Human symmetry detection in dense patterns exhibits a spatial integration range that becomes narrower with distance of the symmetry axis from the fovea. This narrowing violates the general properties of eccentricity that have been found for all previous visual cortical areas, tasks and assessment techniques. This reverse eccentricity scaling may, in conjunction with the long-range matching properties for symmetry described in our previous work, imply that symmetry is processed by a specialized cortical area with non-retinotopic neural architecture.

Introduction

Cortical magnification defines the area of cortex representing each region of the retina. Typically, this magnification provides higher functional resolution of image details at the fovea, decreasing with distance from the fovea (eccentricity of visual angle). The variation of magnification with eccentricity is expressed by an eccentricity scaling function specific to each cortical representation area (e.g., Sereno et al., 1995). Although at base an anatomical concept, the eccentricity scaling function is commonly defined in functional terms, by the variation in retinal extent required to achieve a criterion performance level, either of a physiological signal recorded from a particular cortical location or of a psychophysical task or brain imaging technique measured in human. The parameters of the eccentricity scaling function for a particular task are therefore potentially diagnostic of the cortical area whose properties define the limits of the performance. This concept provides a bridge between anatomy and psychophysical performance. If two tasks exhibit different magnification properties (other than simple sensitivity differences), the implication is that their limits are set by different cortical projection geometries.

In previous studies, we have investigated the perceptual integration width for bilateral symmetry of static and dynamic noise fields by masking the symmetry by a random strip of various widths centered on the symmetry axis. Detection of static symmetry was possible up to as much as a 6º separation of the symmetric elements, for unscaled textures (Tyler et al., 1995) Presumably there was some integration or comparator mechanism that allowed the element similarity to be compared up to, but not beyond, this 6º range (even when random elements were interposed in the gap between the symmetric elements). Dynamic symmetry detection showed an integration width about ten times narrower than this (Jenkins, 1983; Tyler et al., 1995), suggesting that the symmetry detection processes differed at different noise presentation rates.

To evaluate the eccentricity scaling function for human symmetry processing, threshold width-integration functions were measured for static bilateral symmetry around an axis set at various distances from the fovea. As in previous work, the bilateral symmetry around a vertical axis in random dot fields was masked by a random strip of various widths centered on the symmetry axis. The presence of the random strip means that no symmetry information is available out to the edge of the random strip, so that any symmetry detection mechanism must integrate information from beyond the two edges of the strip to perform the detection task. The fall-off in detection sensitivity with strip width represents the integrated sensitivity of the available detection mechanisms to the symmetry information.

Previous studies have reported reduced detectability for static symmetry when the axis is placed in eccentric vision (Julesz, 1971; Corballis & Roldan; 1974; Barlow & Reeves, 1979; Saarinen, 1988; Herbert & Humphrey,1993; Gurnsey et al., 1998). Most of these studies found that sensitivity declined with eccentricity, but the reported declines were surprisingly gradual if symmetry detection is considered as a position-based task (Levi et al. 1985), effectively the discrimination of relative positions of objects in the visual field (Corballis & Roldan, 1974). We therefore wished to determine the peripheral scaling properties for symmetry detection in terms of the spatial range over which symmetry information is integrated. Rather than presupposing an eccentricity scaling for the noise elements (e.g., dashed line in Fig 1e), as did Saarinen (1988) and Tyler and Hardage (1996), the noise here consisted of unscaled binary random elements of fixed size, allowing us to determine the applicable eccentricity scaling empirically from our measurements of the integration width for symmetry detection as a function of eccentricity. Just as measurements of the receptive field width define the eccentricity scaling for spatial integration of luminance, measurements of the summation width for symmetry define its eccentricity scaling. (By presupposing a scaling function and finding that sensitivity was roughly equated, previous studies provided only negative evidence against a deviation from their presuppositions; their data would have revealed a different scaling function only if symmetry detectability varied strongly with spatial frequency content of the target. If sensitivity were invariant with spatial frequency, any size scaling would provide equivalent results. Moreover, previous studies measured only sensitivity to visual symmetry, not its spatial integration properties, which are the object of the present study.)

