The sensitivity of separation discrimination to spatiotemporal jitter

Vision Res. Vol. 30, No. 11,pp.IS%-1560, 1990 Printed in Grest Britain.All rightsreserved

00424989/90 53.00 + 0.00

Copyright0 1990PergamonPresspk

THE SENSITIVITY OF SEPARATION DISCRIMINATION TO SPATIOTEMPORAL JITTER DAVIDR. BADCOCK’and TERRENCE L. WONG* ‘Department of Psychology, University of Melbourne, Parkvillc, Victoria, Australia and 2Graduate Group in Biophysics, University of California, Berkeley, CA 94720, U.S.A. (Received

10 August 1989; in

revtiedform 16 January 1990)

Abstract-Differences of less than 20 set of visual at&e in the separation of a pair of closely spaced parallel lines can be reliably detected. This ability is known as a hyperacuity because the thresholds are smaller than the diameter of one fovea1 cone. It is shown that this ability does not requite a stationary pattern. Indeed, correlated horizontal jitter of the line pair has little detrimental effect on performance for jitter that ranges up to 8 min arc for two lines with a separation of only 6 min am Uncorrelated jitter of the two tines, which allows the actual separation to vary from moment to moment, causes performance to deteriorate at a rate similar to the rise of signal uncertainty. The results reflect the operation of a system which is not only extremely robust to oculomotor instability but is also robust to positional variation that could not be produced by eye movements. Hyperacuity

Position

Noise

Separation discrimination

INTRODUCI’ION

The eyes of human observers are continually in motion (Riggs, Armington & Ratliff, 1954; Ditchbum, 1973; Hallett, 1986; Matin, 1986). In spite of this motion, observers are capable of extremely fine discriminations of the relative position of objects (Berry, 1948; Westheimer, 1975, 1979; Klein & Levi, 1985; Badcock & Westheimer, 1985a, b). Westheimer and McKee (1977) have shown that the ability to align two briefly presented vertical lines is not affected by sweeping the line pair across the retina at speeds up to approximately three degrees per second. Morgan, Watt and McKee (1983) replicated this observation for short stimulus presentations and, further, demonstrated that the improved performance gained by repeated stimulus presentation was affected by drifting the stimuli across the screen. In both cases, Morgan et al. (1983) still have thresholds less than 30 set arc, indicating that despite a degraded performance level with moving stimuli this is still a hyperacuity task. Several investigators (Fahle & Poggio, 1981; Morgan & Watt, 1982; Morgan et al., 1983) have examined the mechanisms capable of interpolation along a linear path which could produce the performance reported by Westheimer and McKee (1977). The direction and extent of oculomotor jitter, however, is not

uniform (Ditchbum, 1973). In spite of this, none of these studies have examined the more realistic situation in which the pattern moves randomly to and fro, rather than in a single direction with a fixed speed during a trial. If the ability to ignore motion of the retinal image is a consequence of a development intended to eliminate noise due to the motions of the eyes, then observers should also be able to ignore jitter that changes direction rapidly and at random. In order to explore this ability, a two line separation task was used. It will be shown that observers are remarkably adept at ignoring jitter, even if that jitter causes the separation between the two lines to randomly vary over time. METHOD In each condition a pair of parallel lines 10 min arc high and substantially narrower than the point spread function of the eye, were presented with a mean separation of 6 min arc for 6OOmsec. After a 1OOmsec dark interstimulus interval another pair of lines were shown for 600 msec. The second pair was either the same separation, 11.25,22.5 or 33.75 set arc wider or narrower than the first. The observers were asked to indicate by setting a switch whether the second line pair appeared narrower or wider than the first.

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DAVIDR. BADCOCKand TERRENCE L. WONG

In each interval the location of the target lines was updated every 30msec and their intensity was increased from zero up to 0.18 cd/m2 in that location for 3 msec (the P4 phosphor employed decayed to 1% in 470 psec). In conditions with no jitter the lines were always in the same location within each interval. However, when jitter was introduced, the lines had equal probability of appearing anywhere within the horizontal jitter range. For example, with 4 min arc jitter a line could appear anywhere within & 2 min arc of the mean location (within the quantization limits imposed by the pixel size of 3.75 set arc on the HP1345 display used in this experiment at the viewing distance of 3 m). Only horizontal jitter was employed because with the two line separation task all the critical information is in that dimension. The amount of jitter employed varied from trial to trial with values of 0, 2, 4, 6 and 8 min arc being interdigitated. Note that the last value produces an overlap in the possible location of the two lines. The average location of a single line within an interval may vary from the central point of the distribution from which the samples are drawn. The variation (u) in the average location (the standard error of the mean) is given by: 0 = ~K~2/12)1/J~;

