February 2009
Volume 9, Issue 2
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Research Article  |   February 2009
Selective attention contributes to global processing in vision
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Journal of Vision February 2009, Vol.9, 6. doi:10.1167/9.2.6
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      J. Edwin Dickinson, Cherese Broderick, David R. Badcock; Selective attention contributes to global processing in vision. Journal of Vision 2009;9(2):6. doi: 10.1167/9.2.6.

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Abstract

Information processing is more effective within attended regions of the visual field and the size of the attended region is variable. This observation conflicts with the assumption, used in measuring the spatial extent of global integration of coherent local orientations, that optimal sensitivity to texture information is immediately available within an appropriately sized neuronal receptive field. Using extended patterns that require global processing to detect the presence of coherent orientation structure, we found that the size and topology of the region of integration of local visual cues is not fixed. Integration can occur out to a radius of at least 10 degrees, an area (314 square degrees) much larger than previously supposed, and can be constrained to annular in addition to circular apertures. The use of such spatial apertures was found to be mediated by observer expectation. The processing of texture information available in selected areas is optimized through the exclusion of noise outside the regions of interest.

Introduction
When a field of randomly distributed dots is superimposed on a geometrically transformed copy of itself, a Moiré pattern with coherent global structure can be perceived (Badcock & Clifford, 2006; Glass, 1969; Glass & Pérez, 1973). These patterns are commonly known as Glass patterns. Rotation creates concentric and expansion radial structure. Perception of the structure relies upon the detection of local correlations between dots across the transformation and their global integration (Wilson & Wilkinson, 1998; Wilson, Wilkinson, & Asaad, 1997). The simple cells in the primary visual cortex (V1) represent elongated spatial filters, line or edge detectors (Hubel & Wiesel, 1968), and an appropriately oriented filter will pass two adjacent dots (Smith, Bair, & Movshon, 2002). Filters for all orientations exist, however, and inappropriately oriented pairs of dots that are neighbors by chance rather than due to the transformation will also be passed. The global percept of coherent structure is therefore subject to noise of the same line-like character as the coherently oriented signal (Glass, 1969; Glass & Pérez, 1973). Restricting the area of the pattern that is in view can abolish the perception of structure (Glass & Pérez, 1973) and this effect has been used to infer an optimal area for integration of coherent orientation. Studies investigating the area of the integration mechanism typically have used patterns with a constant separation between dots in a pair and have imposed coherent orientations on signal pairs and random orientations on noise pairs. Observers are required to discriminate a test pattern, containing a proportion of signal, from a wholly incoherent reference pattern. Wilson et al. (1997) constrained signal to circular and annular regions of a stimulus of fixed radius of 2.43° and developed a neurally motivated computational model to describe human psychophysical thresholds reflecting the proportion of signal in the signal area required for discrimination between the random patterns and those containing coherent structure. The model has optimal response to concentric signal at a radius of 1.4°. An analogous model due to Wilson and Wilkinson (1998) has an optimal sensitivity to radial signal at a radius of 1.1°. Mandelli and Kiper (2005) increased the aperture size on patterns, maintaining dot pair density, and noted a rapid decline in discrimination threshold percentage to an apparent plateau at around 3° radius. Both of these studies make the assumption that integration area is fixed. However, if the data from both of these experiments are plotted as discrimination threshold (as a percentage of the number of dot pairs in the signal area versus the radius of the signal area, see Figure 5), then they are well described by power functions (with indices of approximately −1) and the absence of any discontinuity in the plots suggests that integration of signal occurs out to all pattern radii tested. The indices of the power functions are comparable across the two sets of experiments despite the fact that the signal regions of the stimuli used by Wilson et al. were surrounded by noise while those of Mandelli and Kiper were not. This observation suggests that noise surrounding the signal area in the study of Wilson et al. (1997) is excluded by the integration mechanism. This is inconsistent with the interpretation of the integration area as being fixed. In this study, we set out to repeat and systematically compare the experiments of Mandelli and Kiper (2005) and Wilson et al. (1997) while extending the range of radii tested. We used Glass patterns with circular and annular signal regions to show that signal integration can occur out to a radius of at least 10°, corresponding to an area greater than tenfold larger than that reported by Wilson et al. or Mandelli and Kiper. We also show that integration area is adjusted to include signal and exclude noise areas in order to optimize sensitivity to structure. As the consistency in the indices of the power functions that fit the data of Wilson et al. and Mandelli and Kiper suggest that integration area is flexible, we measured thresholds for different sizes of signal areas in both blocked and interleaved conditions to assess whether the adjustment of the integration area occurs spontaneously or is under volitional control. We present evidence that circular and annular attentional apertures of variable size are applied to stimuli on the basis of knowledge of the extent of the signal area prior to presentation of the test stimuli. Examples of the stimuli used in this study are presented in Figure 1
Figure 1
 
