The magnitude of center–surround facilitation in the discrimination of amplitude spectrum is dependent on the amplitude of the surround

Abstract

Recent studies explored the sensitivity of human perception to natural images, in particular the sensitivity of the visual system to discriminate changes in the amplitude spectrum slope. Previous slope discrimination experiments were carried out with stimuli presented either in the fovea or the parafovea/periphery and show that both yield poor discrimination at very steep or relatively shallow slopes. We verified if the well-known center–surround spatial interactions that operate early on in the visual processing stream influence the perception of real-world images. The results show that amplitude slope discrimination is greatly reduced (i.e., flat) when the stimulus is viewed in isolation. However, when a 2° target is placed within a surround containing an amplitude spectrum slope of 1 or 1.3, we see significant facilitation in detecting variations in the slope of the amplitude spectrum, particularly when the target contains an amplitude spectrum slope of 1 and 1.3. The results suggest that our visual system is sensitive to contextual interactions for stimuli that have the characteristics of natural images.

Introduction

It has been suggested that through evolution and experience, our visual system has become adapted to the properties of our environment (reviewed in Geisler, 2008). Most natural images contain similar statistical regularities that can be described with a single mathematical function (Field, 1994). Therefore, one method of investigating visual perception is to study the types of statistical properties that our environment possesses and observe if changes in those statistics evoke changes in perception. Here, we explore the sensitivity of humans to variations in one such statistic, the slope of the orientation averaged Fourier amplitude spectrum. In the current study, participants conducted a psychophysical task to detect the change in spatial frequency structure of a scene, which is reflected within the slope of the amplitude spectrum. Although this type of experiment has been previously conducted, such studies have always conducted with the stimulus in isolation either centrally (i.e., the fovea) or in the periphery. The aim of the current study was to investigate if human sensitivity to discriminating changes in the amplitude spectrum slope is affected by the characteristics of the background within which it is embedded. 

By using Fourier analysis, it is possible to describe any image as a combination of sine and cosine waveforms. These waves have measurable properties that statistically describe the components of an image (i.e., the amplitude, spatial frequency, phase, and orientation). Fourier analyses of natural scenes reveal that amplitude (i.e., root mean square contrast) peaks at the lowest spatial frequency and falls with increasing spatial frequency (f), in accordance with the 1/f ^α relationship on a logarithmic scale (this formula can also be expressed as amplitude ∝ f ^−α ). When measuring the amplitude spectrum within scene images from the natural world, the slope (α), which describes the falloff of amplitude with increasing spatial frequency, typically ranges from 0.6 to 1.6 (Burton & Moorhead, 1987; Dong & Atick, 1995; Field, 1993; Hansen & Essock, 2005; Ruderman & Bialek, 1994; Thomson & Foster, 1997; Tolhurst, Tadmor, & Chao, 1992; van der Schaaf & van Hateren, 1996). This means that natural images have significantly more contrast energy (or power, i.e., squared amplitude) at lower spatial frequencies than at higher spatial frequencies. Low-level coding mechanisms within the early visual pathways are thought to capitalize on these relationships in scene statistics to simplify perceptual processing, as the receptive fields of the visual cortical neurons (simple cells in V1) are well matched to optimally code the natural world (Simoncelli & Olshausen, 2001). 

