Visual Detection and Discrimination of Luminance Increments
01 Mar 1970-Journal of the Optical Society of America (Optical Society of America)-Vol. 60, Iss: 3, pp 382-389
TL;DR: Over-all results strongly indicate that the mean of this distribution is a positively accelerated function of Luminance of the test flash, and suggest that the standard deviation is a non-monotonic function of luminance.
Abstract: A rating-scale psychophysical method was employed to obtain receiver operating characteristics for detection and for discrimination of luminance increments. These curves were used to estimate the parameters of a normal probability-density function which was assumed to describe the relevant internal effects of the test flash. The over-all results strongly indicate that the mean of this distribution is a positively accelerated function of luminance of the test flash, and suggest that the standard deviation is a non-monotonic function of luminance. It is argued that quantum fluctuations and criterion fluctuations cannot account for these findings, whereas channel uncertainty may be at the root of some of them.
Citations
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TL;DR: The emphasis of this review is on psychophysical studies, but relevant electrophysiological and neuroimaging studies and models regarding how and where neuronal responses are modulated are also discussed.
1,766 citations
Cites background from "Visual Detection and Discrimination..."
...Uncertainty about the target location produces a more noticeable degradation at low than at high performance levels (Eckstein & Whiting, 1996; Pelli, 1985), and uncertainty is larger for less discriminable stimuli (Cohn, 1981; Nachmias & Kocher, 1970; Pelli, 1985)....
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...Thus, uncertainty models predict that the precueing effect would be greater for low contrast stimuli and when localization performance is poor (e.g., Carrasco et al., 2000, 2002; Cohn, 1981; Nachmias & Kocher, 1970; Pelli, 1985)....
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...These two studies dealing with the temporal dynamics of attention further support the idea that the endogenous and exogenous mechanisms represent two attention systems that can affect information processing in distinct ways....
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TL;DR: A masking model is presented that encompasses contrast detection, discrimination, and masking phenomena that includes a linear spatial frequency filter, a nonlinear transducer, and a process of spatial pooling that acts at low contrasts only.
Abstract: Contrast masking was studied psychophysically. A two-alternative forced-choice procedure was used to measure contrast thresholds for 2.0 cpd sine-wave gratings in the presence of masking sine-wave gratings. Thresholds were measured for 11 masker contrasts spanning three log units, and seven masker frequencies ranging +/- one octave from the signal frequency. Corresponding measurements were made for gratings with horizontal widths of 0.75 degrees (narrow fields) and 6.0 degrees (wide fields). For high contrast maskers at all frequencies, signal thresholds were related to masking contrast by power functions with exponents near 0.6. For a range of low masking contrasts, signal thresholds were reduced by the masker. For the wide fields, high contrast masking tuning functions peaked at the signal frequency, were slightly asymmetric, and had approximately invariant half-maximum frequencies that lie 3/4 octave below and 1 octave above the signal frequency. The corresponding low contrast tuning functions exhibited peak threshold reduction at the signal frequency, with half-minimum frequencies at roughly +/- 0.25 octaves. For the narrow fields, the masking tuning functions were much broader at both low and high masking contrasts. A masking model is presented that encompasses contrast detection, discrimination, and masking phenomena. Central constructs of the model include a linear spatial frequency filter, a nonlinear transducer, and a process of spatial pooling that acts at low contrasts only.
1,241 citations
TL;DR: In this article, the uncertainty model of visual contrast detection was proposed, which assumes that the observer is uncertain among many signals and chooses the likeliest with only four parameters, and explains why d' is approximately a power function of contrast and accurately predicts effects of summation, facilitation, noise, subjective criterion and task for near-threshold contrast.
Abstract: More than 20 years ago, Tanner [Ann NY Acad Sci 89, 752 (1961)] noted that observers asked to detect a signal act as though they are uncertain about the physical characteristics of the signal to be detected The popular assumptions of probability summation and decision variable, taken together, imply this uncertainty This paper defines and uncertainty model of visual detection that assumes that the observer is uncertain among many signals and chooses the likeliest With only four parameters, the uncertainty model explains why d' is approximately a power function of contrast ("nonlinear transduction") and accurately predicts effects of summation, facilitation, noise, subjective criterion, and task for near-threshold contrast Thus the uncertainty model offers a synthesis of much of our current understanding of visual contrast detection and discrimination
680 citations
TL;DR: A theory of perceptual decision making based on a diffusion model that accounts for response time and accuracy as a function of both stimulus strength and speed-accuracy instructions and subsume the predictions of Piéron's Law.
