Article Figures & Data
Figures
- Fig. 1.
Four examples of disparity-tuning curves recorded from V1 neurons. The abscissa shows the stimulus disparity, and the ordinate shows the mean firing rate in impulses per second. Error bars represent the SE of the recorded firing rates. For each tuning curve, the steepest portion was used to calculate the neurometric function. For a detailed description of how the parameters for each neuron were calculated, see Results. A, Simple cell from monkey Hg. Neuronal threshold, 2.0 arc min; preferred orientation, 7°; preferred spatial frequency, 2.81 cycles/°; ocular dominance index, 0.14; F1/F0 ratio, 1.25. B, Complex cell from monkey Hg. Neuronal threshold, 0.75 arc min; preferred orientation, 61°; preferred spatial frequency, 1.06 cycles/°; F1/F0 ratio, 0.76. C, Simple cell from monkey Rb. Neuronal threshold, 1.43 arc min; preferred orientation, 75°; preferred spatial frequency, 3.10 cycles per degree; ocular dominance index, 1.0; F1/F0 ratio, 1.33. D, Complex cell from monkey Rb. Neuronal threshold, 4.09 arc min; preferred, orientation, 20°; preferred spatial frequency, 1.13 cycles/°; F1/F0 ratio, 0.52.
- Fig. 2.
Example of the data collection protocol from a complex cell in monkey Hg. This is the same cell (Hg290) presented in Figure 1B. A, The disparity-tuning curve was initially coarsely sampled. B, If the cell appeared to be disparity-tuned, sample spacing was reduced until the steepest monotonic portion of the curve was found (C). In this case, the background reference disparity was set to zero. This threshold of the neuron for detecting differences in disparity was 0.75 arc min (see Fig. 3 for details of the calculation).
- Fig. 3.
A, Neurometric functions were calculated using a neuron–orthoneuron formulation. The top of the diagram represents the stimulus. The bottom left portion shows the disparity tuning of the neuron whose receptive field was matched to the center of the stimulus. The bottom rightportion shows the assumed disparity-tuning function of the orthoneuron. This is a theoretical neuron with identical response properties to the neuron, except that its receptive field is located in the surround portion of the stimulus. During the experiment, the surround has a constant disparity. Hence, the responses of the orthoneuron are assumed to correspond to the responses of the recorded neuron when presented with a center disparity of the same value as the surround disparity (in this case, 0.0°). The bottom left and bottom right tuning curves each have one data point highlighted by asolid symbol. The highlighted points correspond to the case when the disparity of the central patch is at a small crossed disparity (−0.006°) relative to the surround (0.0°). B, The spike distributions of the neuron at the current disparity and the orthoneuron at the disparity of the surround are compared to calculate an ROC curve. The area under the ROC curve gives the probability of successfully discriminating the disparity of the center (−0.006°) from the disparity of the surround (0°). C, This probability is calculated at a number of different stimulus levels to form a neurometric function. A cumulative Gaussian was fit to the data, and the SD, ς, of this curve was used as a measure of the neuronal discriminability. In this case the threshold is 0.012° or 0.72 arc min.
- Fig. 4.
Examples of orientation-tuning and spatial frequency-tuning curves for two neurons. A and B show orientation-tuning curves for neurons Hg282 and Rb526, respectively. The abscissa shows the orientation of the bar stimulus in degrees. The ordinate shows mean firing rate in impulses per second. A Gaussian was fit to this data using an iterative curve-fitting procedure. The preferred orientation was taken to be the peak position of this curve. C and D show the spatial frequency-tuning curves for the same two cells. In each case, the abscissa shows the spatial frequency of the sinusoidal grating stimulus in cycles per degree. The ordinate shows the mean firing rate in impulses per second. A Gaussian in log spatial frequency was fit to this data, using an iterative curve-fitting procedure. The preferred spatial frequency was taken to be the mean position of this curve. Neuron Hg282 had a disparity threshold of 2.1 arc min, a preferred orientation of 1° clockwise from horizontal, and a peak spatial frequency of 1.7 cycles/°. Neuron Rb526 had a disparity threshold of 4.9 arc min, a preferred orientation of 128° clockwise from horizontal, and a peak spatial frequency of 2.4 cycles/°, and an ocular dominance index of 0.55.
- Fig. 5.
The calculated neurometric thresholds (degrees on the left ordinate and the equivalent in minutes of arc on the right ordinate) are plotted against the visual eccentricity of the stimulus center (degrees of visual angle on the abscissa). The threshold is expressed as the SD of the fitted cumulative Gaussian (see Fig. 3). Error bars are 95% confidence limits. Open andclosed symbols indicate data from monkeys Rb and Hg, respectively.
- Fig. 6.
The calculated neurometric thresholds (degrees on the left ordinate and the equivalent in minutes of arc on the right ordinate) are plotted against preferred orientation (degrees rotation from horizontal on the abscissa) as assessed using either bar stimuli or sinusoidal gratings. Neural stereoacuity was good over the full range of preferred orientations. The two data points plotted withcircles indicate the example neurons plotted in Figure 4, A and B.
- Fig. 7.
Plot of calculated neurometric thresholds (degrees on the left ordinate and the equivalent in minutes of arc on the right ordinate) against the stimulus preference of the neuron expressed as the effective horizontal spatial frequency. This was calculated from a combination of spatial frequency and orientation-tuning data (see Results). There is no tendency for the neurometric threshold to decrease as the effective horizontal frequency increases. Thecircles indicate data from the example cells in Figure4.
- Fig. 8.
