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Research Article  |   October 2009
Size tuning and contextual modulation of backward contrast masking
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Journal of Vision October 2009, Vol.9, 21. doi:10.1167/9.11.21
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      Toni P. Saarela, Michael H. Herzog; Size tuning and contextual modulation of backward contrast masking. Journal of Vision 2009;9(11):21. doi: 10.1167/9.11.21.

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Abstract

The strength of contrast masking depends not only on spatial but also on temporal parameters. In a previous study (T. P. Saarela & M. H. Herzog, 2008), we showed that the detection of a briefly presented Gabor patch is most strongly impaired when an iso-oriented grating mask immediately follows the Gabor and that this masking effect is relieved when a surround is added to the mask. Here, we studied the spatial characteristics of this backward masking effect. Gradually changing the size of the iso-oriented masking grating changes contrast detection thresholds in a non-monotonic way that can be explained in terms of contrast-dependent spatial summation and inhibition. However, these spatial interactions seem only to take place when the mask is a uniform grating. When the mask is divided into a small center and a larger surround by changing the surround parameters or by adding a small gap, masking is as strong as with the small center mask only. We suggest that spatial interactions are weaker or even absent when the stimulus elements are perceptually segregated.

Introduction
In contrast masking, contrast thresholds for detecting a target pattern are elevated when the target is superimposed on another pattern, called the mask (e.g., Legge & Foley, 1980). Masking is strong when the target and the mask consist of very similar patterns (in terms of orientation and spatial frequency) that presumably stimulate the same neural mechanisms. This type of masking is often called “within-channel masking.” Masking, although weaker, can also occur when very dissimilar target and mask patterns are used, such as gratings differing in orientation (e.g., Derrington & Henning, 1989; Foley, 1994; Olzak & Thomas, 1991), or spatial frequency (Henning, Hertz, & Broadbent, 1975). These stimuli presumably stimulate separate neural mechanisms, and this type of masking is sometimes referred to as “cross-channel masking.” Various explanations have been suggested for contrast masking. Masking has been explained with models incorporating response non-linearities due to gain-control-like divisive inhibition (e.g., Foley, 1994; Meese & Holmes, 2002; Olzak & Thomas, 1999) or local inhibitory interactions among second-stage filters (Zenger & Sagi, 1996). On the other hand, response-dependent noise can also account for some aspects of masking. There is some debate over whether response non-linearities or response-dependent noise is the cause of within-channel masking (Gorea & Sagi, 2001; Kontsevich, Chen, & Tyler, 2002), but it seems that cross-channel masking involves suppression rather than response-dependent noise (Meese & Hess, 2004). 
Interactions affecting contrast perception do not occur only locally, in the presence of spatially overlapping masks, but also spatially displaced masks have an effect. Grating or Gabor stimuli flanking a target can decrease target detection thresholds (e.g., Ejima & Miura, 1984; Polat & Sagi, 1993). Both physiological (Crook, Engelmann, & Lowel, 2002; Polat, Mizobe, Pettet, Kasamatsu, & Norcia, 1998) and psychophysical (Cass & Spehar, 2005; Polat & Sagi, 2006) evidence suggest that these effects are mediated by lateral connections in early visual cortex. The facilitation of detection depends on the relative positions and separation between the target and the flanking stimuli (Polat & Sagi, 1993, 1994). The effect is also contrast-dependent: facilitation of detection can turn into suppression at higher contrast levels (Ejima & Miura, 1984; see also Petrov & McKee, 2006). Stimuli that surround the target can also suppress supra-threshold contrast perception, as reported from studies on contrast discrimination (Olzak & Laurinen, 2005; Snowden & Hammett, 1998) and perceived contrast (e.g., Cannon & Fullenkamp, 1991; Chubb, Sperling, & Solomon, 1989; Ejima & Takahashi, 1985; Olzak & Laurinen, 1999, Snowden & Hammett, 1998; Xing & Heeger, 2000). This surround suppression effect has its likely physiological counterpart in neural surround inhibition that occurs at early cortical levels of visual processing, presumably mediated by feedback connections from higher visual areas (Angelucci & Bullier, 2003; Bair, Cavanaugh, & Movshon, 2003; Hupé et al., 2001). In accordance with physiological studies on temporal properties of the suppressive surround effects (Bair et al., 2003), there is psychophysical evidence for fast lateral inhibitory mechanisms operating both at (Polat & Sagi, 2006) and above (Kilpeläinen, Donner, & Laurinen, 2007) detection threshold. 
We recently reported that within- and cross-channel masking differ in their time-courses and susceptibility to surround modulation (Saarela & Herzog, 2008). When a brief target and a longer mask duration are used, transient forward masking effects occur in both within- and cross-channel masking conditions. However, in the within-channel case, a very strong backward masking effect occurs when the target is presented immediately before the mask (see Figure 1). No such backward masking effect is evident in cross-channel masking. Further, this backward masking effect is strongly dependent on mask size. A large mask (a combination of a center and a surround mask) produces considerably less masking. Forward masking, on the other hand, is not affected by mask size. The effects of masking and surround modulation are thus tightly coupled to stimulus timing. 
Figure 1
 