Examples of test stimuli. Stimuli were Glass patterns comprised of pairs of dots. Signal dot pairs were oriented coherently (concentrically in examples A and B, and radially in C and D). Noise dot pairs were oriented at random. Signal regions were circular (A and B) or annular (C and D). The outer radius of the circular signal region and the inner radius of the annular signal region were varied across conditions. The circular signal region could be surrounded by noise (B) or not (A). Similarly, the annular signal region could surround noise (D) or not (C). The signal regions of all of these examples have 50% of their dot pairs coherently oriented (180 of 360 dot pairs). Examples B, C, and D have dot pairs extending to the maximum outer radius of 10° and can be used as a scale. The circular signal regions of A and B have radii of 6°. The inner radii of the annular signal regions of examples C and D are 8°.
Figure 1
 
Examples of test stimuli. Stimuli were Glass patterns comprised of pairs of dots. Signal dot pairs were oriented coherently (concentrically in examples A and B, and radially in C and D). Noise dot pairs were oriented at random. Signal regions were circular (A and B) or annular (C and D). The outer radius of the circular signal region and the inner radius of the annular signal region were varied across conditions. The circular signal region could be surrounded by noise (B) or not (A). Similarly, the annular signal region could surround noise (D) or not (C). The signal regions of all of these examples have 50% of their dot pairs coherently oriented (180 of 360 dot pairs). Examples B, C, and D have dot pairs extending to the maximum outer radius of 10° and can be used as a scale. The circular signal regions of A and B have radii of 6°. The inner radii of the annular signal regions of examples C and D are 8°.
Methods
Custom stimuli were created using Matlab 6.5 (Mathworks, Natick, MA, USA) on a PC and drawn from the frame buffer of a Cambridge Research Systems ViSaGe visual stimulus generator to a Sony Trinitron G520 monitor. Screen resolution was 1024 × 768 pixels with each pixel subtending 2′ of visual angle at a viewing distance of 65.5 cm. The viewing distance was stabilized through the use of a chinrest. Screen refresh rate was 100 Hz. Background luminance of the stimuli was 45 cd/m 2 and the screen was viewed in a darkened room with an ambient luminance of <1 cd/m 2. Luminance calibration was performed using an Optical OP200-E photometer (head model number 265) and associated software. A button box was used to record observer responses. 
Seven experienced psychophysical observers participated. CB and ED are authors; the rest were naive to the purpose of the experiments. All had normal or corrected-to-normal visual acuity. 
Radial and concentric Glass patterns were used in parallel sets of conditions. The patterns were composed of pairs of dots with positions defined by the midpoint between the dots of each pair. Pattern radius was 10° of visual angle. Up to 1000 dot pairs were assigned polar positions in a pseudorandom manner. Each dot pair was assigned one of 1000 different values of θ evenly distributed between 0 and 2 π radians, and one of 1000 values of r between 0 and 10° of visual angle distributed in proportion to r. This resulted in a uniform dot pair density of 3.183 dot pairs per square degree on average. Only one dot pair was assigned to each value of r and θ assuring a predictable population of dot pairs across different radii. Signal dot pairs were aligned along radii in the radial patterns and perpendicular to radii in the concentric patterns. Dots had a Gaussian luminance contrast profile to background with a maximum Weber contrast of 1 (maximum luminance = 90 cd/m 2) and a width at half-maximum contrast of 9.4′ of visual angle. The dot centres of each pair were separated by 12′ of visual angle. 
The output of all experiments was the threshold number of signal dot pairs for discrimination of a structured test pattern from a wholly incoherent reference pattern. A two-interval forced-choice (2IFC) paradigm was adopted. The patterns were presented sequentially with an inter-stimulus interval of 500 ms. The order of presentation of the test and reference patterns was randomized. Each pattern was displayed for 160 ms. The task of the observer was to indicate the interval within which the test pattern was presented. Signal level was initiated at the maximum possible and then adjusted using an adaptive staircase procedure. Signal level was reduced after three successive correct responses and raised after each incorrect response. This procedure converges on the 79.4% correct performance level (Cornsweet, 1962; Wetherill & Levitt, 1965). The procedure was followed for 8 reversals in direction of the staircase and the mean of the signal level at the last four reversals adopted as the measure of discrimination threshold. In order to increase the speed of convergence to the threshold, the initial step size (in number of signal dipoles) was set to 8 times the ultimate step size and reduced by half at each of the first 3 reversals (Badcock & Smith, 1989). Five staircases were run for each condition to provide a measure of variability. 
Results
Signal-to-noise ratios at threshold are independent of stimulus area
We measured signal thresholds for discriminating test Glass patterns with coherent concentric or radial signal orientations from incoherent reference patterns. The test and reference patterns were presented sequentially in randomized order and the observer was required to indicate the interval that contained the test pattern. Thresholds for discrimination of the test and reference patterns were arrived at via an adaptive procedure (described in the Methods section), which converged upon the number of signal dot pairs required to allow correct discrimination in 79.4% of trials. This first set of conditions had a constant number of 250 dot pairs in the test and reference stimuli. The dot pairs were distributed evenly across a circular region, the radius of which varied across conditions. Signal was also distributed across the whole stimulus. Discrimination thresholds are plotted against stimulus area in Figure 2
Figure 2
 
