Relationship between threshold and suprathreshold perception of position and stereoscopic depth

Abstract

We seek to determine the relationship between threshold and suprathreshold perception for position offset and stereoscopic depth perception under conditions that elevate their respective thresholds. Two threshold-elevating conditions were used: (1) increasing the interline gap and (2) dioptric blur. Although increasing the interline gap increases position (Vernier) offset and stereoscopic disparity thresholds substantially, the perception of suprathreshold position offset and stereoscopic depth remains unchanged. Perception of suprathreshold position offset also remains unchanged when the Vernier threshold is elevated by dioptric blur. We show that such normalization of suprathreshold position offset can be attributed to the topographical-map-based encoding of position. On the other hand, dioptric blur increases the stereoscopic disparity thresholds and reduces the perceived suprathreshold stereoscopic depth, which can be accounted for by a disparity-computation model in which the activities of absolute disparity encoders are multiplied by a Gaussian weighting function that is centered on the horopter. Overall, the statement “equal suprathreshold perception occurs in threshold-elevated and unelevated conditions when the stimuli are equally above their corresponding thresholds” describes the results better than the statement “suprathreshold stimuli are perceived as equal when they are equal multiples of their respective threshold values.”

Perceived Suprathreshold Depth Under Conditions that Elevate the Stereothreshold

“…This interpretation is supported by manual depth made matches by observers who viewed large-disparity clinical stereotargets while one eye was blurred. 1,3 A similar underestimation of perceived suprathreshold depth for line stereotargets that were identical to those in the current study was reported for conditions of binocular image blur by Patel et al 4 The depth matches of the three observers from Patel et al, 4 who viewed line stereotargets with +2.00 D lenses in front of both eyes, are compared to the results for the monocular-blur condition in the current study in Figure 2A.…”

“…Patel et al 4 demonstrated that increasing the separation between the two lines of the stereotarget also elevates the stereothreshold (see also 5,6 ). However, unlike the introduction of binocular image blur, an increase in the line separation results in no reduction of perceived suprathreshold depth.…”

“…We will refer to conditions 2 – 6 as the threshold-elevating conditions. After determining stereothresholds, the observers subsequently matched the perceived depth of a target in the threshold-elevating condition to that in the normal-viewing condition, using the procedure described by Patel et al 4 Specifically, on the first half of each trial the observer viewed a pair of dichoptic lines in the threshold-elevating condition with either a crossed or uncrossed disparity set to a specific multiple of the observer’s previously determined stereothreshold for that stimulus condition. Lines with crossed and uncrossed disparities were presented in different blocks of 70 trials.…”

“…Neither Somers and Hamilton 1 nor Lindstrom et al 3 addressed whether the amount of perceived depth decreases when the stereothreshold is elevated by factors other than monocular image blur. Patel et al 4 confirmed that the perception of suprathreshold stereoscopic depth is reduced when the images in both eyes are blurred, but found also that observers perceive the same magnitude of suprathreshold depth in a pair of line targets that are separated laterally by 10 arc min and by up to 540 arc min, despite a 30-fold elevation of the stereothreshold in the latter condition. Hasche et al 2 reported similar reductions of perceived suprathreshold depth for the Titmus stereo fly (subtending 3600 arc sec of disparity) in three groups subjects with binocular abnormalities: (1) variable and decompensated phorias, (2) intermittent exotropia, and (3) microstrabismus.…”

Stereo Day-for-Night

“…Note that although the resulting dynamic range compression of perceived depth under scotopic conditions clearly is a suprathreshold effect, the luminance contrast-dependent ratio s() of perceivable disparity thresholds in photopic and scotopic conditions is used for this manipulation. Patel et al [2009] observe that in the presence of blur not only the stereoscopic disparity thresholds are increased, but also the perceived suprathreshold stereoscopic depth is reduced. They attempt to explain their data on the perceived depth reduction using various sensory-perception transducer functions, including the logarithmic compression employed in our work, in which case the gain factor must be reduced.…”