(1)

where i is the jitter range and n is the number of samples (n = 20 on every occasion in the current study). The average separation in the interval may also vary from the nominal separation. The standard error of the variation in the separation depends on the variation in the location of the two lines and the degree of correlation between the jitter of the two lines and is given by: UXP= J[zJ:. + vi - 2ru,o,];

(2)

where vL and vR represent the variation for the left and right lines respectively and r is the correlation in the jitter of the two lines. Four conditions were presented. In the first two, the spatially correlated conditions, the separation between the line pair was fixed; both lines were moved equal amounts each time they were updated. Therefore r = 1 in equation (2) and vHP= 0 for all jitter ranges. If the visual *A simulation was conducted in order to check the ability to produce zero correlation using our method for gencrating jitter. The results indicated that the correlation was very close to zero; the value obtained was 0.016 when calculated using 300 separate estimates, each derived using 20 offset pairs. The 95% confidence limit for r = 0 when n = 300 is 0.113.

system is robust to the type of image motion produced by oculomotor jitter then these conditions should not produce poorer performance. In the second two conditions, the spatially uncorrelated conditions, the instantaneous separation of the line pair was allowed to vary (r E 0 in equation 2).* The location of each line during an interval was again drawn from a rectangular probability distribution. The separation between the centers of the distributions was 6min arc for the first interval and 6 min arc + the offset in the second interval. If the visual system can accumulate an average distance between the jittering lines using many instantaneous separation measurements, then the deterioration in performance should be described by the noise in the separation measurements, or the variance of the mean separation as given by equation (2). When spatially correlated jitter was employed the line pair appeared to maintain a constant separation while rapidly jumping left and right. In the spatially uncorrelated conditions the percept was of two lines undergoing independent movements. In both cases the percept varied haphazardly between being a very jerky motion and instantaneous displacements. Only horizontal motion was perceived. The spatially uncorrelated conditions did not produce apparent depth changes. Both the spatially correlated and uncorrelated conditions were tested with two temporal conditions. In the first, the set of random offsets used in the first interval were also used in the second interval (temporally correlated) while in the second a new set of random offsets was chosen for the second interval (temporally uncorrelated). This manipulation varies extraneous cues such as the width of the envelope of spatial locations over time and the ability to detect changes in particular temporal sequences of locations in addition to altering the variance in the separation difference between the two intervals. The change in variance may be derived by substituting usIp,and ump2for vL and uR respectively in equation (2). Three hundred trials were conducted for each combination of condition and jitter range. The data were analyzed by probit analysis (Finney, 1952) and the thresholds to be reported are equivalent to half the distance between the 25 and 75% correct points on the best-fitting cumulative gaussian. This threshold estimate is identical to that used by Westheimer and McKee (1977).

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Sensitivity of separation caption 90

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Fig. 1. Threshold spar&on disrimination for vertical lines jittering horixontally in location over the range specified on the X-axis. The lines moved either; together, maintaining the same 6 min arc separation (SC:open symbols) or independently allowing the spatial separation to vary from the 6 min arc average (SWsolid symbols). The set of random changes in location were either the same (tc: dashed lines and circles) or different (tu: solid lines and squares) in the two observation intervals. The dotted lines indicate changes in the signal certainty calculated as described in the text.