Discrimination thresholds plotted against area of a circular signal region for a constant number of dot pairs. All stimuli in this set of conditions contained 250 dot pairs and so dot pair density varied with circle radius. The regions of the stimuli external to the signal region were empty. Reported thresholds and error bars for each condition, for this and subsequent figures, are the means and standard deviations of five staircases. Power functions fitted to the data have indices consistent with zero showing that discrimination thresholds are independent of area when the total number of dot pairs is constant. The errors quoted for the indices of the power functions in these and subsequent graphs are the 95% confidence intervals.
Figure 2
 
Discrimination thresholds plotted against area of a circular signal region for a constant number of dot pairs. All stimuli in this set of conditions contained 250 dot pairs and so dot pair density varied with circle radius. The regions of the stimuli external to the signal region were empty. Reported thresholds and error bars for each condition, for this and subsequent figures, are the means and standard deviations of five staircases. Power functions fitted to the data have indices consistent with zero showing that discrimination thresholds are independent of area when the total number of dot pairs is constant. The errors quoted for the indices of the power functions in these and subsequent graphs are the 95% confidence intervals.
Power functions (Threshold = α ×Area β) are fitted to the data throughout this paper and power functions with an index ( β) of zero represent the data in Figure 2 well. This, of course, only demonstrates that discrimination thresholds remain constant with change in area when the total number of dot pairs is constant. Throughout the rest of the experiments, dot pair density was kept constant in the middle of the range tested in this first experiment, but the areas of regions containing signal were varied. Coherence discrimination thresholds are always plotted against the area of the signal region (except in Figure 5 where a comparison is made to data from other studies), but it is important to note that this area is proportional to the total number of dot pairs within the region. The coherence threshold does not vary with area per se, as has been demonstrated in this first experiment, but with the number of contained dot pairs. This first experiment does however imply that integration occurs over the whole stimulus. 
Integration of coherent orientation occurs over large areas
The following sets of conditions used stimuli with a constant dot pair density in the middle of the range tested above (3.183 dot pairs per square degree). The dot pairs, signal and noise, were constrained to lie within circular or annular regions. The radius of the outer edge of the circle or the inner edge of the annulus was varied between conditions. The outer edge of all annuli was at a radius of 10°. Examples A and C in Figure 1 show sample stimuli. Example A is a circular concentric pattern and Example C is an annular radial pattern. Both have 50% signal and noise orientations assigned at random. The results for both sets of conditions are shown in Figure 3. Discrimination thresholds are plotted against the circular or annular areas of the stimuli that contain the dot pairs. The data are all well described by power functions. The top row of graphs in Figure 3 shows discrimination thresholds for the circular stimuli. These results extend the results of Mandelli and Kiper (2005) from a radius of 7° (154 square degrees) to 10° and importantly show that the performance does not plateau at 3° (28 square degrees). The thresholds for the annular stimuli are shown in the bottom row along with the functions fitted to the thresholds for the circular stimuli (dotted lines). The slopes of the lines (power function indices) describing the thresholds for concentric and radial patterns with circular and annular signal regions did not differ significantly (F(3,382) = 1.853, p = 0.1370). For all of the functions fitted, the indices were less than 1 showing that the ratio of signal-to-noise dot pairs in the stimuli at threshold decreases as the total number of dot pairs in the stimuli increases. Consequently, optimal sensitivity to structure will be achieved for these conditions if signal is integrated over the whole of the stimulus. No discontinuities are evident in the data suggesting that no edge has been reached in the area over which integration can occur. 
Figure 3
 
