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

Abstract

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.

The wisdom of crowds for visual search

“…We hypothesize that the dissociations across algorithms and tasks described above arise from an interaction between the foveated properties of the human visual system (high acuity at fixation and low acuity in the periphery) and observers' nonexhaustive search patterns. Because the target is of medium spatial frequency (six cycles per 1°), its detectability degrades rapidly with retinal eccentricity (68). This low target detectability using peripheral vision plays a role in the search task, where the target could be viewed foveally or peripherally, as opposed to the single-location task, where the target is always viewed foveally.…”

“…The applicability of our findings to real world search tasks requires two conditions: (i) a detectability for the target that degrades rapidly with retinal eccentricity (78) and (ii) individuals not thoroughly fixating all image regions (79,80). In our search task, these conditions were guaranteed by using a limited viewing time (2,000 ms) and a midfrequency Gabor target (six cycles per 1°) that degrades rapidly in detectability with retinal eccentricity (68). Although studies with realistic targets in naturalistic scenes (81) and medical images (82) have shown steep degradations in detectability with retinal eccentricity (thus meeting the first condition), real world searches can have unlimited viewing time, allowing observers to thoroughly fixate all image regions if desired.…”

The limits of visual resolution in natural scene viewing

“…The Limits of Visual 6 frequencies, measured by sensitivity to contrast at each frequency, is described by a contrast sensitivity function (CSF) (Campbell & Robson, 1968;De Valois & De Valois, 1988), which varies as a function of distance from the fovea, or retinal eccentricity (Anderson, Mullen, & Hess, 1991;Banks, Sekuler, & Anderson, 1991;Cannon, 1985;Peli, Yang, & Goldstein, 1991;Pointer & Hess, 1989;Robson & Graham, 1981). Contrast thresholds increase as a function of retinal eccentricity much faster for higher spatial frequencies than for lower spatial frequencies.…”

Gaze-Contingent Multiresolutional Displays: An Integrative Review

“…An important finding for the creation of multi-resolutional displays is that the human visual system shows a welldefined contrast sensitivity by retinal eccentricity relationship. As shown in Figure 2, Panel A, contrast sensitivity to higher spatial frequencies drops off as a function of retinal eccentricity 2 (e.g., Peli, Yang, & Goldstein, 1991;Pointer & Hess, 1989;Thibos et al, 1996). Therefore, in order to save bandwidth, a multi-resolutional image can exclude high-resolution information that is below contrast threshold at each eccentricity.…”

“…As shown in panel A of Figure 2, we assume that there is an ideal useful resolution function that is highest at the fovea and drops off at more peripheral locations. Such functions are well established for acuity and contrast sensitivity (e.g., Peli et al, 1991;Pointer & Hess, 1989;Thibos et al, 1996). Nevertheless, the possibility is left open that the "useful resolution" function may be different from these in cases of complex, dynamic displays, perhaps on the basis of attentional allocation factors (e.g., Yeshurun & Carrasco, 1999).…”