Time-course of iso-orientation masking. A 40 ms Gabor target was presented at various SOAs relative to a 100 ms mask (mask duration depicted by the black bar, mask type by icons). The highlighted region shows the strong backward masking effect with a small mask and the decreased masking effect with a larger mask. The experiments reported in this paper use the highlighted timing conditions only, that is, a Gabor target immediately followed by a grating mask. Adapted from Saarela and Herzog (2008).
Figure 1
 
Time-course of iso-orientation masking. A 40 ms Gabor target was presented at various SOAs relative to a 100 ms mask (mask duration depicted by the black bar, mask type by icons). The highlighted region shows the strong backward masking effect with a small mask and the decreased masking effect with a larger mask. The experiments reported in this paper use the highlighted timing conditions only, that is, a Gabor target immediately followed by a grating mask. Adapted from Saarela and Herzog (2008).
In our earlier experiment, only one target size and spatial frequency was used. The purpose of the current experiments is to better characterize the spatial properties of the backward masking effect. In the first two experiments, we investigate the size tuning of backward masking by measuring the dependence of the spatial extent of masking on spatial frequency, target size, and mask contrast. In the final experiment, we test the selectivity of surround modulation for the spatial parameters of the surround. 
General methods
Observers
Four observers (18–31 years, 1 female) participated in the experiments. All had normal vision, with visual acuity of 1.0 (corresponding to 20/20) or better in at least one eye. Visual acuity was measured using the Freiburg visual acuity test (Bach, 1996). The participants were explained the general purposes of the experiments, but they were naive to the exact experimental questions. The experiments were approved by the local ethical committee. Participants signed an informed consent before taking part in the experiments. 
Equipment
The stimuli were presented on a Philips 201B4 CRT monitor, driven by a 10-bit Radeon 9200 SE graphics card. The monitor was linearized by applying gamma correction to each color channel individually. Monitor refresh rate was 100 Hz and spatial resolution 1024 × 768 pixels, covering 14.6 × 11.0 degrees of visual angle from the viewing distance of 150 cm used in the experiments. Mean luminance of the screen was 45.0 cd/m 2
Stimuli
The stimuli were grayscale luminance modulations around the mean luminance of the screen. The target was a Gabor patch with a luminance profile described by:  
G ( x , y ) = L · [ 1 + c exp ( ( x 2 + y 2 ) / σ 2 ) · sin ( 2 π f y + ϕ ) ] ,
(1)
where L is the mean luminance of the screen, c is the contrast, f is the spatial frequency (SF), and ϕ is the spatial phase of the Gabor. σ is the space constant of the Gaussian envelope. The target carrier was always horizontal. Target details are given in the Stimuli section of each experiment. 
The masks consisted of sinusoidal gratings. In the Experiments 1 and 2, the mask was shaped either as a circular patch (overlapping mask) or an annulus (surround mask). In the third experiment, the mask consisted of a circular patch surrounded by an annulus. The mask details are given in the Stimuli section of each experiment. 
The overall spatial phase of the stimuli was randomized across trials to prevent adaptation effects. The relative phase between the target and the mask depended on the experimental condition. 
Procedure
The experiments were run in a dimly illuminated room. The observer was seated 150 cm from the monitor and viewed the screen binocularly. The stimuli were presented foveally in the middle of the screen. Contrast thresholds for detecting the target were measured using a 2IFC procedure. 