The direct measurement approach was taken by Gurnsey et al. (1998), who found a marked fall-off with eccentricity, especially with a patch of symmetric dots embedded in a random noise field. However, their paradigm presupposed that the patch was large enough to encompass any symmetry integration mechanism. Since the dots that they used were about 5 min in width at a density of 6 per sq. degree, they had a low density could stimulate only low spatial frequency mechanisms. Such previous work would have led to the prediction of a rapid fall-off in the detectability of an unscaled stimulus, but our results with high density noise dots will be seen to violate this prediction in two surprising ways.

Fig. 1. Static symmetry detection as a function of eccentricity of the symmetry axis. a) Example of a fully symmetric pattern test stimuli shown with an eccentric fixation marker (a red dot was used in the experiment in place of the black cross); b) symmetric pattern but with the central 40 pixels replaced with random dots to evaluate the integration width, by measuring sensitivity with different widths of a randomized central strip separating the halves of the symmetry pattern; c) completely random null pattern.

Methods

Stimuli

The stimuli were generated on the screen of a Macintosh IIfx with a visual angle of 23.5 deg wide by 17.6 deg high at a viewing distance of 57 cm. Stimulus patterns consisted of 307,200 randomly black and white 2.2’ pixels at a 100% contrast and 25% density with a pixel luminance of 160 cd/m^2. The symmetric patterns were made of random dots reflected around the vertical axis of symmetry, while the asymmetric null patterns were purely random. The vertical axis of symmetry was located in the center of the monitor, and a red fixation point was placed at 2º, 5º or 10º to the right of fixation. Lighting was ambient fluorescent, with the screen hooded to reduce glare.

Procedure

Measurements of percent correct for durations from 30 ms to 1800 ms were taken by the method of constant stimuli. Each trial consisted of a brief (<300 ms) pretest period of dynamic random fields at a frame rate of 15 ms, followed by the symmetric or asymmetric stimulus of stationary dots, followed by another 300 ms period of dynamic random fields (designed to eliminate onset and offset effects).

?Test runs consisted of blocks of 50 Yes/No trials for each duration and eccentricity condition. The task employed was a Yes/No decision for single presentations of either a symmetric or an asymmetric pattern on each trial. Detectability of the symmetry was measured by in terms of duration psychometric functions, which are specified in percent correct as a function of the duration of symmetry presentation. Tyler et al. (1995) and Tyler and Hardage (1996) established the validity of duration sensitivity as a measure of perceptual response to complex stimuli and showed that criterion bias effects were minimal in this paradigm. The observers showed no significant tendency to change their bias from Yes to No, or the reverse, as the width of the interpolated noise strip width was increased. The criterion response therefore represents a pure measure of sensitivity to the symmetry stimulus. Observers were given practice to become familiar with the detection task and the position and orientation of the symmetry axis to be detected.

The derivation of a measure of duration sensitivity for symmetry detection is described in previous work (Tyler et al., 1995; Tyler and Hardage, 1996). Briefly, percent correct performance as a function of duration of the symmetry epoch allowed interpolation to the duration that would have produced a 60% detection level. (This low level is on the steepest portion of the symmetry psychometric functions, which have an unusual decelerating form that is analyzed in detail in Tyler et al.(1995). The 60% criterion was therefore chosen to maximize the accuracy of the derived sensitivity measure.)

Results

The two independent variables were width of the random gap and distance of the axis of symmetry from fixation. Specification of this integration range is most meaningful if normalized in terms of peak sensitivity without the masking noise strip. Both are retinal position variables and thus the data for both variables may be plotted on the same abscissa. When full symmetry was present, duration sensitivity for symmetry was relatively invariant out to 10º eccentricity, showing a reduction of less than a factor of two (where a factor of 10 would be expected for a position-based task; Levi et al., 1985). These conditions are represented by the peaks of the functions plotted in Fig. 2 (left panel). Similarly good performance was reported at these eccentricities for symmetry detection with eccentricity-scaled stimuli (Saarinen, 1988), but the stable peak sensitivities in Fig. 2 show that there is little degradation symmetry processing even with unscaled stimuli, perhaps because of the broad spatial-frequency spectrum of the noise targets.

