Spatial summation effects on two-component grating thresholds

Abstract

Some experimental studies of subthreshold summation between sinusoidal grating components have been interpreted as showing very narrow channel bandwidths in human visions. This paper discusses an alternative interpretation of these experiments based on consideration of probability-summation effects among spatially distributed detectors. We conclude that frequency-selective channels must still be hypothesized in order to fit the data, but the channel bandwidth may be much wider than earlier interpretations suggest.

Lack of convexity of threshold curves for compound grating: implications for modelling visual pattern detection

“…To be more exact, a number of empirical curves like this in Fig. 5 have been found by other investigators (Sachs et al 1971;Quick and Reichert 1975;Quick et al 1978;Graham et al 1978;Graham and Robson 1987;Watson 1982) but none like this in Fig. 2.…”

“…Admittedly, further exploration of the threshold curve's convexity, with more subtle and elaborate statistical testing procedure, is needed for a final decision to be made. But even this preliminary result is quite enough to cast doubt on many of the models proposed so far of visual detection, both single-channel (Blackwell 1963;Campbell et al 1969;Matin 1975;Limb and Rubinstein 1977;Blackwell et al 1978) and multi-channel (Sachs et al 1971;Mostafavi and Sakrison 1976;Graham 1977Graham , 1980Quick et al 1978;Wilson and Bergen 1979;Thomas 1985;Watson 1982) because they are inconsistent with the failure of convexity for even one threshold curve.…”

“…Experiments on detection of two-component stimuli (Sachs et al 1971;Quick and Reichert 1975;Quick et al 1978;Graham et al 1978;Graham and Robson 1987) provide a critical source of evidence in this area. The reason is that contrast threshold curves for such stimuli provide a way of distinguishing between the main detection theories which have been put forward.…”

Uncertainty about spatial frequency, spatial position, or contrast of visual patterns

“…(See Graham, 1981, for a review. ) A particular quantitative version of this theory has been extremely successful in predicting the thresholds for a wide variety of patterns (e.g., Bergen, Wilson, & Cowan, 1979;Graham, 1977;Graham, Robson, & Nachmias, 1978;Mostafavi & Sakrison, 1976;Quick, Mullins, & Reichert, 1978;Robson & Graham, 1981;Watson, 1982;. Although a name for this model has not become standard, we will call it the Quick pooling model since its current use in vision originates with Quick (1974) and it is much quicker to use than alternative models.…”

Efficient integration across spatial frequencies for letter identification in foveal and peripheral vision

“…Classical findings on grating detection and discrimination suggest that integration across features is inefficient when there is a large difference in the spatial frequency of the features (e.g., Graham, Robson, & Nachmias, 1978; Quick, Mullins, & Reichert, 1978). For example, the probability of detecting a compound grating that is comprised of two simple gratings with spatial frequencies more than a factor of two (one octave) apart is found to be approximately equal to the sum of the probabilities of detecting each of component gratings presented alone.…”