One approach to test the hypothesis that the visual system is designed to process information with a 1/f ^α spatial structure has been to measure visual sensitivity to a change in the slope of the amplitude spectrum of natural and artificial (broadband visual noise) images (Hansen & Hess, 2006; Knill, Field, & Kersten, 1990; Tolhurst & Tadmor, 1997b). Changes in the spectrum slope of a natural image can cause the image to be seen as unnatural. In particular, changes that cause the slope of the spectrum to increase and become steeper (α > 1) tend to lead to the images being perceived as more blurred, due to the overrepresentation of the low spatial frequency contrast energy within the image. Conversely, shallow slopes (α < 1) lead to perceptually “whitened” high-contrast images, due to the increased representation of the high spatial frequency contrast energy. It is important to note that these changes only occur when the amplitude spectrum is artificially manipulated to a steeper or shallower slope value. In reality, however, natural scenes contain a wide range of slope values (Burton & Moorhead, 1987; Dong & Atick, 1995; Field, 1993; Hansen & Essock, 2005; Ruderman & Bialek, 1994; Thomson & Foster, 1997; Tolhurst et al., 1992; van der Schaaf & van Hateren, 1996), which do not perceptually appear blurred or whitened when viewed in their natural context. In a foveal task, Knill et al. (1990) found that human sensitivity to a change in the slope of the amplitude spectrum is best around α of 1.4 to 1.8, while Tolhurst and Tadmor (1997a), using a parafoveal task, found a strong peak (i.e., lowest sensitivity) at shallower αs (0.8). Lastly, Hansen and Hess (2006) compared the discrimination thresholds for the slope of the amplitude spectrum of images presented in either the fovea or parafovea. They found that in comparison to the parafovea, the fovea is most sensitive at discriminating a change in α for natural and artificial images that have an α similar to that found in natural images (i.e., when the slope α of the amplitude spectrum ranges from 1.2 to 1.4 for broadband noise and 0.95 to 1.4 for natural scenes). This method has also been used to show that our ability to discriminate the amplitude spectrum seems to reflect the development of the visual channels and that it does not show adult maturity until 10 years of age (Ellemberg, Hansen, & Johnson, 2007). Interestingly, for both children and adults, peak sensitivity lies outside the range of amplitude spectra typically observed within natural scenes. One possible explanation for this difference could be the method by which amplitude spectrum experiments are normally conducted. 

Psychophysical experiments on the amplitude spectrum are typically conducted by presenting a localized stimulus that usually varies according to a single parameter, in this case, the slope of the amplitude spectrum. However, within the natural world, rarely do we see image patches in isolation. Instead, objects are embedded within a background. Indeed, one of the primary roles of vision is image segmentation to overcome the figure–ground problem. Previous research has shown that the fovea and periphery interact (Xing & Heeger, 2001), and the perception of fovea-presented stimuli is influenced by the characteristics of the image presented in its surround. For example, narrowband stimuli produce strong center–surround spatial interactions that influence the perception of contrast (Bonneh & Sagi, 1998; Cannon & Fullenkamp, 1991; Experiment 4 in Chubb, Sperling, & Solomon, 1989; Ellemberg, Wilkinson, Wilson, & Arsenault, 1998; Olzak & Laurinen, 1999; Xing & Heeger, 2001), spatial frequency (Ellemberg et al., 1998; Polat & Sagi, 1993), and orientation (Petrov, Carandini, & McKee, 2005). The consensus is that when surround contrast is higher than the center, it suppresses the perception of center contrast (Cannon & Fullenkamp, 1991; Ellemberg et al., 1998; Snowden & Hammett, 1998; Xing & Heeger, 2001). Conversely, when the surround is of a lower contrast than the center, there are some reports that the perception of center contrast is facilitated (Cannon & Fullenkamp, 1991; Olzak & Laurinen, 1999; Polat & Sagi, 1993; Xing & Heeger, 2001). Center–surround interactions appear to be at their strongest if the center and the surround have similar spatial frequency and orientation content within an octave range of each other (Cannon & Fullenkamp, 1991; Chubb et al., 1989; Ellemberg et al., 1998), suggesting within-channel interactions. 

Center–surround interactions have also been shown to exist within natural images. McDonald and Tadmor (2006) investigated the perceived contrast of a luminance texture when imbedded within a background and found that when the surround contained “unnatural” image statistics (i.e., random noise) there was minimum suppression of perceived contrast. However, when the background contained statistics similar to those of natural scenes, perceived contrast was suppressed. Maximum suppression occurred when the surround contained an amplitude spectrum with a slope α of 1.0. However, the task that observers performed was a contrast discrimination task and not an amplitude spectrum discrimination task. 