The observer initiated a block of trials by pressing a button. A fixation dot was presented for 500 ms, followed by a 250 ms blank period, the first stimulus interval, a 750 ms blank period, and the second stimulus interval. The mask was always presented in both intervals and the target was presented in only one interval. The target was presented for 40 ms and it was immediately followed by a 100 ms mask. This timing was chosen based on an earlier study (Saarela & Herzog, 2008, see Figure 1). The target interval was selected randomly on each trial with equal probabilities for the two intervals. Auditory markers indicated the target onset and the corresponding time in the no-target interval. The observer indicated by a button press in which interval the target had appeared. Auditory feedback was provided after incorrect responses. The response initiated the next trial. 
An adaptive procedure (Taylor & Creelman, 1967) was used to determine the target contrast for each trial. One block consisted of 80 trials, and the mask type was held fixed in each block (the conditions were not mixed within a block). Each condition was repeated 2–4 times to achieve a good fit for the psychometric function. The order of conditions was randomized for each observer. Experiment 1 was conducted before Experiment 2, so the two observers who participated in these experiments did the high-contrast conditions before the low-contrast conditions. 
Data analysis
All data from repetitions of the same experimental condition were pooled for analysis. Psychometric functions were fitted to the proportion-correct data with a maximum-likelihood method, using the psignifit toolbox version 2.5.6 for Matlab ( http://bootstrap-software.org/psignifit/; Wichmann & Hill, 2001a). The target carrier contrast corresponding to 75% of correct responses was taken as the empirical threshold. Standard errors (68% confidence intervals) were found by a bootstrap procedure implemented in psignifit (Wichmann & Hill, 2001b). 
Experiment 1: Size tuning
In this experiment, we investigated the size tuning of backward contrast masking using different target sizes and mask types (spatially overlapping and surrounding mask). 
Stimuli
Three different Gabor patches were used as a target: SF = 4 cycles per degree (cpd) and σ = 0.25 degrees, SF = 4 cpd and σ = 0.5 degrees, and SF = 2 cpd and σ = 0.5 degrees. This way, the first two had the same SF but different window size, the last two had the same window size but different SF, and the first and the last ones were just scaled versions of each other. 
The mask always had the same orientation and spatial frequency as the target and a Michelson contrast of 40%. The diameter of the overlapping 4 cpd mask was varied between 1 and 32 cycles (0.25 and 8 degrees). The 4 cpd surround mask had an outer diameter of 32 cycles and the inner diameter was varied between 1 and 16 cycles. The 2 cpd overlapping mask diameter was varied between 1 and 16 cycles. In an additional condition, a full screen mask was used (marked as “32 cycles” in the figures). The 2 cpd surround mask had an outer diameter of 16 cycles and the inner diameter was varied between 1 and 8 cycles. The mask and target carriers were always spatially in phase. 
As a baseline condition, detection thresholds were measured for the target in the absence of a mask. 
Results
Figures 2 and 3 show the results from the two observers who participated in Experiment 1. Figures 2A and 3A show the results obtained with overlapping masks, and Figures 2B and 3B show the results obtained with surround masks. The mask size (or the size of the aperture in case of the surround mask) on the x-axis is shown relative to the target size, as the ratio of the mask diameter to the target Gabor σ
Figure 2
 