Neurometric thresholds are plotted against the F1/F0 ratio. Typically cells are classified as complex if this ratio is <1. Although there is a majority of complex cells in the data set, there is no evidence to suggest that either type of cell is superior at discriminating horizontal disparity in the random dot stereograms.
- Fig. 9.
Plot of the calculated neurometric thresholds (degrees on the left ordinate and the equivalent in minutes of arc on the right ordinate) against the ocular dominance index of the cell (abscissa). An ocular dominance index of 0.5 indicates that the cell had evenly balanced inputs. Ocular dominance indices at the extremes of the distribution indicate that the cell was driven only by the contralateral or ipsilateral eye.
- Fig. 10.
The simultaneous psychometric threshold is plotted against the neurometric threshold. The diagonal lineindicates the locus of points where both thresholds are the same. Points below this line indicate experiments in which the neurometric threshold was greater than the psychometric threshold. The histogram shows the distribution of the N:P threshold ratio. The neuronal thresholds are on average slightly higher than the psychometric thresholds.
- Fig. 11.
A, Neurometric function for calculation of neuronal threshold. Sampling was optimized for this calculation. The measured neurometric threshold was 5.35 arc min. B, The circles and solid curve show results from the simultaneous recording of behavior. The stimulus spacing for this task was considerably greater than was necessary. The monkey fails to consistently maintain 100% performance at the suprathreshold stimulus levels. This causes the curve fitting to overestimate the threshold to be 5.32 arc min. The squaresand dashed curve depict subsequently measured psychophysical behavior for a random dot stereogram with identical stimulus parameters but a more appropriate disparity range. The measured behavioral threshold was then considerably smaller at 0.35 arc min. C, A second neurometric function for calculation of neuronal threshold. Again, sampling was optimized for this calculation. The neurometric threshold was 2.12 arc min. D, The stimulus spacing for the simultaneous psychophysical task was considerably greater than was necessary (circles, solid curve), and the threshold is estimated to be 1.21 arc min. However, in this case, the curve is a good fit to the data. When behavior was remeasured with more appropriate stimulus values (squares, dashed line), the measured behavioral threshold was also considerably smaller at 0.30 arc min.
- Fig. 12.
The subsequent psychometric threshold is plotted as a function of the simultaneous psychometric threshold. For each point on the graph, the stimuli were identical apart from the disparities used. The diagonal line indicates the locus of points where both thresholds are the same. Points above this line indicate experiments where the simultaneous threshold was greater than the subsequent threshold. The subsequent threshold is lower than the simultaneous threshold in every case for monkey Rb and for most measurements in monkey Hg. The histogram shows the distribution of the simultaneous:subsequent threshold ratio.
- Fig. 13.
The subsequent psychometric threshold is plotted as a function of the neurometric threshold. Again the diagonal line indicates the locus of points where both thresholds are the same, and the N:P ratio is one. Points below this line indicate experiments where the neurometric threshold was greater than the psychometric threshold. For both monkey Hg and monkey Rb, most points are below this line. The histogram shows the distribution of the N:P ratio collapsed over both animals. The mean N:P ratio is slightly >4, indicating that on average the observer performs approximately four times better than the V1 neurons in this sample.
- Fig. 14.
The revised measurements of psychometric threshold for behavioral depth discrimination are plotted as a function of eccentricity. Solid symbols show cases in which the absolute disparity of the pedestal (the disparity of the surround patch) was within 0.1° of the binocular fixation point, whereasopen symbols show cases in which the pedestal disparity was larger. Thresholds were generally best when both the pedestal disparity and the eccentricity were small. The gray bar indicates the range of human performance for four observers as measured using similar stimuli at an eccentricity of 4.0°.
- Fig. 15.
Example psychometric thresholds for depth discrimination in three conditions. When the background is present, the threshold is low. When the background is uncorrelated or absent, the psychometric thresholds are an order of magnitude higher. This is shown for one stimulus configuration in monkey Hg (A) and one in monkey Rb (B).
- Fig. 16.
The N:P ratio for the condition with no background is plotted on the ordinate against the N:P ratio for the condition with the background present on the abscissa, for the eight cases in which the neurometric function had been measured around zero disparity. For each point, the measurement of neuronal performance was the same for both ratios. The psychophysical component of each ratio consists of the subsequently measured thresholds in the presence or absence of a zero disparity background patch. All of the data points fall below the diagonal line, which indicates that the psychophysical performance was always worse in the absence of a background. Thedashed line shows the mean change in the N:P ratio, which falls by a factor of 10.8 (geometric mean) when the background is absent.
- Fig. 17.
Comparison of the neurometric and psychometric measurements made here and in Britten et al. (1992). In our study, the observer judges the disparity of the center part of the stimulus relative to the surround, after a single stimulus presentation. The observers in Britten et al. (1992) also saw a single stimulus presentation and judged the direction of the signal dots (solid arrows and dots) in the presence of noise dots (open arrows and dots). Thus the two psychophysical tasks are formally equivalent (single interval binary forced choice). However, the neurometric analyses are different. Our neurometric analysis comprises one neuron that measures the center disparity and a theoretical orthoneuron that measures the surround. This compares the firing of the neuron to a nonzero disparity with the firing when the disparity was zero. Britten et al. (1992) compared responses of each neuron with a theoretical antineuron, (a neuron with opposite direction selectivity). This compares the firing of the neuron to one signal with the firing to a signal of the same strength but of opposite sign. The signal difference between the two stimuli under comparison is twice as large for the neuron–antineuron formulation as for the neuron–orthoneuron formulation. Depending on the shape of the tuning curve, estimates of neurometric thresholds can be up to a factor of two smaller, even when the calculations are performed on identical tuning curves.
In this issue
