Two eccentricity-dependent limitations on subjective contour discrimination

New variations of intrahemispheric and interhemispheric processing indexed by the dimond paradigm

We report 2 experiments designed to demonstrate that unilateral tachistoscopic stimulation would yield a response time (RT) advantage over bilateral stimulation in a simple experiment, whereas the opposite pattern would occur in a complex version of the same task, as predicted by the intrahemispheric resource limitation model of Banich and colleagues. Experiment 1 was a go/no-go task in which participants had to press a key when two shapes (circles or squares) were identical on the computer screen. A unilateral field advantage was obtained that was accentuated in several task conditions that yielded overall longer RTs, mostly in the bilateral condition. Experiment 2 was similar but required a more complex judgment: The go trials were to 2 stimuli identical on 1 dimension (shape or color) but not both or neither. The RTs were significantly and substantially longer than in Experiment 1 and exhibited a nonsignificant bilateral field advantage, which differed significantly from the unilateral field advantage obtained in Experiment 1. These results support the intrahemispheric resource limitation model of Banich and colleagues. However, several within-experiment effects are in direct opposition to this model and are best explained as limitations of commissural relay of perceptual information.

Foveal and extra-foveal orientation discrimination

Performance can often be made equal across the visual field by scaling peripherally presented stimuli according to F = 1 + E/E (2) where E (2) is the eccentricity at which stimulus size must double to maintain foveal performance levels. Sally and Gurnsey (Vision Res 43:1375-1385, 2003 and Vision Res 44:2719-2727, 2004) have previously shown that estimates of E (2) for orientation discrimination are significantly larger (i.e., less spatial scaling is required) at stimulus contrasts near detection threshold than at contrasts well above detection threshold. To examine the nature of this effect parametrically we measured orientation discrimination thresholds at 0 degrees and 10 degrees eccentricity for three levels of Michelson contrast (3, 12 and 48%) and three stimulus length-to-width aspect ratios (36.4, 9.1 and 2.3) for a range of line sizes (0.19 degrees -36 degrees visual angle). On average, E (2) values decreased as stimulus contrast decreased, consistent with the previous results of Sally and Gurnsey (Vision Res 43:1375-1385, 2003 and Vision Res 44:2719-2727, 2004). It is proposed that contrast reductions have a proportionally larger effect on small orientation-selective units than large ones and thus produce a greater rightward shift of acuity functions (orientation threshold vs. size) at the fovea than in the periphery. This explains why less spatial scaling is required to equate foveal and peripheral acuity functions at low contrasts than at high contrasts.

A biologically plausible model of human radial frequency perception

Several recent studies have used radial frequency patterns to investigate intermediate-level shape perception, a critical precursor to object recognition. Here, we developed the first neural model of RF perception based on known V4 properties that exhibits many of the characteristics of human RF perception. The model is composed of two main parts: (1) recovery of object position using large-scale non-Fourier V4-like concentric units that respond at the center of concentric contour segments across orientations, and (2) curvature detectors that encode local shape information. Each curvature mechanism combines multiplicatively the responses of three oriented filters, the positions and orientation preferences of which determine the curvature mechanism's tuning properties for position, orientation, and degree of curvature. When responding to RF patterns, peak responses occur at points of maximum curvature. Shape is represented as curvature responses as a function of orientation around the object center, and the cross-correlation of that function with a sine wave peaks when the frequency of the sine wave matches the number of peaks in the stimulus. Cross-correlation strength can be used to model human performance. Model and human performance are comparable for detection, identification, and lateral masking tasks. Moreover, the model also shows size invariance of detection performance due to scaling of the curvature mechanisms. The model is then used to make novel predictions.

Orientation discrimination across the visual field: size estimates near contrast threshold

Performance in detection and discrimination tasks can often be made equal across the visual field through appropriate stimulus scaling. The parameter E2 is used to characterize the rate at which stimulus dimensions (e.g., size or contrast) must increase in order to achieve foveal levels of performance. We calculated both size and contrast E2 values for orientation discrimination using a spatial scaling procedure that involves measuring combination size and contrast thresholds for stimuli with constant size-to-contrast ratios. E2 values for size scaling were 5.77 degrees and 5.92 degrees. These values are three to four times larger than those recovered previously using similar stimuli at contrasts well above detection threshold (Sally & Gurnsey, 2003). E2 values for contrast scaling were 324.2 degrees and 44.3 degrees, indicating that for large stimuli little contrast scaling (.3% to 2.3% increase) was required in order to equate performance in the fovea and the largest eccentricity (10 degrees). A similar pattern of results was found using a spatial scaling method that involves measuring contrast thresholds for target identification as a function of size across eccentricities. We conclude that the size scaling for orientation discrimination at near-threshold stimulus contrasts is much larger than that required at suprathreshold contrasts. This may arise, at least in part, from contrast-dependent changes in mechanisms that subserve task performance.