The aim of the current study was to examine how sensitivity to the characteristic statistical properties of natural images (amplitude spectrum slope) is affected by the characteristics of their background amplitude spectrum slope. Specifically, we measured discrimination thresholds to a change in the slope of the amplitude spectrum of a fovea-presented artificial (broadband visual noise) image as a function of the amplitude spectrum of its background. 

Methods

Participants

Five adults aged between 22 and 46 years participated in all experiments (Age_Mdn = 24). All participants were experienced psychophysical observers with normal or corrected-to-normal vision, and all were naive to the aims of the experiments. All participants were consenting volunteers and treated according to Tri-Council Policy Statement: Ethical Conduct for Research Involving Humans (Medical Research Council of Canada (MRRC), 2003). 

Apparatus

Stimuli were presented using a Dell Intel Pentium D (3.40 GHz) processor equipped with a 4-GB RAM. Stimuli were displayed using a linearized lookup table (generated by calibrating with a Color Vision Spyder 2 Pro) and were presented on a 21-inch View Sonic G225f CRT driven by an NVIDIA Quadro FX3500 Graphics card with 10-bit grayscale resolution. Maximum luminance was 100 cd/m², frame refresh rate was 150 Hz, and the resolution was 1024 × 768 pixels. Single pixels subtended 0.032 deg visual angle (i.e., 1.92 arcmin) as viewed from 70 cm. Participant head position was maintained using a chin rest. 

Stimuli

All stimuli consisted of synthetic amplitude spectrum noise and were constructed in the Fourier domain using MATLAB (Mathworks, Natick, MA., ver. 2009b) and corresponding Image Processing (ver. 6.4) toolbox. The visual noise stimuli were created by constructing a 512² polar matrix and assigning all coordinates the same arbitrary amplitude coefficient (except at the location of the DC component, which was assigned a zero). The result is a flat isotropic broadband spectrum (i.e., α = 0.0), referred to as the “template” amplitude spectrum. In this form, the α of the template spectrum could be adjusted by multiplying each spatial frequency's amplitude coefficient by 1/f ^−α . The phase spectra were constructed by assigning random values from π to −π to the different coordinates of a 512² polar matrix, while maintaining an odd symmetric phase relationship (for details, see Hansen & Hess, 2006). The phase spectrum was randomized from trial to trial. The noise patterns were rendered in the spatial domain by taking the inverse Fourier transform of an α-altered template amplitude spectrum and any given random phase spectrum. All noise patterns were scaled in the spatial domain to have the same grayscale mean (0.50 on a 0–1 scale) and RMS contrast (0.14) to assure that the total power across all of the noise images (regardless of their assigned α value) was equivalent. From each 512² noise image, an image patch was cropped from its center and windowed with a cosine-tapered circle, which ramped 5% of the image pixels in the proximity of the circle's edge to mean luminance (i.e., 50 cd/m²). The above procedure was repeated to create the surround content. To create the stimuli for the center–surround condition, the test image was embedded within a surround image. To reduce the influence of edge artifacts, 5% of image pixels on either side of the border were blended together using a cosine taper. Stimuli were generated with respect to the five reference slope α values (0.4, 0.7, 1.0, 1.3, and 1.6). 

