The results of the present study clearly show that the critical variable determining alignment performance is the number of available samples rather than sample separation—as proposed by Morgan and Watt (
1982). Instead, our findings are consistent with Kontsevich and Tyler (
1998) who showed that positional judgements were invariant with sample separation for a fixed distribution width provided at least 3–4 samples were present. Kontsevich and Tyler stated that these alternate accounts could be explained by differences in stimulus arrangement. In Morgan and Watt's task, observers were required to make a relative localization judgment of two sampled difference of Gaussian functions (DoG), one presented above fixation and the other below. Importantly, the sample positions above and below fixation were identical, regardless of the sample separation value. Kontsevich and Tyler suggested that the similarity between the two distributions to be localized may have allowed a low level or local luminance comparison to mediate judgements. However, our results make an explanation based on the local similarity of the two distributions seem unlikely. In the present study, identical distributions were presented above and below fixation in a similar fashion to Morgan and Watt. The critical difference between our study and theirs was that sample location was not fixed but randomly jittered from trial to trial. This process, coupled with the use of a dynamic noise carrier, ensured that any local luminance cue, if present, would be rendered unreliable and instead judgements would need to be based on the distribution as a whole. A comparison of localization thresholds suggests that this may indeed be the case. Morgan and Watt reported threshold values in the region of 10–20 arc seconds in comparison with our optimum thresholds that are between 1–2 arc minutes for luminance-defined distributions (at a sample separation of 1.9 arcmin). The thresholds found in this study are more similar to those reported by Kontsevich and Tyler (
1998). Their slightly poorer threshold values (around 4–5 arcmin) probably results from the fact that their luminance-defined test and reference stimuli were of opposite polarity—a factor known to elevate thresholds on positional tasks (Levi, Jiang, & Klein,
1990; Levi & Westheimer,
1987; O'Shea & Mitchell,
1990). The small differences in absolute sample number between this study (6 samples) and Kontsevich and Tyler (3–4 samples) likely reflects the fact that we sampled our distributions both above and below fixation rather than localizing a single sampled distribution relative to a fixed luminance reference marker. Interpolation performance for 2nd-order, or contrast-defined, distributions were qualitatively similar to their 1st-order counterparts. Threshold values were generally higher for localizing 2nd-order distributions but the overall pattern of results for both sample separations was identical. Once again, if 6 or more samples were available to the observer, thresholds became invariant of sample number. Sukumar and Waugh (
2007) have previously shown larger summation areas for 2nd-order stimuli when mapping thresholds against stimulus area while employing stimuli created using very similar methods. Given that result it would be expected that 2nd-order stimuli should be able to tolerate broader sample separations before performance declined.
Figure 5 presents performance for three of the observers as a function of sample separation. While performance does decline with increasing separation there is no apparent difference in dependence on separation between the results for 1st- and 2nd-order stimuli. Sukumar and Waugh (
2007) estimated that the summation zones for the detection thresholds of 1st- and 2nd-order stimuli presented at the fovea were fitted by Gaussians with standard deviations (
σ) of approximately 13 and 37 arcmin respectively. These values seem unlikely to pertain to our localization task, since at our largest sample separation of 8.7 arcmin only two or three samples would fall into a ±1
σ summation zone for 1st-order stimuli while 2nd-order detectors should be able to use approximately 8. This should result in a larger decline in performance for 1st- than 2nd-order stimuli at the largest sample separation. That result is not obtained here. However, estimates of the size of Ricco's area, the region in which stimulus intensity and area are inversely proportional at threshold, do vary across observers and with eccentricity (Sukumar & Waugh,
2007), even over the relatively small extent of our current stimuli. The area also varies with luminance (Cornsweet & Yellott,
1985) although Sukumar and Waugh (
2007) used a mean luminance of 52 cd.m
−2 (Waugh, 2008, personal communication) which is very similar to the 54.2 cd.m
−2 used here. In future the summation zones for contrast detection thresholds and localization should be determined within the same observers and using the same stimuli.