Non-monotonic changes in performance with eccentricity modeled by multiple eccentricity-dependent limitations

Eccentricity-dependent resolution losses are sometimes compensated for in psychophysical experiments by magnifying (scaling) stimuli at each eccentricity. The use of either pre-selected scaling factors or unscaled stimuli sometimes leads to non-monotonic changes in performance as a function of eccentricity. We argue that such non-monotonic changes arise when performance is limited by more than one type of constraint at each eccentricity. Building on current methods developed to investigate peripheral perception [e.g., Watson, A. B. (1987). Estimation of local spatial scale. Journal of the Optical Society of America A, 4 (8), 1579-1582; Poirier, F. J. A. M., & Gurnsey, R. (2002). Two eccentricity dependent limitations on subjective contour discrimination. Vision Research, 42, 227-238; Strasburger, H., Rentschler, I., & Harvey Jr., L. O. (1994). Cortical magnification theory fails to predict visual recognition. European Journal of Neuroscience, 6, 1583-1588], we show how measured scaling can deviate from a linear function of eccentricity in a grating acuity task [Thibos, L. N., Still, D. L., & Bradley, A. (1996). Characterization of spatial aliasing and contrast sensitivity in peripheral vision. Vision Research, 36(2), 249-258]. This framework can also explain the central performance drop [Kehrer, L. (1989). Central performance drop on perceptual segregation tasks. Spatial Vision, 4, 45-62] and a case of "reverse scaling" of the integration window in symmetry [Tyler, C. W. (1999). Human symmetry detection exhibits reverse eccentricity scaling. Visual Neuroscience, 16, 919-922]. These cases of non-monotonic performance are shown to be consistent with multiple sources of resolution loss, each of which increases linearly with eccentricity. We conclude that most eccentricity research, including "oddities", can be explained by multiple-scaling theory as extended here, where the receptive field properties of all underlying mechanisms in a task increase in size with eccentricity, but not necessarily at the same rate.

Orientation discrimination across the visual field: matching perceived contrast near threshold

Performance can often be made equal across the visual field by scaling peripherally presented stimuli according to F=1+E/E2 where E2 is the eccentricity at which stimulus size must double to maintain foveal performance levels. Previous studies suggest that E2 for orientation discrimination is in the range of 1.5 degrees -2 degrees when stimuli are presented at contrasts well above detection threshold. Recent psychophysical and physiological evidence suggests spatial reorganization of receptive fields at near-threshold contrasts. Such contrast-dependent changes in receptive field structure might alter the amount of size scaling necessary to equate task performance across the visual field. To examine this question we measured orientation discrimination thresholds for a range of stimulus sizes and eccentricities (0 degrees -15 degrees ). We used the same procedure previously employed except that stimuli were presented at near-threshold contrasts. We controlled for the effects of perceptual contrast on thresholds through a matching procedure. A standard line of 3 degrees in length presented at fixation was set to 2 just noticeable differences above detection threshold. The perceived contrast of all other stimuli was adjusted by the subject to match this one. Orientation discrimination thresholds were then obtained at these matching contrasts for all stimulus sizes and eccentricities. E2 values of 3.42 degrees and 3.50 degrees were recovered for two subjects; these values were about a factor of two larger than E2 values previously found for this task when stimuli were presented at higher physical contrasts.

Backward masking and the central performance drop

Kehrer [Spatial Vision 2 (1987) 247] found that texture discrimination performance sometimes peaks in the parafovea rather than at the fovea, and he referred to this phenomenon as the central performance drop (CPD). Kehrer used a backward mask to limit performance and Morikawa [Vision Res. 40 (2000) 3517] argued that in some cases the temporal aspects of the backward mask may be critical to the emergence of the CPD. In one experiment Morikawa showed that the CPD does not emerge when a simultaneous noise-mask (different from the mask used by Kehrer) is used to limit performance. In another experiment Morikawa showed that unmasked texture displays comprising short lines do not elicit the CPD. In both cases, changes in the temporal aspects of the texture displays were accompanied by changes in the spatial structure of the mask or stimulus. For the spatio-temporal theory of the CPD to be sustained one would have to show that noise masks elicit a CPD when used as backward masks and that the short-line textures elicit a CPD when followed by backward masks. Our evidence provides little if any support for either of these predictions. Furthermore, an analysis of a simple filter-rectify-filter model of texture segmentation shows that a greatly attenuated CPD is to be expected when a noise mask is used as a source of spatial noise.

Orientation discrimination in foveal and extra-foveal vision: effects of stimulus bandwidth and contrast

The parameter E2 is used in many spatial scaling studies to characterize the rate at which stimulus size must increase with eccentricity to achieve foveal levels of performance in detection and discrimination tasks. We examined whether the E2 for an orientation discrimination task was dependent on the spatial frequency bandwidth of the stimulus used. Two methods were employed. In Experiments 1 and 2 stimuli were presented at a fixed high level of contrast across viewing conditions. In both experiments the E2s recovered for narrowband stimuli were larger than those recovered for broadband stimuli. In Experiment 3 we controlled for the potentially confounding effects of perceptual contrast by measuring orientation thresholds over a range of stimulus contrast levels. Only thresholds which had reached an asymptotic level, such that increases in stimulus contrast led to no further changes to thresholds, were included in the calculation of E2. We observed that E2s recovered in the latter condition were in the range of 1.29 degrees -1.83 degrees and similar for narrowband and broadband stimuli. We conclude that a failure to consider the role of perceptual contrast may result in inflated estimates of E2.