Procedure

In all experiments, the stimuli were viewed binocularly. Participants were informed to maintain fixation at the center of the screen for the duration of the trial. Participants performed a temporal three-interval, two-alternative forced-choice task like the one used by Hansen and Hess (2006) and were asked to select the stimulus that contained the odd amplitude spectrum—different from the other two. All images were windowed with a cosine-tapered envelope, subtending 2° in diameter (Figure 1A). For any given trial, all stimuli had identical phase spectrum, with the only difference between the reference patch and the test patch being the change in amplitude spectrum α. Two of the images had the reference amplitude spectrum, while a third had the test spectrum. At the start of each trial, a fixation cross subtending 0.3° in diameter was presented for 1 s at the center of the screen. This was followed by three stimulus presenting intervals, each lasting 250 ms. Each stimulus interval was followed by a 500-ms isotropic broadband noise mask (white noise with the same mean luminance and RMS contrast as the preceding image) to eliminate any potential retinal afterimage cue (Figure 1). The second interval always contained the reference amplitude spectrum set at one of the five fixed reference α values (0.4, 0.7, 1.0, 1.3, and 1.6). One other interval (either the first or the third) contained the same reference image; the other interval, however, contained the test amplitude spectrum with a slope α value steeper than the α in the reference image. The intervals that contained the test amplitude spectrum were randomized and counterbalanced within each block. At the end of each trial, the display was set to mean luminance, and the fixation point reappeared. Participants indicated via a keyboard press if they perceived the first or third interval as being the “odd-man-out” in comparison to the second reference interval (note that although the test and reference α may be physically different, participants may perceive them as being the same). The duration of the response interval was unlimited. 

Figure 1

 

Procedure and example of stimuli used within experiments. (A) Temporal sequence of the procedure (see text for details). (B) Central test image consisting of artificially generated amplitude spectrum with a spectral slope α of 1. (C) Central 2° test image containing an amplitude spectrum slope α of 0.7, imbedded within a surround (4° in diameter) containing a steeper amplitude spectrum slope of 1.3. (D) Central 2° test image containing an amplitude spectrum slope α of 0.7, imbedded within a surround (4° in diameter) containing a steeper amplitude spectrum slope of 1.3.

The trial-to-trial changes in the test image's α were controlled by a “weighted” 1-up, 2-down staircase procedure (Kaernbach, 1991) using the PAL_AMUD_setupUD and PAL_AMUD_updateUD functions of the Palamedes toolbox for MATLAB (Prins & Kingdom, 2009). The staircase approached the reference α from above, that is, the α values were greater than the reference α. The starting slope α of the test image was pseudorandomly generated at the start of each block to avoid any possible learning effects but always started at least 0.4 above the reference α of the test image (e.g., if the reference α was 1.0, then the staircase would initialize at 1.4). The α of the test image was decreased in linear steps (up step size of 0.03, down step size of 0.01) toward the reference stimulus α after two correct responses and increased after a single incorrect response. The procedure targeted the 86.6% performance level on a psychometric function (Prins & Kingdom, 2009). For each staircase run, the minimum stimulus value of the PAL_AMUD_setupUD was set to the reference α. Staircase data were inspected post hoc to confirm that the target α always remained greater than the reference α. The experimental block continued until twelve reversals of the staircase had occurred, at which point the block terminated. To reduce the variation in results that might be caused by adaptation effects, the first two staircase reversals were excluded from the analysis. Consequently, discrimination thresholds were calculated by averaging over the last ten staircase reversals. 

Before data collection, participants performed a practice block to familiarize themselves with the task. In the initial target-only condition, the experiment was divided into five blocks, one block for each of the reference amplitude (0.4, 0.7, 1.0, 1.3, and 1.6). All blocks were conducted in random order. 

To investigate if a surround and surround amplitude slope had an effect on amplitude slope discrimination thresholds at fixation, the center stimuli were embedded within a surround subtending 4° in diameter, relative to the central patch (see Figure 1B). Within a block, the amplitude slope exponent (α) of the surround was constant and set to 0.7, 1.0, or 1.3, with the exponent of the center varying from trial to trial. In addition, to investigate the spatial interaction of the surround, a gap measuring 20, 40, or 60 arcmin was introduced between the center and the surround. Consequently, the surround conditions comprised of sixty blocks—5 center amplitudes (0.4, 0.7, 1.0, 1.3, 1.6) × 3 surround amplitudes × 4 gap sizes between the target and the surround (0, 20, 40, and 60 arcmin.). The sixty blocks corresponded to an average of 8 h of testing per participant. Participants were instructed to fixate on the center test image, ignoring the content of the surround. All blocks were presented in random order. 