Discrimination thresholds plotted against area of signal regions for stimuli with circular and annular signal regions and no dot pairs outside these regions. Icons have been added to two of the graphs illustrating the sizes and shapes of the regions containing dot pairs. The positions on the graphs where examples A and C in Figure 1 would lie are also marked. All data sets are well represented by power functions. The top row of graphs display thresholds for stimuli with circular and the bottom row annular signal areas. The dashed lines in the bottom row are the fits to the data of the top row. The indices of the power functions do not differ significantly.
Figure 3
 
Discrimination thresholds plotted against area of signal regions for stimuli with circular and annular signal regions and no dot pairs outside these regions. Icons have been added to two of the graphs illustrating the sizes and shapes of the regions containing dot pairs. The positions on the graphs where examples A and C in Figure 1 would lie are also marked. All data sets are well represented by power functions. The top row of graphs display thresholds for stimuli with circular and the bottom row annular signal areas. The dashed lines in the bottom row are the fits to the data of the top row. The indices of the power functions do not differ significantly.
Integration area is flexible
The results shown in Figure 3 indicate that the lowest possible discrimination threshold will be achieved if integration of signal and noise extends over the whole stimulus area. This does not explicitly show that the size of the integration area changes, only that it is large enough to enclose the largest stimulus. The indices of the power functions describing the data of Mandelli and Kiper (2005) and Wilson et al. (1997), when plotted as threshold number against area of the signal region, are very similar, suggesting that, in the experiments of Wilson et al. (1997), integration occurs only over the circular region that contains signal and that noise external to this area is ignored. This implies that the area over which integration occurs is adjusted to optimize sensitivity. We repeated the experiments of Wilson et al. (1997) but with a larger stimulus outer radius than their 2.43° to test if the power function relationship is maintained over larger areas. Stimulus outer radius was held constant at 10° of visual angle and the radius that separated regions of signal and noise in the test stimulus was varied. B and D in Figure 1 are sample stimuli. Discrimination thresholds for circular signal regions, arrived at by the same procedure described previously, are plotted against area of the signal region in the top row of graphs in Figure 4. A power law is again a good description of the data. The indices of the power functions fitted to the data approximate 0.6, demonstrating that the observers do not simply integrate signal and noise over the whole stimulus as this would result in an index of zero since the total number of dot pairs in the stimulus is constant. The size of the integration area must be scaled to enhance sensitivity by maximizing the signal area and excluding noise. The bottom row of graphs in Figure 4 shows discrimination threshold data for stimuli with annular signal regions surrounding noise. These data again conform to power functions comparable to those of the stimuli with circular signal regions. The functions fitted to the data corresponding to the circular signal areas have been superimposed on the graphs of these data (dotted lines) and the fits can be seen to be approximately collinear. Once again the indices of power functions fitted to the four data sets do not differ significantly (F(3,432) = 0.4933, p = 0.6871). It appears that not only can noise external to a circular signal region be disregarded but so too can noise internal to an annular signal region. The indices of the power functions describing thresholds for stimuli surrounded by noise are somewhat smaller than those without noise external to the signal region but this may be due to some uncertainty in the position of the boundary between the signal and noise regions leading to a slightly degraded signal-to-noise ratio for the smaller signal regions. 
Figure 4
 
Discrimination thresholds plotted against area of signal regions for stimuli with noise dot pairs outside the signal regions. In the icons illustrating the stimuli, the regions including signal and noise dot pairs are dark gray and the regions containing only noise are light gray. The positions on the graphs where examples B and D in Figure 1 would lie are marked. All data sets are again well represented by power functions with similar indices.
Figure 4
 
