# ARVO 1996: Threshold Psychophysics, Probability Summation and the Analysis of Spatial Summation Behavior

##### Christopher W. Tyler

Purpose. The paradigm of length summation can reveal the properties of the receptive fields underlying human visual sensitivity (when effects of retinal inhomogeneity and probability summation over retinal inputs are controlled). If detection is performed against an invariant background target, the inferred summation fields represent those operating for suprathreshold vision.

Analysis. The exact signal detection theory of probability summation was developed for the 2AFC paradigm with Gaussian noise. The 2AFC probability summation predictions of the exact theory differ substantially from Pelli’s (1985, JOSA) approximation, especially when the log psychometric function slope approaches 1. Numerical analysis indicates that 2AFC probability summation is independent of and predicts improvement of no more than x 4 over more than x 100 increase in extent. Uncertainty effects, which are predicted to generate variations in with stimulus size, also can be taken into acount through application of the theoretical analysis.

Methods. To evaluate suprathreshold length summation, 2AFC thresholds were measured for 1 s ramped Gaussian bars 1 to 128 line-widths in length (with matched Gaussian blur ends), presented on the steady background of a long Gaussian bar pedestal of 50% contrast. Uncertainty effects were nulled analytically.

Results. For the static target on its suprathreshold pedestal, there was no evidence for length summation beyond the width of the elongated bar stimulus, either in central fovea or in a homogeneous peripheral location. With no pedestal, length summation approximated ideal observer behavior up to ~20 times bar width.

Conclusions. The absence of suprathreshold summation here (or for the grating stimuli of Tyler, ARVO 1995) implies that neither physiological nor probability summation is operative in the presence of high-contrast masks. Thus, the mechanisms of human suprathreshold sensitivity for static targets seem to be purely punctate, i.e., mediated by local attention to small circular receptive fields.