Spatial extent of backward contrast masking, observer DW. A: contrast detection thresholds for a Gabor target that is masked by a spatially overlapping grating mask. (In the 2 cpd conditions, the mask size “32 cycles” was a full screen grating.) B: detection thresholds for a Gabor target masked by a surrounding grating mask. The insets show the mask types, see text for exact stimulus details.
Figure 2
 
Spatial extent of backward contrast masking, observer DW. A: contrast detection thresholds for a Gabor target that is masked by a spatially overlapping grating mask. (In the 2 cpd conditions, the mask size “32 cycles” was a full screen grating.) B: detection thresholds for a Gabor target masked by a surrounding grating mask. The insets show the mask types, see text for exact stimulus details.
Figure 3
 
As Figure 2, observer FB.
Figure 3
 
As Figure 2, observer FB.
First, as expected, the unmasked thresholds (points where mask diameter = 0) were lower for the large 4 cpd target ( σ = 0.5) compared to the small 4 cpd target ( σ = 0.25). When the size of the overlapping mask increased, the thresholds first sharply increased and then decreased, as observed before (Saarela & Herzog, 2008). Also in line with previous studies on simultaneous masking, when the inner diameter of the surround mask was increased (dashed lines), masking strength decreased monotonically (Petrov & McKee, 2006). 
All the curves in Figures 2A and 3A peak at the same mask/target size ratio. That is, the extent of masking scales with the target sizes. This happens both when the target is scaled (the 2 cpd target is a scaled version of the small 4 cpd target) and when the size of the Gabor target's Gaussian envelope is changed. The initial steep increase in thresholds is very similar with all three targets, but the tails of the curves are different in shape. In the results of observer DW, the decrease in thresholds after the peak is steepest with the 2 cpd target, less steep with the small 4 cpd target, and most gradual with the large 4 cpd target. With observer FB, the decrease in thresholds observed with the large 4 cpd mask is much less steep than with the other two targets. 
With all three targets, there is a very steep and monotonic decrease in detection thresholds when the mask distance (inner diameter of the surround mask) is increased ( Figures 2B and 3B). This decrease seems to level off earlier with the large 4 cpd target than with the other two targets. However, note that the x-axis is in units of the target. If the mask size was plotted in the number of cycles, the deflection points of the curves would occur at the same size. Thus, in the presence of a surround mask, detection performance depends on the number of cycles in the target that are not occluded by the mask. 
Experiment 2: Effect of mask contrast on size tuning
This experiment focused on the effect of mask contrast on the size tuning of backward contrast masking. 
Stimuli
The target was a 4 cpd Gabor patch with σ = 0.25 degrees. The mask had the same orientation, spatial frequency, and spatial phase as the target. The diameter of the overlapping mask was varied between 1 and 32 cycles (0.25 and 8 degrees). The surround mask had an outer diameter of 32 cycles and the inner diameter was varied between 1 and 16 cycles. Thus, the target and mask sizes were the same as in the “small target” condition in Experiment 1. The Michelson contrast of the mask was either 5% or 10%. As in Experiment 1, detection thresholds were also measured for the target in the absence of a mask. 
Results
Results for the two observers who participated in the experiment are shown in Figures 4 and 5. Figures 4A and 5A show the detection threshold as a function of the outer diameter of the overlapping mask (in units of target σ) Figures 4B and 5B show the thresholds as a function of the inner diameter of the surround mask. For comparison, the corresponding condition with a higher contrast (40%) mask is re-plotted from Figures 2 and 3
Figure 4
 
Spatial extent of backward contrast masking measured with different mask contrasts, observer DW. A: contrast detection thresholds for a Gabor target that is masked by a spatially overlapping grating mask. B: detection thresholds for a Gabor target masked by a surrounding grating mask. The curves with mask contrast of 40% are replotted from Figure 2. The insets show the mask types, see text for exact stimulus details.
Figure 4
 
Spatial extent of backward contrast masking measured with different mask contrasts, observer DW. A: contrast detection thresholds for a Gabor target that is masked by a spatially overlapping grating mask. B: detection thresholds for a Gabor target masked by a surrounding grating mask. The curves with mask contrast of 40% are replotted from Figure 2. The insets show the mask types, see text for exact stimulus details.
Figure 5
 
As Figure 4, observer FB.
Figure 5
 
As Figure 4, observer FB.
The masking strength, as expected, depends on mask contrast: high contrast masks produce stronger masking than low contrast masks. The difference between the effects of different mask contrasts is larger with the overlapping mask than with the surrounding mask. Interestingly, with observer FB, low contrast surround masks (5% or 10%) actually caused the detection thresholds to drop below the baseline with large target-mask separations ( Figure 5B). With the overlapping mask, reducing the mask contrast flattens the curves, so that the differences in thresholds as a function of mask size are much more pronounced with 40% contrast masks than with 5% masks. There also seems to be a small shift in the peak of the masking function: as the mask contrast decreases, the peak of the masking function shifts to smaller mask sizes. 
Experiment 3: Selectivity to surround parameters
This experiment tested how changing the surround parameters affects backward contrast masking. First, we chose a mask which produced a strong masking effect. Then, we measured how this masking was modulated by the presence of various surrounds to study the selectivity of surround modulation. 
Stimuli
The target was a 4 cpd Gabor patch with σ = 0.25 degrees. The mask center was a circular patch of a 4 cpd horizontal grating 4 cycles (1 degree) wide. The target and the mask center carriers were spatially in phase. 
Five different mask surrounds were used: (1) a horizontal 4 cpd grating in phase with the center, (2) a vertical 4 cpd grating, (3) a horizontal 8 cpd grating, (4) a horizontal 2 cpd grating, and (5) a horizontal 4 cpd grating out of phase with the center. The surround outer diameter was 8 degrees (32 cycles for the 4 cpd masks and 16 cycles for the 2 cpd mask). The center and surround masks were either abutting or separated by a 7.5 arc min gap of mean luminance. The Michelson contrast of the mask was always 40%. Examples of the masks are shown as insets in Figure 6. Detection thresholds were also measured (1) with the center mask only and (2) in a baseline condition without a mask. 
Figure 6
 
