Area summation in human vision at and above detection threshold

Abstract

The initial image-processing stages of visual cortex are well suited to a local (patchwise) analysis of the viewed scene. But the world's structures extend over space as textures and surfaces, suggesting the need for spatial integration. Most models of contrast vision fall shy of this process because (i) the weak area summation at detection threshold is attributed to probability summation (PS) and (ii) there is little or no advantage of area well above threshold. Both of these views are challenged here. First, it is shown that results at threshold are consistent with linear summation of contrast following retinal inhomogeneity, spatial filtering, nonlinear contrast transduction and multiple sources of additive Gaussian noise. We suggest that the suprathreshold loss of the area advantage in previous studies is due to a concomitant increase in suppression from the pedestal. To overcome this confound, a novel stimulus class is designed where: (i) the observer operates on a constant retinal area, (ii) the target area is controlled within this summation field, and (iii) the pedestal is fixed in size. Using this arrangement, substantial summation is found along the entire masking function, including the region of facilitation. Our analysis shows that PS and uncertainty cannot account for the results, and that suprathreshold summation of contrast extends over at least seven target cycles of grating.

Figure 1

Stimuli used in experiments 2 and 3: (a) full stimulus (b) ‘white’ checks (c) ‘black’ checks. All three stimulus types served as pedestal (mask) and target in various combinations. They had a diameter of 9° displayed on a uniform square grey region with a width of 20.5° in the centre of the monitor. Closely related stimuli were used in experiment 1.

Figure 2

Area summation results from experiment 1 and model predictions (thick curves). Error bars show ±1 s.e. The inset shows the weighting function of the filter used in the modelling. The abscissa refers to the area bounded by the outer edge of the stimulus plateau. The dotted lines are fiducial contours with slopes of −1/2 and −1/4. The thin curve beneath the open squares is described in the Discussion.

Figure 3

Contrast-masking (dipper) functions. (a) Results from experiment 2 averaged across two observers (L. M. and L. W.; approx. 800 or 1600 trials per point). The average standard error was 1.28 dB for L. M. and 0.92 dB for L. W. (b) Behaviour of the main model (using equation (3.1)). Two parameters (z and k; see appendix B) control the ‘dip’ and were adjusted to match the data by eye. (c) Matched model, the same model as in (b) except that the region of summation on the numerator of equation (3.1) is restricted to the high-contrast parts of the target in the checks-on-full condition. Data and models are normalized by the sensitivity to the full stimulus with 0% pedestal contrast (left-most points).

Figure 4

Results from experiment 2 where the pedestal was always a full stimulus. Error bars show ±1 s.e. across observers, or for Y.R as appropriate. (a) Dipper functions averaged across six observers. (b) Sensitivity ratios for full target and average of ‘black’ and ‘white’ checks for the six observers in (a) (approx. 7200 trials per point) and a seventh observer Y.R. The function for Y.R is offset laterally by 1 dB for clarity. The model prediction (using equation (3.1)) is shown by the dashed curve.

Figure 5

Detection and identification of ‘white’ checks and full targets for (a(i)(ii)) T.S.M. and (b(i)(ii)) R.J.S. for pedestal contrasts of (a(i),b(i)) 0% and (a(ii),b(ii)) 20%. The insets report spatial summation (the difference between the upper and lower contrast axes dB) and the lateral shift of the identification threshold relative to the detection threshold of the full stimulus (ID offset). The average slopes of the psychometric functions at detection threshold were $\hat{\beta }=3.2$ and $\hat{\beta }=3.08$ for detection and identification, respectively. For the 20% pedestal, they were $\hat{\beta }=1.5$ and $\hat{\beta }=1.9$.

Figure 6

Summation levels as functions of the diameter of a circular summation aperture. Different symbols are for different models (see text for details).