. The neurons in A and B are the same as those shown in Figure 3, A and B, respectively. The orientation, spatial frequency, and temporal frequency of the envelope and the carrier are described in the legend to Figure 3. The difference of the response magnitude of these neurons between this figure and Fig. 3 is simply attributable to the fact that the data were obtained at different times. For the neuron in C, the envelope and the carrier spatial frequency were 0.18 and 1.2 c/deg, respectively. Envelope and carrier orientations were 115 and 210°, respectively. The envelope and carrier were both drifted at 2 Hz. Spontaneous firing rates were 0 for all the three neurons.
Possible models of the binocular pathway for processing envelope stimuli. (The luminance pathway is not shown for clarity.) A, First-stage convergence model. Signals from left- and right-eye first-stage filters are linearly combined at the first-stage neurons. These signals are then integrated at a second-stage neuron via the second-stage filter. Signals of second-stage cells are then half-wave rectified and squared. First-stage and second-stage filters are both modeled by Gabor functions. The model contains 16 overlapping arrays of identical first-stage cells. That is, within a given array, the first-stage filters have the same monocular and interocular phases selected from four possible phases: 0, 90, 180, or 270°, resulting in a total of 16 pairings as shown in C. Only the array for zero monocular and interocular phases is shown for clarity (a pair inside a dashed rectangle in C). A second-stage filter receives pooled signals from these first-stage cell arrays. B, Second-stage convergence model. Signals from left and right first-stage filters are monocularly processed through the first-stage neurons and carried to left and right monocular second-stage filters, respectively. The model contains four overlapping arrays of first-stage cells, although only the zero-phase filter array is shown. Outputs of the second-stage filters for the two eyes are then combined at the second-stage neurons. These signals are then half-wave rectified and squared. This neuron can be tuned to various disparities, depending on the relationship of shapes of the second-stage filters between the eyes. Note that a non-zero envelope disparity preference, as illustrated, is generated by the phase difference based on the phase model (Anzai et al. 1999), although the similar envelope disparity tunings may be produced by the position model as well. C, 16 pairings of 4 possible monocular and interocular phases for first-stage cells are shown. XL, x-axis for left eye; XR, x-axis for right eye; XB, binocular x-axis.
Results of simulations of the binocular version of the filter-rectify-filter models are shown. Spatial frequencies of the carrier and envelope of the stimuli are 1 and 0.1 c/deg, which are approximately the same as the average values used for the physiological experiments. A, Results of simulations for the first-stage convergence model. The left, middle, and right panels show results when left and right first-stage filters of the first-stage cells had position disparities of −4.0, 0, and 4.0° of visual angle, respectively. B, Results of simulations for the second-stage convergence model. The left, middle, and right panels show results when the interocular phase of the second-stage filters is −144, 0, and 144°, respectively.
A binocular convergence model incorporating the luminance and envelope processing pathways (A) and stimuli to test this model (B). A, Signals from the luminance and envelope processing pathways from the two eyes converge linearly at a single neuron. These signals are then half-wave rectified and squared. B, Four types of dichoptic stimuli to test this single-point linear convergence model. The left two columns show conventional stereo stimuli (same-cue stimuli). The top and second rows are luminance and contrast-envelope stimuli, respectively. The right two columns show those in which the two eyes receive different types of stimuli (cross-cue stimuli). For each binocular stimulus, the interocular phase was varied in 30° steps over one cycle. These binocular stimuli, together with monocular and blank (null) stimuli, were interleaved randomly in a single run. XL, x-axis for left eye; XR, x-axis for right eye.
Cue-invariant phase tuning of neurons in area 18. A–D, Interocular phase tuning of two cells in cat area 18 to luminance, contrast-envelope, and cross-cue stimuli. A, Mean discharge rates of a cell to binocular luminance and contrast-envelope stimuli are plotted as functions of the interocular phase with open circles and filled squares, respectively. Fitted sinusoids are indicated by dashed and solid curves for luminance and contrast-envelope stimuli, respectively. Left- and right-eye monocular responses are indicated by triangles at the left and right margins, respectively (open triangles, luminance; filled triangles, contrast-envelope stimuli). Note that the optimal interocular phases for the two stimuli are approximately the same, indicating cue invariance. Error bars indicate the SEM. A dashed line almost overlapping the horizontal axis depicts the level of spontaneous discharge. B, Responses to cross-cue stimuli for the neuron in A. The inverted triangles indicate responses for the conditions in which luminance and contrast-envelope stimuli are presented for the left and right eye, respectively. Filled diamonds indicate responses to the other cross-cue stimuli pairing (see Fig. 7B). Tuning curves for the same-cue stimuli are shown again with thin lines. Note the clear modulations of these tuning curves. C, D, Data for another neuron, shown in the same format as for the first neuron. The spatial frequency of the luminance stimuli and envelope of the contrast-envelope stimuli was 0.13 c/deg for the cell in A and 0.08 c/deg for the cell in C. The spatial frequency for the carrier was 1.35 c/deg for both cells. For both neurons, the envelope was drifted at 2 Hz, and the carrier was stationary.
Comparison of responses of envelope-responsive neurons for luminance and contrast-envelope stimuli. A, Peak binocular response of each neuron to binocular luminance stimuli is plotted against that for the contrast-envelope stimuli. Solid circles indicate neurons that were disparity selective for both stimuli (n = 23). Open squares and solid triangles indicate those that were disparity selective for only luminance (n = 32) and contrast-envelope (n = 2) stimuli, respectively. The x symbols indicate those that were disparity selective for neither stimulus (n = 13). See C for illustration of the meaning of these markers. B, Peak-to-trough difference of disparity-tuning curves is compared for luminance and contrast-envelope stimuli. The convention of the markers is the same as that in A. C, Classification of the data population. The table shows the classification of 70 envelope-responsive neurons into four groups according to their disparity selectivity for luminance and contrast-envelope stimuli. The sum of these numbers are shown in the right column and the bottom row, respectively. The proportion (percentage) of these sums of the total population (n = 70) is indicated by the number in parentheses. The markers used in Figure 9, A and B, indicating these groups are also shown within the corresponding cells. D, Optimal interocular phases for contrast-envelope stimuli are plotted against those for luminance stimuli (n = 23). Most neurons are within a narrow range about the diagonal, indicating cue invariance. Black symbols indicate cells with a statistically significant shift of optimal phases between the two conditions. Dashed lines indicate a 1 SD limit of ± 33°. Data for the neurons in Figure 8, A and C, are indicated by letters. E, Modulation depth for the cross-cue stimuli. The average modulation depth of two phase tuning curves for the cross-cue condition is plotted against that of the two phase tuning curves for the same-cue condition. Notice that the two indices are correlated (r = 0.72; p < 0.0001; n = 66), although the modulation depth for the cross-cue stimuli was generally weaker. The oblique line indicates a regression line (slope, 0.38). F, Optimal interocular phases for each of the same-cue stimuli (binocular luminance or contrast-envelope stimuli) are plotted against those for the cross-cue stimuli, for 20 neurons that were disparity selective for both of the same-cue stimuli and at least either of the two cross-cue stimuli. Data for each cell are represented by up to four symbols (depending on significance), because there are four possible pairings of same-cue and cross-cue stimuli (see inset). The inset shows the symbol legend depicting left–right pairings of luminance (l) and contrast-envelope (e) stimuli (n = 16, 16, 17, and 17 from top to bottom). Filled symbols indicate data with a statistically significant shift of optimal disparities between the two conditions. Dashed lines representing the 1 SD limit are at ±52°. Data for the neurons in Figure 8, B and D, are indicated by letters.