Results

Figure 2 presents the mean discrimination thresholds for the five participants tested. The x-axis shows the five reference amplitude spectra tested (0.4, 0.7, 1, 1.3, and 1.6) and each line represents a difference condition when the target was presented without a surround (black) or imbedded within a surround (colored). The current study aimed to establish whether the sensitivity to changes in the amplitude spectrum slope within a 2° window was affected by a surround and its spectral content. To assess the effect of the surround, we first measured amplitude discrimination thresholds for a test image with no surround. The results, presented in Figure 2, show similar measured thresholds (M _Δα = 0.43, SD = 0.02) at all reference amplitude spectra. The results were submitted to a one-way repeated measures ANOVA using the Matlab Statistics toolbox (ver. 7.2); in subsequent analyses, the reported p-values correspond to those obtained following the Greenhouse–Geisser correction for violations of sphericity (Greenhouse & Geisser, 1959), and we report the estimated partial eta squared (η _p ² = SS_effect / (SS_effect + SS_error) as an effect size measure. The advantage of effect size measures is that their expected values are independent of sample size (Kline, 2004). However, for a fixed η _p ² in the population, the corresponding F-ratio (F = SS_effect / SS_error * df _error / df _effect) increases with the number of degrees of freedom in the error term. Consequently, a trivially small effect size (η _p ²) becomes statistically significant with sufficient degrees of freedom. Conversely, relatively large values of η _p ² may not be statistically significant if there are insufficient degrees of freedom. Therefore, an estimate of the size of the effect is a useful addition or replacement to p-values when interpreting results from psychophysical studies with a small number of participants. The ANOVA found no significant effect for slope α in the target-only condition, F(4,20) = 0.14, p = 0.964, η _p ² = 0.03. 

Figure 2

 

Mean discrimination thresholds for the five different amplitude spectra of the center test image with (color symbols) and without (black symbols) the presence of a surround. Error bars represent ±1 standard error of the mean (averaged across observers).

However, when the 2° target is placed within a 4° surround, we obtain a different pattern of results. As shown in Figure 2, when the target was placed within the surround, we observed an overall facilitation effect of the surround, with increased sensitivity (i.e., decreasing thresholds) at all reference α levels, with the exception of 0.4. A two-way ANOVA (with surround α and reference α as independent factors) showed significant main effects on the thresholds for surround α, F(3,80) = 17.35, p = 0.0001, η _p ² = 0.39, and for target α, F(4,80) = 6.51, p < 0.0001, η _p ² = 0.25, but not for their interaction, F(12,80) = 1.31, p = 0.23, η _p ² = 0.16. Another interesting pattern within the results is that when the surround α was 1 (Figure 2, green symbols) or 1.3 (Figure 2, red symbols), we see an increase in performance, with discrimination thresholds dropping from 0.43 to ∼0.2 when the reference α was 1 or 1.3. However, when the surround α was 0.7 (Figure 2, blue symbols), we see no change in discrimination threshold when the reference α varies between 0.7 and 1.6 (although we do see an increase in thresholds at a target α of 0.4). Therefore, the surround has an effect on discrimination thresholds. It could be argued that observers overtly or covertly use the border between the central target and the surround to complete the discrimination task. However, this is unlikely given that thresholds remain constant for center αs greater than 0.7, irrespective of the surround content. If the border were being used, then we would expect significant increases in thresholds when the surround contained a different slope than the center, which we do not see in our data. Further, all observers were experienced and instructed to fixate only the center of the target, and all reported that they only used the center to perform the task. 

