Image invariance with changes in size: the role of peripheral contrast thresholds

The appearance of objects generally does not change with changes in the size of their retinal image that occur as the distance from the observer increases or decreases. Contrast constancy ensures this invariance for suprathreshold image features, but fully robust size invariance also requires invariance at threshold, so that near-threshold image features do not appear or disappear with distance changes. Since the angular size and the eccentricity of image features covary with distance changes, the threshold requirement for invariance could be satisfied approximately if contrast thresholds were to vary as the product of the spatial frequency and the eccentricity from the fovea. This model fits contrast thresholds for orientation identification over spatial frequencies of 1-16 cycles/deg and for retinal eccentricities of as much as 23 deg. Contrast detection thresholds from six different studies conform to this model over an even wider range of spatial frequencies and retinal eccentricities. The fitting variable, the fundamental eccentricity constant, was similar for all three studies that measured detection along the horizontal meridian and was higher for the orientation identification contrast thresholds along the same meridian. The eccentricity constant from studies that measured detection along the vertical meridian was higher than the constant calculated for the horizontal meridian and lower than the eccentricity constant for chromatic isoluminance gratings. Our model and these results provide new tools for analyzing the visibility of displays and for designing equal-visibility or variable-visibility displays.