Effect of surround parameters on surround modulation in backward contrast masking. The mask center was the same in all conditions (same orientation, spatial frequency, and spatial phase as the target), and the surround parameters were varied. Each surround type was tested twice, with and without a gap between the center and surround masks. See Supplementary Figure for data from individual observers. The insets show the mask types, see text for exact stimulus details.
Figure 6
 
Effect of surround parameters on surround modulation in backward contrast masking. The mask center was the same in all conditions (same orientation, spatial frequency, and spatial phase as the target), and the surround parameters were varied. Each surround type was tested twice, with and without a gap between the center and surround masks. See Supplementary Figure for data from individual observers. The insets show the mask types, see text for exact stimulus details.
Results
The results are shown in Figure 6. A small center mask greatly increased the detection thresholds relative to baseline (the second bar from the left in Figure 6A). Adding an abutting surround with an identical carrier grating to the center greatly reduced the strength of masking (the third bar in Figure 6A). This is the same effect as demonstrated in Experiment 1, where increasing the mask size eventually led to a decrease in masking. However, when the surround was separated from the center either by a small gap or a by a difference in orientation, spatial frequency, or spatial phase, the thresholds were again highly elevated. In many cases the threshold was at or close to the level measured without a surround mask. When the center and surround differed in orientation, spatial frequency, or spatial phase, adding a gap did not have any further effect. 
Discussion
Size tuning
A grating mask immediately following the presentation of a Gabor target can raise target detection thresholds many-fold relative to a no-mask condition and also relative to simultaneous presentation of the target and the mask (Saarela & Herzog, 2008), showing that the strength of contrast masking delicately depends on stimulus timing. In the first experiment of the current paper, masks of variable size were used to study the spatial extent of this backward masking effect. This so-called Westheimer paradigm has been widely used in visual psychophysics to study the spatial properties of mechanisms mediating visual detection and discrimination. Initially it was used to reveal center-surround antagonism underlying brightness discrimination (Crawford, 1940; Westheimer, 1965, 1967). Later studies have provided evidence for cortical components of the “Westheimer function” (Yu & Levi, 1997a) and demonstrated a psychophysical equivalent for end-stopping in cortical neurons in simultaneous masking experiments (Yu & Essock, 1996; Yu & Levi, 1997b). We found that in backward masking, the function relating mask size to target detection thresholds has a shape very typical for a Westheimer function: a sharp initial rise followed by a reduction that finally reaches an asymptote. 
The conditions with the 4 cpd small target and the 2 cpd target in the first experiment were spatially scaled versions of each other. The masking functions measured with these stimuli were to a large extent scaled versions of each other as well, indicating scale invariance of the masking effect. This is seen in Figures 2A and 3A, which show that the two functions peak at the same mask diameter when the diameter is measured in units of target size ( σ of the Gaussian envelope of the target). When the target size is increased by increasing the number of cycles (large 4 cpd target vs. small 4 cpd target), the function again peaks at the same mask size / target size ratio. The extent of masking thus depends on the target size; increasing the number of cycles in the target shifts the peak masking effect to larger masks. This is in line with earlier results on psychophysical end-stopping (Yu & Essock, 1996; Yu & Levi, 1997b), where an analogous dependence on target length has been observed. Further, when the target is larger (in terms of cycles), not only does the peak masking effect occur at larger mask diameters, but the shape of the masking function is different as well. With a larger target, the decrease in masking after the peak is much more gradual than that observed with the other targets (a similar effect was found in psychophysical end-stopping by Yu & Essock, 1996, who observed stronger spatial antagonism with shorter line targets). 
However, there is a notable difference between our results and one that investigated psychophysical end-stopping using simultaneous masking: Yu and Levi (1997b) found phase independence of end-zone masking, whereas we found strong phase selectivity of surround modulation. We will return to this issue in the next section. Also, interestingly, when using brief target and longer mask durations, the surround only has an effect in backward masking conditions (Saarela & Herzog, 2008), not with temporally overlapping target and mask presentation. Thus, while the spatial characteristics of the phenomena we measured agree with those reported by Yu and Essock (1996) and Yu and Levi (1997b), there are differences in the temporal properties. 
On a more general level, this “bigger is weaker” effect that we observed, where an increase in mask size leads to weaker masking, is not limited to contrast masking with gratings. It can be observed with different stimuli such as line segments, and different tasks such as fine (Wehrhahn, Li, & Westheimer, 1996) and coarse (Põder, 2006) orientation discrimination as well as vernier discrimination (Herzog & Koch, 2001). 