Given that the surround increases sensitivity to discriminating changes within the center, we wanted to investigate if this increase in sensitivity was caused by local interactions or by a global comparison process. To address this question, we repeated the above experiment but introduced a gap between the target and the surround. The gap size varied from 0 (no gap) to 60 arcmin in 20-arcmin steps. A three-way ANOVA (with reference α, surround α, and gap size as independent factors) found a significant effect of reference α, F(4,264) = 34.25, p < 0.0001, η _p ² = 0.34, and for gap size, F(2,264) = 12.69, p < 0.0001, η _p ² = 0.13, but not for the surround α, F(3,264) = 2.44, p = 0.09, η _p ² = 0.02. In addition, there were no significant effects of interactions between any the independent factors. 

To investigate this significant effect of gap size, but the non-significant effect of the surround α, we decided to separate each set of results into the three surround α conditions. Figure 3 presents the results separated into three panels, each representing a different surround α content (A = 0.7, B = 1.0, and C = 1.3) and each line on the graph representing a different gap size. It is interesting to note that while the lines for Figures 3B (surround α = 1) and 3C (surround α = 1.3) overlap, the lines in Figure 3A (surround α = 0.7) do not. When the surround α equaled 0.7, we observed a decrease in the threshold as a function of gap size, reflecting increased sensitivity to detecting changes in the target α. These thresholds were submitted to a two-way ANOVA (with reference α and gap size as independent factors). There was a significant main effect for reference α, F(4,80) = 8.7, p < 0.0001, η _p ² = 0.30, and for gap size, F(3,80) = 10.81, p < 0.0001, η _p ² = 0.29, but not for their interaction, F(12,80) = 0.6, p = 0.8, η _p ² = 0.08. We repeated the same analysis on the thresholds obtained when the surround α was 1.0 and 1.3. For surround α of 1.0, we found a significant effect for reference α, F(4,80) = 8.59, p < 0.0001, η _p ² = 0.30, but not for gap size, F(3,80) = 2.1, p = 0.107, η _p ² = 0.07, or their interaction, F(12,80) = 0.36, p = 0.97, η _p ² = 0.05. For surround α of 1.3, we found a significant effect for reference α, F(4,80) = 17.79, p < 0.0001, η _p ² = 0.47, but not for gap size, F(3,80) = 2.18, p = 0.107, η _p ² = 0.1, or their interaction, F(12,80) = 0.41, p = 0.96, η _p ² = 0.06. Therefore, gap size had an effect on the discrimination thresholds when the surround α was 0.7 but not when the surround α was 1.0 or 1.3. 

Figure 3

 

Mean discrimination thresholds as a function of introducing a gap between the center and the surround. Each panel represents a difference surround alpha [(A) 0.7, (B) 1, and (C) 1.3]. Error bars represent ±1 standard error of the mean (averaged across observers).

Discussion

It is well documented that humans are sensitive to changes in the amplitude spectrum typically observed within natural scenes, and this is usually interpreted as the indication that the human visual system is tuned to the known spatial frequency regularities within natural scenes (Hansen & Hess, 2006; Knill et al., 1990; Párraga, Troscianko, & Tolhurst, 2005; Tolhurst & Tadmor, 1997b). To date, investigations of the sensitivity of the human visual system to the characteristic amplitude spectrum of natural images were carried out with single localized image patches. However, in our natural environment, the object of interest along with its contextual background often covers the entire visual field. In addition, most local patches of the image often contain a different amplitude spectrum slope than the surround they are embedded in (Hansen & Hess, 2006). The aim of the current study was to investigate if this surround content had an effect on the sensitivity to changes in the slope (α) of the amplitude spectrum. Our results indicate that embedding the target within a surround facilitates the discrimination of amplitude spectrum that fall within the range for which we are most presented to in the natural world (0.7 to 1.6) but not for amplitude slopes that are less frequently observed in the natural world (0.4). Further, discrimination is enhanced within the range of 1.0 to 1.3 (compared to 0.4, 0.7, and 1.6) in the presence of a surround possessing a slope between 1 and 1.3 but not for a surround of 0.7. Finally, increasing the gap between the center and the surround does not have an impact on the thresholds when the surround contains an amplitude spectrum slope of 1 or 1.3 but does have an effect when the surround contains an amplitude spectrum slope of 0.7. 

