Theodore E. Cohn

Detectability of a luminance increment: Effect of spatial uncertainty*

The theory of signal detectability (TSD) predicts that uncertainty of the spatial location of a luminance-increment stimulus should influence the detectability of the stimulus. If d′ is the detectability, E is the increment luminance, N2 is the variance of the noise that obscures the signal, and M is the number of equally likely non-overlapping stimuli, TSD predicts (d′)2 = loge{1–1/M + 1/M exp(E2/N2)}. TSD also predicts that the slope of the ROC curve on probability paper should decrease in the presence of stimulus-position uncertainty. Both predictions were confirmed in psychophysical tests of human observers for foveally viewed stimuli.

Why luminance discrimination may be better than detection

Abstract Signal Detection Theory (SDT) predicts that the presence of uncertainty will diminish the observers sensitivity to visual signals, and increase the exponent of the psychometric function. The first prediction has been confirmed previously with spatial and chromatic uncertainty. The second prediction is confirmed in this paper. The psychometric function is commonly found to be a positive accelerating function of intensity. This has been explained by two competing theories: the uncertainty hypothesis and the nonlinear transducer theory. A second experiment is conducted to distinguish between these theories. The results of this experiment are inconsistent with the nonlinear transducer theory.

Detectability of a luminance increment

The psychometric function for the detection of a foveal luminance increment was studied in human observers. The signal to be detected was a modulation of a 1300 cd/m2 6′ circular red target. For an ideal photodetector, the theory of signal detectability predicts that d′, the index of detectability, should rise linearly with the luminance, E, of the luminance increment unless the observer has some uncertainty concerning the parameters of the signal to be detected. Uncertainty is expressed by the parameter M that indicates the number of orthogonal signals possible. If M is greater than 1.0, (d′)2 = ln {1 − 1/M +(1/M) exp(E2/N2)} where N2 is the variance of the noise that obscures the signal. In addition, the theory predicts that the slope of the receiver operating characteristic (ROC curve) should decrease with increasing M. In one experiment, in which E was varied, a nonlinear psychometric function and an ROC curve of relatively low slope were found. In another experiment that included a pulsed background (pedestal) whether or not the signal was presented, the predicted linear M = 1 psychometric function was found. Finally, the ROC slope that was measured in rating experiments increased when the pedestal was used. Presumably, the pedestal provides the signal-parameter information that the observer could not remember. We conclude that the human observer acts like an ideal photodetector that has imperfect memory concerning the signal to be detected.

Detection of a luminance increment: effect of temporal uncertainty

The theory of signal detectability predicts that uncertainty about signal parameters depresses sensitivity to visual signals and to the slope of the receiver operating characteristic. These predictions were tested and confirmed by depriving the observer of knowledge of the temporal location of a signal.

Quantum fluctuation limit in foveal vision

Abstract A unique test of the hypothesis that only quantum fluctuations limit the detectability of foveal luminance change is presented. 10.9′ dia target spots were incremented or decremented in luminance. ROC curves for detection of both luminance increments and decrements were measured and found to conform to theoretical curves predicted on the basis of Poisson distributions of photon arrival. Four different parameters of the ROC curves lead independently to estimates of quantum efficiency with values of about 2 × 10 −4 . The measured quantum efficiency increases by about a factor of 10, to as high as 0.018, when the target is reduced to 1.2′ dia. This is consistent with the view that lateral inhibition causes many of the photons caught from a large target to be ineffectual in the task of detecting the luminance change signal.

Spatial summation of foveal increments and decrements

Abstract Foveal spatial summation was investigated in light-adapted subjects. Stimuli were luminance increments or decrements of two 1.5′ square targets separated by 2.5′ to 15′. Stimuli included increment-increment, decrement-decrement, decrement-increment and increment-decrement. For a separation of 2.5′, increment-increment combinations were detected most easily. At a separation of 7.5′, increment-decrements were most readily detected. At the 15′ separation all stimulus combinations were equally detectable. While perfect spatial summation was not found at any separation, summation was most efficient at the smallest separation. Inhibitory effects, which were inferred from the greater sensitivity to increment-decrements at 7.5′, were large even at 2.5′. A model based on excitation and inhibition was proposed to explain the observed interactions including the inhibition. It postulates two complementary channels, one that sums quanta-over a small region of the retina and another that compares the quantum sums at two small regions and signals their difference. The model also explains inhibition phenomena observed between increments and decrements separated by time or by wavelength.

Effect of large spatial uncertainty on foveal luminance increment detectability

In principle, the ability to detect a luminance increment is lowered when there is uncertainty for its spatial location. Frequency-of-seeing curves were generated for small foveal targets. When fixed in space the targets detectability was more than 10 times higher than when it could occur at one of 140 locations.

Binocular luminance detection: Availability of more than one central interaction

Abstract Predictions of the theory that there exists two separate central interactions, summing and differencing, between signals from two eyes were investigated. Similar monocular stimuli to two eyes, such as binocular increments, are more masked by identical luminance noise in the two eyes than are dissimilar monocular stimuli, like an increment to one eye and a decrement to the other. The converse also holds. Further, equally detectable, though different binocular stimuli (e.g. a pair of luminance increments compared to an increment/decrement pair) are discriminable. These results rule out a single binocular combination mechanism but are consistent with the theory under test.

Effect of chromatic uncertainty on detectability of a visual stimulus

The detectability of a brief color shift towards red or towards green of a foveally viewed yellow target is less by 25% if the observer is uncertain as to the direction of the color shift. This result matches a prediction of the theory of signal detectability: When signal parameters become uncertain, detectability declines.

Postural stability and stereo-ambiguity in man-designed visual environments

Measuring postural stability in the presence of a stereoambiguous stimulus is discussed. The existence of the following elements of the theoretical chain of events which leads to disorientation is shown for the first time: (a) inappropriate binocular convergence consistent with false fusion, and the wallpaper illusion, (b) heightened postural instability, and (c) correlation between subjective disorientation and postural instability. The modern rectilinear visual environment contains visual stimuli for which evolution has not had time to optimally shape visual processing. One such stimulus, periodic stripes, is known to lead to visual depth ambiguity. The authors show that postural instability, as measured by the variance of fore and aft sway, is increased by viewing such stimuli. This instability may be the precursor of falls. Designers must evaluate the visual impressions conveyed by their systems in order to avoid postural instability due to visual ambiguity.<<ETX>>