On the relation between summation and facilitation

Summation refers to the small reduction of threshold contrast as a signal is extended in space or time, or when multiple signals are presented simultaneously. Facilitation refers to the large reduction in the threshold contrast increment when it is superimposed on a near-threshold pedestal contrast. Separate hypotheses relate each of these effects to distinct measures of the log-log steepness of the psychometric function. This note shows that for 2-alternative forced-choice (2afc) proportion correct, the Weibull function P(c) = 1-(1-gamma) exp[-(c/alpha) beta] and the d' power law d'(c) = (c/c0.76)b are practically indistinguishable. Furthermore, their steepness parameters are proportional to each other, beta = 1.247 b. This implies a simple relation between 2afc summation and facilitation which can be tested without measuring the psychometric function.

[1]  Jacob Nachmias,et al.  On the psychometric function for contrast detection , 1981, Vision Research.

[2]  G. Legge.  A power law for contrast discrimination , 1981, Vision Research.

[3]  Julius Lieblein.  Two early papers on the relation between extreme values and tensile strength , 1954 .

[4]  Gordon E. Legge,et al.  Light and dark bars; contrast discrimination , 1983, Vision Research.

[5]  J. M. Foley,et al.  Contrast masking in human vision. , 1980, Journal of the Optical Society of America.

[6]  R. Duncan Luce,et al.  Parallel psychometric functions from a set of independent detectors , 1975 .

[7]  J. Robson,et al.  Probability summation and regional variation in contrast sensitivity across the visual field , 1981, Vision Research.

[8]  D G Pelli,et al.  Uncertainty explains many aspects of visual contrast detection and discrimination. , 1985, Journal of the Optical Society of America. A, Optics and image science.

[9]  J P Thomas,et al.  Underlying psychometric function for detecting gratings and identifying spatial frequency. , 1983, Journal of the Optical Society of America.

[10]  G S Brindley.  The Order of Coincidence Required for Visual Threshold , 1954 .

[11]  N. Graham.  Visual detection of aperiodic spatial stimuli by probability summation among narrowband channels , 1977, Vision Research.

[12]  J Nachmias,et al.  Letter: Grating contrast: discrimination may be better than detection. , 1974, Vision research.

[13]  W. Weibull.  A Statistical Distribution Function of Wide Applicability , 1951 .

[14]  G. Legge.  Sustained and transient mechanisms in human vision: Temporal and spatial properties , 1978, Vision Research.

[15]  N Graham,et al.  Simultaneous measurement of spatial-frequency summation and uncertainty effects. , 1985, Journal of the Optical Society of America. A, Optics and image science.

[16]  J. M. Foley,et al.  Contrast detection and near-threshold discrimination in human vision , 1981, Vision Research.

[17]  Quick Rf.  A vector-magnitude model of contrast detection. , 1974 .