We found no significant effect of the amplitude spectrum slope (α) on the discrimination threshold of a single noise stimulus presented locally in the fovea. That is, thresholds for discriminating changes in the spectrum slope were similar across the range of slope α tested (0.4, 0.7, 1, 1.3, and 1.6). These results differ from the previous findings of Hansen and Hess (2006) and Tadmor and Tolhurst (1994), that humans are less capable of discriminating between changes in amplitude levels below an α = 0.8. Another difference between the current data and those of Hansen and Hess is the overall threshold levels. For the current study, the average discrimination thresholds within the target-only condition was ∼0.43. Conversely, the highest threshold reported by Hansen and Hess was ∼0.24. One explanation for these discrepancies could be the method for calculating the discrimination thresholds. Hansen and Hess used a staircase that approached the reference amplitude slope from above and below, and then averaged the absolute difference. On the other hand, the current study only approached the reference amplitude slope from above (steeper values of alpha). The reasoning behind only approaching from above was that the number of trials in the current study was ∼5400 per observer, representing several hours of psychophysics per observer. Another explanation could be the difference with the size of the stimulus. Hansen and Hess employed a 1° test stimulus, whereas the current study employed a 2° test stimulus. This increase in test stimulus size could result in a greater region of stimulation on the retina or a larger sample region over which to integrate the content of the amplitude spectrum, increasing thresholds. Because of these differences, the role of the spatial extent of the stimulus on α discrimination needs to be investigated in future studies. 

When the 2° test image is embedded within a 4° surround—as is common within the natural world (Hansen & Hess, 2006)—we find that the surround has a facilitation effect on spectrum slope discrimination. This facilitation by the center–surround interactions appears to be strongest when the content of both are similar, suggesting within-channel interactions (Cannon & Fullenkamp, 1991; Chubb et al., 1989; Ellemberg et al., 1998). Similar interactions have also been found in natural scene statistics (McDonald & Tadmor, 2006). These center–surround interactions, for narrowband stimuli and natural scenes, could be a possible explanation for the reduced thresholds found when the test image and surround amplitude slope α matched. Thresholds for the test image at both slopes α of 1 and 1.3 were lowest when their surround was of a similar slope, indicating that a within-channel interaction might facilitate discrimination. The spatial similarities between the center and the surround might aid the participant to detect changes in the center stimulus and, consequently, reduce thresholds. Similarly, although not statistically significant, threshold values at a slope of 0.7 were lowest when the surround embedding it was also of a slope α of 0.7. The center–surround interaction may still be responsible when both components of the stimuli are similar (center = 0.7, surround = 0.7), yet diminished due to our general insensibility to shallower slopes (α < 1; Hansen & Hess, 2006). 

Another interesting finding is that this facilitation appears to work both on local and non-local levels. When the surround α is 0.7, there is a significant effect on threshold when the gap size is increased, suggesting that interactions are operating locally. However, when the surround α is 1.0 or 1.3, then the increase in gap size does not alter the results, suggesting that the mechanism for the facilitation appears to operate non-locally (i.e., globally), providing evidence that the participants are not using the border between the center and the surround to perform the task. Mareschal, Sceniak, and Shapley (2001) have previously suggested that surround influences on center content might depend not only on the low-level neuronal interactions but also on global cues arising from image segmentation. By placing a gap between the center and the surround in the current study, a physical break is created between the two stimuli. Consequently, although local low-level neuronal interactions may not be present, it may be possible that participants bind the two contents together coherently across the gap. This binding of the global properties of the stimulus may, therefore, be as important as local interactions in center–surround effects. However, the effect of introducing a gap is controversial, as it has been shown by others to either facilitate (Mareschal et al., 2001) or inhibit (Saylor & Olzak, 2006) center–surround effects. 