Abstract: Both the speed and the accuracy of a perceptual judgment depend on the strength of the sensory stimulation. When stimulus strength is high, accuracy is high and response time is fast; when stimulus strength is low, accuracy is low and response time is slow. Although the psychometric function is well established as a tool for analyzing the relationship between accuracy and stimulus strength, the corresponding chronometric function for the relationship between response time and stimulus strength has not received as much consideration. In this article, we describe a theory of perceptual decision making based on a diffusion model. In it, a decision is based on the additive accumulation of sensory evidence over time to a bound. Combined with simple scaling assumptions, the proportional-rate and power-rate diffusion models predict simple analytic expressions for both the chronometric and psychometric functions. In a series of psychophysical experiments, we show that this theory accounts for response time and accuracy as a function of both stimulus strength and speed-accuracy instructions. In particular, the results demonstrate a close coupling between response time and accuracy. The theory is also shown to subsume the predictions of Pieron's Law, a power function dependence of response time on stimulus strength. The theory's analytic chronometric function allows one to extend theories of accuracy to response time.
668 citations
Cites background from "Visual Detection and Discrimination..."
...This proportional scaling can be generalized by allowing d′ to be a power function of stimulus strength (Nachmias & Kocher, 1970; Pelli, 1987)....
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TL;DR: It is concluded that low threshold theories can account for simple visual search without invoking mechanisms such as limited capacity or serial processing.
458 citations
References
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TL;DR: A brief review of the theory of statistical decision is reviewed and a description of the elements of the theories appropriate to human observers is presented, including a quantitative measure of the criterion.
Abstract: About 5 years ago, the theory of statistical decision was translated into a theory of signal detection. Although the translation was motivated by problems in radar, the detection theory that resulted is a general theory for, like the decision theory, it specifies an ideal process. The generality of the theory suggested to us that it might also be relevant to the detection of signals by human observers. Beyond this, we were struck by several analogies between this description of ideal behavior and various aspects of the perceptual process. The detection theory seemed to provide a framework for a realistic description of the behavior of the human observer in a variety of perceptual tasks. 1 This paper is based upon Technical Report No. 40, issued by the Electronic Defense Group of the University of Michigan in 1955. The research was conducted in the Vision Research Laboratory of the University of Michigan with support from the United States Army Signal Corps and the Naval Bureau of Ships. Our thanks are due H. R. Blackwell and W. M. Kincaid for their assistance in the research, and D. H. Howes for suggestions concerning the presentation of this material. This paper was prepared in the Research Laboratory of Electronics, Massachusetts Institute of Technology, with support from the Signal Corps, Air Force (Operational Applications Laboratory and Office of Scientific Research), and Office of Naval Research. This is Technical Report No. ESD-TR-61-20. 2 For a formal treatment of statistical decision theory, see Wald (1950) ; for a brief and highly readable survey of the essentials, see Bross (1953). Parallel accounts of the detection theory may be found in Peterson, Birdsall, and Fox (1954) and in Van Meter and Middleton (1954). The particular feature of the theory that was of greatest interest to us was the promise that it held of solving an old problem in the field of psychophysics. This is the problem of controlling or specifying the criterion that the observer uses in making a perceptual judgment. The classical methods of psychophysics make effective provision for only a single free parameter, one that is associated with the sensitivity of the observer. They contain no analytical procedure for specifying independently the observer's criterion. These two aspects of performance are confounded, for example, in an experiment in which the dependent variable is the intensity of the stimulus that is required for a threshold response. The present theory provides a quantitative measure of the criterion. There is left, as a result, a relatively pure measure of sensitivity. The theory, therefore, promised to be of value to the student of personal and social processes in perception as well as to the student of sensory functions. A second feature of the theory that attracted us is that it is a normative theory. We believed that having a standard with which to compare the behavior of the human observer would aid in the description and in the interpretation of experimental results, and would be fruitful in suggesting new experiments. This paper begins with a brief review of the theory of statistical decision and then presents a description of the elements of the theory of signal detection appropriate to human observers.