Duration sensitivities were further measured for several different widths of occluding noise separating the symmetric halves of the patterns, to generate a width integration function for symmetry processing at each retinal eccentricity (Fig. 2). Each reflected pair of points represents a duration sensitivity for a particular width of occluding noise, plotted at the position of the edges of the noise strip. Values were measured up to a maximum of 1800 ms duration according to the limiting sensitivity for each condition, but the plots only go to 1000 ms to provide a uniform limit for all eccentricities. The resulting width integration functions represent the sensitivity of a hypothetical symmetry processor to the region of the field beyond the plotted positions (since there is no symmetry information, only random information up to those positions). Thus, when sensitivity has become negligible (defined as >1000 ms), there is no mechanism available that can extract the symmetry property across the gap of that width. Note that even the widest gaps were only 1/4 of the screen width, so that they provided minimal (~0.1 log unit) reduction in the symmetry information available to an ideal observer.

As expected from the previous study, sensitivities were highest at the center of each integration function when symmetry pattern halves were not masked. The fall-off in sensitivity forms a bell-shaped integration curve with distance of the edges of the random occluding strip from the symmetry axis; curves were measured separately for several positions of the axis on the retina. Strictly speaking, the functions represent the integrated sensitivity of the mechanisms processing symmetry as a function of distance from the symmetry axis. The local sensitivity would be measured by the derivative of these functions. However, in practice plotting derivatives is a noisy procedure, so it was deemed preferable to stay closer to the measured data and plot them in their integral form. The main analysis here concerns the measured tuning widths, which are monotonically related to their derivatives if the tuning functions themselves are monotonic. For example, if the symmetry processing mechanism had a Gaussian sensitivity profile, the integration function as measured here would take the form of a cusp with skirts in the form of a cumulative Gaussian fall-off in each direction, which seems to be a good description of several of the data sets (particularly for observer CA).

The widths of these integration functions decreased with eccentricity, when measured near the base of the functions as a way of capturing their full width. The width was measured by linear interpolation between the nearest sensitivity points (some of which are below the axis limit of 1000 ms, as described above). Normalized to a criterion of 1/20 of the peak detectability (i.e., at -26 dB relative to the peak sensitivity at each retinal eccentricity), integration widths show a statistically significant decrease (p < 0.05, t-test corrected for multiple applications) from a mean width of 4.8º +1.2º at the fovea to mean widths of 2.1º +1.5º at 5º and 2.0 +1.6º at 10º eccentricity (Fig. 2, right panel). This is the first perceptual task that shows a reverse scaling with eccentricity, from broader spatial integration at the fovea to narrow spatial integration in peripheral retina. This reversal is particularly surprising for a task of relative position estimation such as symmetry detection, because the magnification function that underlies most position-based tasks shows a particularly steep degradation with eccentricity (dashed line in Fig 2; Tyler, 1991; Levi et al., 1985). 

Fig. 2. Left panel: Symmetry integration functions, in terms of the duration required to reach 60% correct detection as a function of the extent of the randomized strips, measured at several eccentricities of the symmetry axis from the fovea. (Data are reflected about each axis corresponding to the symmetric configuration of the stimulus, as indicated by the dashed interpolation lines.) Thus, both the shape of the integration functions and their retinal location may be represented on the same abscissa of retinal location. Right panel: Width of the symmetry integration functions in (d) measured at a sensitivity level of 1/20 of the unmasked duration sensitivity (typically about 1 s duration). If these symmetry integration widths matched the magnification from retina to human striate cortex, they would fall up the dashed line. In fact, symmetry integration width declines with eccentricity, representing a reverse magnification property.