The current study shows that center–surround interactions are present for discriminating changes within the amplitude spectrum. Using similar amplitude spectrum stimuli, McDonald and Tadmor (2006) showed that the perceived contrast of a luminance texture was suppressed when the surround contained an amplitude spectrum slope α = 1.0. However, our results show that discrimination of changes in the amplitude spectrum slope is best when center and surround contain similar spectral content. Differences in paradigm can possibly account for these seemingly opposing findings. The current study used a discrimination task related to the particular set of statistical characteristics of natural images, whereas McDonald and Tadmor measured perceived contrast that can be best understood in terms of divisive gain control (Heeger, 1992). 

Several models have been proposed in the literature to explain why human observers are able to discriminate between different spectrum content of synthetic and natural stimuli. These models are based on processing of band-limited contrast within one channel (Tadmor & Tolhurst, 1994; Tolhurst & Tadmor, 1997a, 1997b) or by pooling over multiple channels (Párraga et al., 2005). However, such models are designed to work on a single localized stimulus containing uniform amplitude spectrum content and cannot be used to interpret the center–surround interactions that are observed in the current study. In addition, images with 1/f amplitude spectrum produce equal responses in a population of spatial-frequency-selective neurons (Burton & Moorhead, 1987; Field, 1987). Therefore, the receptive field properties of individual neurons and the cortical interactions between these neurons must compensate for the 1/f spatial content seen in natural scenes, although the nature of these interactions is currently unknown (Field & Brady, 1997). Nevertheless, a recent attempt to simulate the neuronal computations conducted early in the visual system in response to a 1/f amplitude spectrum has produced a model that predicts some of the psychophysical properties of human participants (Tajima & Okada, 2010). However, such a model could not be used to predict the results of the current study as the unknown factor of the interactions between spatial frequency channels is compounded when the test image is placed within a surround. Previously, Chubb et al. (1989) investigated the spatial interactions within center–surround stimuli. Using a broadband noise texture that was filtered into one spatial frequency band, they showed that when the spatial frequency of the center and surround are within one octave of one another, there is a reduction in the perceived contrast of the center image (Figure 5, Chubb et al., 1989). However, when the spatial frequency content of the center and surround differed by one octave, this interaction was reduced. Although this explains how the surround affects a single spatial frequency channel, it does not explain what would happen when a target contains a broadband spatial frequency content. 

One potential confound in interpreting the results in the current study is what role the inter-stimulus mask has on the amplitude spectrum discrimination. The physical properties of masks, which are necessary to prevent direct comparison of stimuli, can have complex interactions with discrimination thresholds, changing individual sensitivity and improperly reflecting the visual systems' ability to discriminate changes. The current study used isotropic broadband noise as a mask between stimuli, to be consistent with the methodology used in the previous research (e.g., Hansen & Hess, 2006). In addition, because the noise has a flat amplitude spectrum (α = 0), it is easier for observers to tell the stimulus and noise masks apart. However, if the mask had had a similar amplitude spectrum, this might have caused facilitation effects in thresholds. Recently, we found lower thresholds when the inter-trial mask had a different phase spectrum but similar amplitude spectrum to the test images (Richard & Johnson, 2011). 

In conclusion, our results suggest that our visual system is sensitive to contextual interactions for stimuli that have the characteristics of natural images. Specifically, there is a center–surround effect on discrimination of changes in the amplitude spectrum when the target is placed within a surround. Further, these interactions appear to operate on both local and global levels, depending on the content of the surround. 

Acknowledgments

This research was supported by individual NSERC Discovery Grants to Aaron Johnson and Dave Ellemberg. 

Commercial relationships: none. 

Corresponding author: Aaron Johnson. 

Email: [e-mail]. 

Address: Department of Psychology, Concordia University, 7141 Sherbrooke St. West, Montreal, Quebec H4B 1R6, Canada.