We also measured the spatial extent of masking using (annular) surround masks, by keeping the outer diameter of the mask constant while varying the inner diameter. With these masks, strong masking occurs only when the inner diameter of the mask is very small. When the diameter is increased, there is a steep decrease in masking that quickly asymptotes ( Figures 2B and 3B). A similar monotonic decrease of a surround effect as a function of distance has also been observed in simultaneous masking of contrast detection in the periphery (Petrov & McKee, 2006) and in perceived contrast (Cannon & Fullenkamp, 1991), as well as in backward masking with two flanking Gabor patches as masks (Polat & Sagi, 2006). However, when comparing data obtained with the three targets used in Experiment 1, the pattern of results is different when surround masks rather than overlapping masks are used. With surround masks, the decline in thresholds seems to asymptote earlier with the large 4 cpd target than with the two other targets (Figures 2B and 3B). The mask size in the figures is indicated in units of target σ. As the large 4 cpd target was larger than the other two in terms of number of cycles, this means that the masking extent scales with the stimulus spatial frequency and also shows independence of the number of cycles in the target. Thus, the spatial extent of masking (or the size of the “perceptive field”) depends not only on the target, but also on the mask type used. 
The overall shapes of the masking functions measured with overlapping masks and surround masks resemble the patterns of neural responses measured in the primary visual cortex with similar stimuli (e.g., Cavanaugh, Bair, & Movshon, 2002a; Jones, Grieve, Wang, & Sillito, 2001; Sengpiel, Sen, & Blakemore, 1997). This suggests the possibility that similar mechanisms of spatial summation and inhibition produce these psychophysical and physiological phenomena. According to this view, the mask would be most effective when the neural responses it elicits are strongest, and would lose its effectiveness when spatial inhibition reduces the neural responses. From physiology it is known that the balance between summation and inhibition is dependent on stimulus contrast: inhibition is weaker at low contrasts, and thus low contrast stimuli produce apparently larger summation fields than high contrast stimuli (Cavanaugh et al., 2002a; Jones et al., 2001; Kapadia, Westheimer, & Gilbert, 1999; Sceniak, Ringach, Hawken, & Shapley, 1999; Sengpiel et al., 1997). To test whether a similar effect can be seen psychophysically (as is the case in motion perception, see Tadin, Lappin, Gilroy, & Blake, 2003), we measured the size tuning of backward contrast masking at various mask contrasts. In accordance with the physiological results, spatial antagonism in masking is weaker at low contrasts: the difference between the peak masking effect and the subsequent asymptotic levels of the masking functions is greater with high mask contrast than with low mask contrast (Figures 4A and 5A). However, at the same time the peak masking effect seems to shift to smaller masks, seemingly at odds with physiological data where an increase in the summation area is usually observed. This might happen because, overall, the detection thresholds are lower when the mask contrast is low. As the target is a Gabor patch, at low contrast it effectively becomes “smaller” because of the Gaussian windowing. Thus, the observed shift might parallel the observation from Experiment 1: the psychophysically measured masking functions are always coupled to the size of the target pattern used. An interesting further experiment would be to test various surround contrast while keeping the center mask contrast constant. In simultaneous masking, there is evidence that the effect of a surround on pedestal masking depends on the relative contrasts of the pedestal and the surround (Chen & Tyler, 2008; Yu, Klein, & Levi, 2003). 
Selectivity to surround parameters
In the third experiment, only the iso-oriented, abutting, in-phase surround modulated the masking caused by the overlapping center mask. When the center and surround masks were separated by a difference in orientation, spatial frequency, spatial phase, or just by a narrow gap of uniform luminance, surround modulation was practically absent (that is, the detection thresholds were as high as with the center mask only). These effects are reminiscent of other pattern (Herzog & Fahle, 2002) and metacontrast (Duangudom, Francis, & Herzog, 2007) masking studies in which various spatial changes in the masks have strongly modulated masking strength. 
We first discuss the effect of changing the surround parameters. Similar selectivity of surround modulation has been previously observed in the contrast–contrast phenomenon. The surround's effect on perceived target contrast decreases when the two differ in orientation (Cannon & Fullenkamp, 1991; Solomon, Sperling, & Chubb, 1993), spatial frequency (Cannon & Fullenkamp, 1991; Chubb et al., 1989), or spatial phase (Olzak & Laurinen, 1999). This psychophysical selectivity parallels the properties of neurons at early levels of cortical processing, suggesting that interactions are strongest between groups of neurons having similar tuning properties. Indeed, this has been found to be the case in neurophysiology (Cavanaugh, Bair, & Movshon, 2002b). In simultaneous masking, an orthogonal surround can decrease masking as well, especially if it's contrast is high (Yu & Levi, 2000). 
On the other hand, the fact that a narrow gap between the center and surround can abolish the surround modulation suggests that an explanation based on the tuning properties of single neurons is not alone sufficient. Rather, it seems that whenever the center and surround are clearly segregated, no interactions occur between the mechanisms responding to them. Similar observations have been reported by Saylor and Olzak (2006) in simultaneous masking using centers and surrounds that differed in mean luminance, and by Olzak and Laurinen (2005) who used a gap between the center and surround (but see also Mareschal, Sceniak, & Shapley, 2001). One possibility is that at a relatively early stage of visual processing, the visual scene is segmented into distinct regions, and the (psychophysically measurable) effect of lateral interactions does not cross the borders of these regions. Within these regions, however, the interactions can be strong. The fact that suppression can be very strong among mechanisms responding to the same texture can also act as a type of redundancy reduction: if an area consists of similar local features, responses to them can be suppressed as not all features have to be individually represented. A distinct region within a larger texture, on the other hand, is likely to contain relevant information and ”pops out” as it is not suppressed. 