Discussion

The results obtained may appear to contrast with a the recent report of a rapid fall-off with eccentricity for symmetry detection in unscaled random blob stimuli (Gurnsey et al., 1998). However, at a similar dot size they also report about a factor of two drop in sensitivity out to comparable eccentricities for their non-embedded condition. Again, they may regard this is a substantial loss in sensitivity, but we view it as modest compared with the factor of 30 or so that could be measured in our paradigm.

The occurrence of a reverse eccentricity scaling behavior for symmetry summation width is remarkable, and may require reconsideration of the normal view of magnification as a projective scaling in the retinal connections to a uniform cortical analysis structure. Instead it may imply that the foveal region has a specialized long-range sensitivity exhibiting properties that are the reverse of magnification. In other words, for most tasks visual performance is improved by a finer grain of cortical projection toward the fovea, but for a global process such as symmetry perception the issue is not to provide finer grain but to identify long-range pattern similarities. For such a task, foveal specialization may generate the reverse of the normal property of finer grain: an increase of long-range connectivity in the fovea, resulting in a larger spatial integration area in this region of specialization.

Recent results from function magnetic resonance imaging (fMRI) suggest that the presence of symmetry generates little differential activity in known retinotopic projection areas (V1-V4), but activates a poorly characterized region of occipital cortex around the middle occipital gyrus on the lateral surface (Tyler & Baseler, 1998). This finding is consonant with the present psychophysical results of a unique eccentricity scaling property. Moreover, the activation in the middle occipital gyrus shows no evidence of retinotopy, being better described as a global response independent of the eccentricity or orientation of the symmetry axis. The reverse magnification reported in the present study has, however, not been evaluated in the fMRI paradigm; it is a new property whose cortical substrate remains to be determined.

Acknowledgments. I thank Lani Hardage for her contributions to this work.

Bibliography

Barlow, H. B., & Reeves, B. C. (1979). The versatility and absolute efficiency of detecting mirror symmetry in random dot displays. Vision Research, 19, 783-793.

Corballis, M. C. & Roldan, C. E. (1974). On the perception of symmetrical and repeated patterns. Perception & Psychophysics, 16, 136-142.

Gurnsey, R., Herbert, A.M., Kenemy, J. (1998). Bilateral symmetry embedded in noise is detected accurately only at fixation. Vision Research, 38, 3795-3803.

Herbert, A. M., & Humphrey, G. (1993). Bilateral symmetry detection: detectability as a function of axis orientation and eccentricity. Investigative Ophthalmology & Visual Science, 34, 1866.

Jenkins, B. (1983). Spatial limits to the detection of transpositional symmetry in dynamic dot textures. Journal of Experimental Psychology Human Perception and Performance, 9, 258-269.

Julesz, B. (1971). Foundations of Cyclopean Perception. Chicago, IL: U. Chicago Press.

Levi, D. M., Klein, S. A., & Aitsebaomo, A. P. (1985). Vernier acuity, crowding and cortical magnification. Vision Research, 25, 963-978.

Saarinen, J. (1988). Detection of mirror symmetry in random dot patterns at different eccentricities. Vision Research, 28, 755-759.

Sereno M.I., Dale A.M., Reppas J.B., Kwong K.K., Belliveau J.W., Brady T.J., Rosen B.R. & Tootell R.B. (1995) Borders of multiple visual areas in humans revealed by functional magnetic resonance imaging. Science 268, 889-893

Tyler, C. W. (1991). Cyclopean vision. In D. Regan (Ed.), Binocular Vision., (Vol. 9, pp. 38-74). New York: Macmillan.

Tyler, C. W., Hardage, L., & Miller, R. (1995). Multiple mechanisms in the detection of mirror symmetry. Spatial Vision, 9, 79-100.

Tyler, C. W., & Hardage, L. K. (1996). Mirror symmetry detection: predominance of second-order pattern processing throughout the visual field. In C. W. Tyler (Ed.), Human Symmetry Perception and its Computational Analysis. Zeist, The Netherlands: VSP BV (pp. 157-172).

Tyler, C.W. and Baseler, H. A. (1998) fMRI signals from a cortical region specific for multiple pattern symmetries. Investigative Ophthalmology & Visual Science, Supp. 39, 169.