1,268 citations
1,217 citations
TL;DR: The results clarify the nature of the fluctuations shown by an organism in response to a stimulus, and show that at the threshold it is the stimulus which is variable, and that the properties of its variation determine the fluctuations found between response and stimulus.
Abstract: 1. Direct measurements of the minimum energy required for threshold vision under optimal physiological conditions yield values between 2.1 and 5.7 x 10–10 ergs at the cornea, which correspond to between 54 and 148 quanta of blue-green light.
2. These values are at the cornea. To yield physiologically significant data they must be corrected for corneal reflection, which is 4 per cent; for ocular media absorption, which is almost precisely 50 per cent; and for retinal transmission, which is at least 80 per cent. Retinal transmission is derived from previous direct measurements and from new comparisons between the percentage absorption spectrum of visual purple with the dim-vision luminosity function. With these three corrections, the range of 54 to 148 quanta at the cornea becomes as an upper limit 5 to 14 quanta actually absorbed by the retinal rods.
3. This small number of quanta, in comparison with the large number of rods (500) involved, precludes any significant two quantum absorptions per rod, and means that in order to produce a visual effect, one quantum must be absorbed by each of 5 to 14 rods in the retina.
4. Because this number of individual events is so small, it may be derived from an independent statistical study of the relation between the intensity of a light flash and the frequency with which it is seen. Such experiments give values of 5 to 8 for the number of critical events involved at the threshold of vision. Biological variation does not alter these numbers essentially, and the agreement between the values measured directly and those derived from statistical considerations is therefore significant.
5. The results clarify the nature of the fluctuations shown by an organism in response to a stimulus. The general assumption has been that the stimulus is constant and the organism variable. The present considerations show, however, that at the threshold it is the stimulus which is variable, and that the properties of its variation determine the fluctuations found between response and stimulus.
1,028 citations
TL;DR: The hypothesis that noise in the optic pathway limits its sensitivity is formulated quantitatively, and shown to be able to account for the above experiment, and also the disagreement in the literature between those who believe that the absorption of two quanta can cause a sensation, and thosewho believe that 5 or more are required.
Abstract: It is shown that the absorption of one quantum can excite a rod in the human retina, but that at least two, and probably many more, excited rods are needed to give a sensation of light. It is suggested that noise in the optic pathway limits its sensitivity, and this idea is subjected to an experimental test. The hypothesis is then formulated quantitatively, and shown to be able to account for the above experiment, and also the disagreement in the literature between those who believe that the absorption of two quanta can cause a sensation, and those who believe that 5 or more are required. The formulation of the hypothesis is used to calculate the maximum allowable noise (expressed as a number x of random, independent events confusable with the absorption of a quantum of light) in the optic pathway for the absorption of various fractions of the total number of quanta incident at the cornea.
424 citations
TL;DR: An attempt is made to determine the value of intrinsic retinal noise, and to test whether the idea that thresholds are efficient statistical judgements of constant fallibility can be applied to the differential threshold of the human eye at low intensities.
Abstract: It was shown by Hecht, Shlaer & Pirenne (1942) and Van der Velden (1944, 1946) that the quantal nature of light is largely responsible for the variability of response of human subjects to near-threshold visual stimuli. At about the same time Rose (1942, 1948) and de Vries (1943) suggested that the inescapable variability in the number of quanta absorbed from a constant light limits the accuracy with which its intensity can be judged, and that the differential threshold is set at as low a level as is compatible with this limit. If this suggestion is correct, one's concept of the nature of a psycho-physical threshold needs to be altered considerably; instead of recalling the all-or-nothing behaviour of a nerve fibre, one should consider the 'threshold' of sensitivity of a galvanometer which is constantly perturbed by noise, or some other example of a limit which is set in accordance with statistical criteria. It has been shown that such a view of the nature of threshold is entirely compatible with the data for the absolute sensitivity of the eye if it is assumed that there is a certain low level of intrinsic retinal noise, even in complete darkness (Barlow, 1956). In the present paper an attempt is made to determine the value of this retinal noise, and to test whether the idea that thresholds are efficient statistical judgements of constant fallibility can be applied to the differential threshold of the human eye at low intensities.
402 citations