As mentioned earlier, when studying psychophysical end-stopping, Yu and Levi (1997b) found phase independence of end-zone masking. Our results, on the other hand, show strong dependence of surround modulation on the relative phases of center and surround. The reason for this difference is unclear, but we note that the stimuli used in these two studies differ substantially. We used annular masks that surrounded the center on all sides, whereas Yu and Levi used “end-zone” masks. One possibility is that the mask configuration we used leads to stronger perceptual segregation when the center and surround differ in phase. A second obvious difference between the two studies is the timing of the mask (simultaneous vs. backward mask) which could also account for the difference. Phase dependency has previously been reported in the contrast–contrast phenomenon: the surround's effect is reduced when it differs in phase from the center (Olzak & Laurinen, 1999). 
Finally, when the center and surround differed in orientation, spatial frequency, or spatial phase, adding a gap did not have any further effect. Either kind of segmentation cue (surround parameters or gap) substantially raised the thresholds, and we observed no summing of their effects. This observation is similar to that reported by van der Smagt, Wehrhahn, and Albright (2005). They found that both an orientation and contrast polarity difference lead to a reduction in surround modulation in simultaneous masking, but they found no summing of the effects of orientation and polarity. On the other hand, the lack of synergy between the segmentation cues that we observed could also be a ceiling effect: either cue alone was sufficient to raise the thresholds to or near the level measured without the surround. Summation of the effects of the two cues could possibly be observed if the orientation, spatial frequency, or phase difference was smaller. One might expect that a smaller difference between center and surround would lead to weaker segmentation, which could then be strengthened by adding a gap in between them. 
Alternative explanations
In addition to the center–surround interactions suggested above, there are other possible explanations for the decreased masking effect in the presence of a surround. When the mask is larger than the target, there is a spatio-temporal edge in the stimulus that is not present when the target and the mask are roughly equal in size. This additional cue could contribute to the better detection performance when the mask is large. Changing the surround parameters might reduce the strength of this spatio-temporal cue, leading to higher thresholds such as those shown in Figure 6
There are, however, reasons why we think that the explanation based on center–surround interactions is more likely to account for our results. First, in our previous study (Saarela & Herzog, 2008), we did not observe a similar decrease in forward masking, although in that case there is a spatio-temporal cue available as well when the mask is larger than the target. Second, it is clear that changing the surround parameters (e.g., orientation) can make the cue less effective, but why does the surround effect disappear even when the center and surround are separated by a narrow gap? In the gap condition with the iso-oriented, in-phase mask, the spatio-temporal cue is still there, although there is also an additional spatial edge, caused by the gap. We observed no relief from masking due to the surround in this condition. 
Disregarding temporal factors, one might argue that adding a small central target to a large mask changes the task to that of detecting a contrast increment in the middle of an otherwise uniform contrast grating, thus making the task easier. First, we emphasize that the target and the mask were not temporally overlapping in this study. However, in a previous study we had such conditions when the stimulus onset asynchrony between the target and the mask was varied (Saarela & Herzog, 2008, Figure 3; see also Figure 1 of the current paper). The only conditions where adding a surround to the central mask lowered detection thresholds were the backward masking conditions. No surround effect was evident when the target and the mask were temporally overlapping. We conclude that the lower detection thresholds in the presence of the large mask, and with the temporal parameters we used, are not alone due to second-order cues. 
Concluding remarks
The spatial properties of backward contrast masking generally agree well with known physiology of early visual cortex and suggest that masking strength is modulated by contrast-dependent spatial summation and inhibition mechanisms. However, the extent of masking and the exact shape of the size tuning function (and thus the “perceptive field”) crucially depend on the target stimulus chosen. Also in agreement with a large amount of psychophysical and physiological data, the surround modulation of backward contrast masking is selective to relative orientations, spatial frequencies, and phases of the center and surround. However, the same effect can also be achieved by simply separating the surround from the center with a narrow gap, suggesting that stimulus segmentation plays an important role in determining the strength of lateral interactions. 
Supplementary Materials
Supplementary Figure - Supplementary Figure 
Acknowledgments
We thank Marc Repnow for technical support and Maria Olkkonen for comments on the manuscript. TS was supported by the Swiss National Science Foundation (SNF). 
Commercial relationships: none. 
Corresponding author: Toni P. Saarela. 
Email: saarela@nyu.edu. 
Address: Department of Psychology, New York University, 6 Washington Place, Room 957, New York, NY 10003, USA. 
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Figure 1
 