spatially uncorrelated jitter conditions. The thresholds do rise as the amount of jitter increases for jitter ranges in excess of 4 min arc. Jitter has little effect on the thresholds in the spatially correlated conditions. This finding supports the notion that the visual system is able to discount the type of image motion produced by oculomotor instability by using positional difference signals. uRPis zero for all jitter ranges RESULTS as indicated by equation (2) and thus perThe data from the observers who participated formance should not change if it is limited by in the full set of conditions are plotted in Fig. 1. V _,. However oculomotor instability rarely if Lines with open symbols represent the spatially ever produces such extreme jitter in normal correlated conditions while solid symbols are observers (Riggs et al., 1954). used for the spatially uncorrelated conditions. In assessing the data for the spatially uncorreSolid lines and squares represent temporally lated conditions (solid symbols) the change in uncorrelated results and dotted lines with circles the precision of the signal caused by varying the indicate the temporally correlated data. separation between the line pairs must also be It is readily apparent that spatially correlated considered. For the temporally correlated conjitter up to 8 min arc in extent has little effect on dition (circles) the same set of samples is used in the separation discrimination thresholds even both intervals, thus the stimulus uncertainty is though the possible positions of the lines can produced solely by the variation in the mean overlap during the display sequence. That there separation within an interval. The lower, dotted was no consistent difference between temporally prediction line in Fig. 1 indicates one standard correlated and uncorrelated conditions shows deviation of the mean separation in each that the performance was not a result of com- interval. This was generated computationally paring the offsets of the outermost of each set of by taking 300 means (one for each trial) of lines since that cue would vary and produce 20 random location samples (6OOmsec with poorer performance in the latter condition than samples every 30 msec) using the same methods in the former. The two data lines in Fig. 1 with employed in the experiment. The variance solid symbols show performance under the of a single bar’s average location was then The two authors served as the main observers. A third observer who was unaware of the aims of the research was used in a subset of the conditions to confirm the major findings. All three had corrected-to-normal visual acuity and were experienced in hyperacuity tasks. Viewing was binocular and feedback was provided.

tsss

DAVIRR. BADCXCK and TF~RRENCZ L. WONG

calculated. Since both bars were jittered over the same range the variance in their location was the same. The combined variance for the bars is obtained by adding the individual variances. Taking the square root then yields the standard deviation. This estimate of signal variability increases with a similar slope to the thresholds in the temporally correlated condition. The results show that observers can even discount jitter that could not be produced by any pattern of oculomotor instability. The reduction in performance can be accounted for by the reduction in signal certainty. When both spatial and temporal correlations are removed the standard deviation of the separation signai increases again by a factor of J2. In this case, the critical source of uncertainty in the signal is the variation in the mean separation between the two intervals. Using the same methods outlined above, estimates of the change in the standard deviation of this value as a function of jitter range were obtained. The upper dotted line rising from zero in Fig. 1 shows the expected decay caused by jitter and is very similar to the theo~tical line that would be generated by equations (1) and (2). Once again, the change in threshold closely matches the change in signal certainty reinforcing our interpretation that jitter itself does not impose great difficulties for the process that determines separations.

have yielded larger variances. The temporal limits of this averaging are currently being investigated (Badcock & Wong, in preparation). In addition, the assumption that one-standard deviation of the variance is the critical liit is also being tested. At this stage, both assumptions seem reasonable given the correspondence between the data and the predictions. If these assumptions are justified, the point where the thresholds and the statistical predictions coincide provides an estimate of the internal noise in separation discrimination. Figure 1 indicates that the internal noise is equivalent to approx. 3-5 min arc jitter. This value is quite similar to the centroid generating zone described by Westheimer and McKee (1977). Our results differ slightly from those of Morgan et al. (1983) who, based on a vernier alignment task, concluded that when unlimited viewing time was used to produce optimal performance, pattern motion did cause performance to deteriorate. We also show some deterioration in the equivalent spatially correlated conditions but not nearly the factor of four reported by Morgan et al. (1983). As a control measure we conducted an experiment to assess observer’s ability to disc~minate separation differences for a 600 msec, 6 min arc separation with no jitter. Identical methods to those employed earlier were used, but on this occasion the condition was not interdi~~t~ with others. This control was an attempt to ascertain the best possible thresholds for GENERAL DISCUSSION the baseline separation task. The thresholds The results presented show that the visual obtained were 12.14 St 1.49 set for DRB and system is very resistant to noise produced by 15.66 + 1.64 set for TW. The values are very spatial jitter when performing a separation dis- similar to those plotted in Fig. I and thus the c~mination task. A comparison has been made interdigitation of conditions cannot fully exbetween the fall off in performance and that plain the difference. The disagreement may be expected from the reduction in precision of the attributable to differences between the separsignal. With spatially correlated jitter the results ation and vernier alignment tasks. Another possible tactic for ~rfo~ing the regect the lack of variation in the separation signal. However, it should be noted that some task is to compare the width of the outermost dete~~ration in th~sholds did occur. Perfornt- line elements in each interval. If observers were ante in the spatially uncorrelated conditions using this tactic performance should be poorer were also adequately described by the statistical in the temporally uncorrelated conditions where limits for larger jitter ranges. The observers the relative locations of the outermost lines may seemed to be able to derive temporally averaged vary between the two intervals within a trial. separation estimates from the instantaneous There was no consistent difference between the com~a~sons. Without this ability, performance two conditions with spatially correlated jitter, leading us to reject this simple strategy for those in these tasks would have been poorer. The statistical predictions assumed all 20 conditions. To further assess this possibility samples were used in each interval. Since the separation disc~mination was measured as a variation described by equation (1) falls in function of base separation, without jitter. The proportion to ,,/a using fewer samples would results are plotted on appropriately modified

Sensitivity of separation discrimination

r

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TW

A WWth

Rongo of jlttsr Mn arc) Fig. 2. A comparison between the thresholds obtained in the spatially and tcmporaIIy uncorrciatcd jitter condition (su-tu: squares) from Fig. 1 and separation caption as a fimction of base separation when there is no jitter (triangks). The X-axis has the same scale as in Fig. 1 whcm the base separation was 6 mie arc (dashed lines and squares). In order to make the conditions comparable 6 min arc was subtracted from the separation used in each width condition (solid lines and triangics). The dotted lines show thcor&al curves described in the text.

scales in Fig. 2 for each observer. A 6 min arc separation has been compared to zero jitter, 10 min arc to 4 min arc jitter (that is, 6 & 2) and so on. The jitter condition that produced the worst performance (su_tu in Fig. I) has been replotted for comparison (squares). Width discrimination (triangles) was found to produce poorer performance than actually obtained in the jitter conditions. However, the maximum separation within any particular interval is rarely the maximum possible separation. Thus the comparison just described may be inappropriate. The average maximum separation in a single interval that was presented in the experiment was calculated. This value rises more slowly with increasing jitter range to a maximum of 11.7min arc (il.05) with 8min arc jitter. The dotted line with symbols in Fig. 2 shows the threshold expected (obtained by linear interpolation from the width conditions) as a function of jitter range. Note that this calculation assumes that the interval has a fixed separation equal to its average maximum separation. The line provides a close match to the data and has been presented for this reason. However the line is not the appropriate one to compare to the data. Observers must discriminate between the maximum separation difference in the two intervals. In the temporally uncorrelated condition plotted in Fig. 2 the standard deviation of the

maximum separation difference between intervals rises very rapidly. The one standard deviation values are indicated in Fig. 2 by the dotted line rising from zero. This is a more appropriate comparison for discriminations based on the outer envelope width and performance does not change rapidly enough to be explained by such a strategy. Thus envelope width discrimination seems unlikely to be the cue based by our observers. These results support the conclusions based on the failure to find a difference between the two temporal conditions with spatially correlated jitter. Clearly some variant of a width discrimination is being performed by our observers in the tasks they were presented with. What is being questioned here is the likelihood that only the location of the outermost lines in each interval were being used in the task. The mechanisms actually involved in making instantaneous width judgments cannot be fully specified at this stage. We conclude that the visual system is remarkably resistant to jitter when performing separation discrimination tasks. Our results extend those of earlier studies demonstrating that linear motion has minimal influence on thresholds (Westheimer & McKee, 1977; Morgan et al., 1983) by showing that neither the direction nor velocity need be constant. The results with correlated jitter would be the desirable outcome in a system that needed to

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discount oculo-motor instability. However, those obtained with spatially uncorrelated jitter show that the system is much more proficient than would be required by that constraint. No pattern of eye movements can produce spatially uncorrelated movement of the lines within a monocular image. The results are consistent with the suggestion of Westheimer (1979) and Klein and Levi (1985) that width discriminations are made using decisions based on instantaneous separation judgments. We extend this suggestion by presenting results compatible with the averaging of such judgments over time. Acknowledgements-The authors would like to thank Professor G. Westheimer for providing the equipment used for this research. Dr Badcock was on sabbatical leave from the University of Melbourne during the course of the research. Mr Wong was supported by NIH 8rant 5T32GM07379. The authors are srateful for helpful comments provided by Professor G. We&e&r, Dr P. Patterson and Mr B. Coutant.

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