Time-course of iso-orientation masking. A 40 ms Gabor target was presented at various SOAs relative to a 100 ms mask (mask duration depicted by the black bar, mask type by icons). The highlighted region shows the strong backward masking effect with a small mask and the decreased masking effect with a larger mask. The experiments reported in this paper use the highlighted timing conditions only, that is, a Gabor target immediately followed by a grating mask. Adapted from Saarela and Herzog (2008).
Figure 1
 
Time-course of iso-orientation masking. A 40 ms Gabor target was presented at various SOAs relative to a 100 ms mask (mask duration depicted by the black bar, mask type by icons). The highlighted region shows the strong backward masking effect with a small mask and the decreased masking effect with a larger mask. The experiments reported in this paper use the highlighted timing conditions only, that is, a Gabor target immediately followed by a grating mask. Adapted from Saarela and Herzog (2008).
Figure 2
 
Spatial extent of backward contrast masking, observer DW. A: contrast detection thresholds for a Gabor target that is masked by a spatially overlapping grating mask. (In the 2 cpd conditions, the mask size “32 cycles” was a full screen grating.) B: detection thresholds for a Gabor target masked by a surrounding grating mask. The insets show the mask types, see text for exact stimulus details.
Figure 2
 
Spatial extent of backward contrast masking, observer DW. A: contrast detection thresholds for a Gabor target that is masked by a spatially overlapping grating mask. (In the 2 cpd conditions, the mask size “32 cycles” was a full screen grating.) B: detection thresholds for a Gabor target masked by a surrounding grating mask. The insets show the mask types, see text for exact stimulus details.
Figure 3
 
As Figure 2, observer FB.
Figure 3
 
As Figure 2, observer FB.
Figure 4
 
Spatial extent of backward contrast masking measured with different mask contrasts, observer DW. A: contrast detection thresholds for a Gabor target that is masked by a spatially overlapping grating mask. B: detection thresholds for a Gabor target masked by a surrounding grating mask. The curves with mask contrast of 40% are replotted from Figure 2. The insets show the mask types, see text for exact stimulus details.
Figure 4
 
Spatial extent of backward contrast masking measured with different mask contrasts, observer DW. A: contrast detection thresholds for a Gabor target that is masked by a spatially overlapping grating mask. B: detection thresholds for a Gabor target masked by a surrounding grating mask. The curves with mask contrast of 40% are replotted from Figure 2. The insets show the mask types, see text for exact stimulus details.
Figure 5
 
As Figure 4, observer FB.
Figure 5
 
As Figure 4, observer FB.
Figure 6
 
Effect of surround parameters on surround modulation in backward contrast masking. The mask center was the same in all conditions (same orientation, spatial frequency, and spatial phase as the target), and the surround parameters were varied. Each surround type was tested twice, with and without a gap between the center and surround masks. See Supplementary Figure for data from individual observers. The insets show the mask types, see text for exact stimulus details.
Figure 6
 
Effect of surround parameters on surround modulation in backward contrast masking. The mask center was the same in all conditions (same orientation, spatial frequency, and spatial phase as the target), and the surround parameters were varied. Each surround type was tested twice, with and without a gap between the center and surround masks. See Supplementary Figure for data from individual observers. The insets show the mask types, see text for exact stimulus details.
Supplementary Figure
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