Discrimination thresholds plotted against area of signal regions for stimuli with noise dot pairs outside the signal regions. In the icons illustrating the stimuli, the regions including signal and noise dot pairs are dark gray and the regions containing only noise are light gray. The positions on the graphs where examples B and D in Figure 1 would lie are marked. All data sets are again well represented by power functions with similar indices.
For comparison, Figure 5 plots data for concentric pattern stimuli with circular signal areas from this series of experiments and comparable data from Mandelli and Kiper (2005) and Wilson et al. (1997). The data are plotted as the percentage threshold coherence level in the signal area versus the radius of the signal area, the convention used in the earlier studies. Power functions with indices of around −1 are a good fit to the data. 
Figure 5
 
Comparison of data from this study with those of Mandelli and Kiper (2005) and Wilson et al. (1997). Coherence thresholds (as a percentage of the total number of dot pairs within the critical radius) are plotted against the critical radius. All data shown are for concentric patterns with circular signal areas. The signal areas in the stimuli of Wilson et al. (1997) were surrounded by a region containing noise dot pairs while those of Mandelli and Kiper (2005) were not. The corresponding data from this study are also plotted. A power function is a good fit to the data over the whole range of radii.
Figure 5
 
Comparison of data from this study with those of Mandelli and Kiper (2005) and Wilson et al. (1997). Coherence thresholds (as a percentage of the total number of dot pairs within the critical radius) are plotted against the critical radius. All data shown are for concentric patterns with circular signal areas. The signal areas in the stimuli of Wilson et al. (1997) were surrounded by a region containing noise dot pairs while those of Mandelli and Kiper (2005) were not. The corresponding data from this study are also plotted. A power function is a good fit to the data over the whole range of radii.
As a direct test of the hypothesis that signal is integrated around the annulus but ignored in the center, a set of conditions was run where the signal in the test stimulus was constrained to sectors of an annulus with an inner radius of 6°. Four equally spaced sectors each subtended 90°, 45°, or 22.5° at the center of the stimulus and therefore when combined represented 100%, 50%, or 25% of the total area of the annulus, respectively. The polar positions of the sectors containing signal were always equally spaced but were randomized on a trial by trial basis. The remainder of the annulus, and the circular region within it, contained only noise dot pairs. Staircases converging on thresholds for the three conditions were interleaved. The results are presented in Figure 6
Figure 6
 
Discrimination thresholds plotted against area of signal regions: Signal constrained to sectors of an annulus. The signal regions for these conditions were four sectors of an annulus with an inner radius of 6°. The sectors represented 100%, 50%, or 25% of the annulus. Icons on the graph illustrate the signal and noise distribution within the stimuli. Dark-colored regions of the icons contain signal and noise dot pairs, the light-colored regions contained noise pairs only. The dashed lines are the fits to the thresholds for the annular stimuli reported in Figure 4. The indices of the fitted power functions are small indicating almost perfect integration of signal and noise around the annulus.
Figure 6
 
Discrimination thresholds plotted against area of signal regions: Signal constrained to sectors of an annulus. The signal regions for these conditions were four sectors of an annulus with an inner radius of 6°. The sectors represented 100%, 50%, or 25% of the annulus. Icons on the graph illustrate the signal and noise distribution within the stimuli. Dark-colored regions of the icons contain signal and noise dot pairs, the light-colored regions contained noise pairs only. The dashed lines are the fits to the thresholds for the annular stimuli reported in Figure 4. The indices of the fitted power functions are small indicating almost perfect integration of signal and noise around the annulus.
The results are well described by power functions with indices only slightly greater than zero indicating that threshold is a constant proportion of the dot pairs in the entire annulus. The function fitted to the annular stimulus data displayed in Figure 4 is shown as a dashed line. The intersection of the two lines is at approximately 200 square degrees on the x-axis, which corresponds to the area of the annulus that is divided into sectors for this set of conditions. This demonstrates explicitly that signal and noise are integrated around the annulus but noise at a radius less than the inner radius of the annulus is ignored. 
Extent of the integration area is mediated by prior knowledge
Thresholds for circular and annular signal regions described in the previous sections were determined using independent staircases. The signal level of the test stimulus was initiated at 100% coherence in orientation in all conditions. The observers were therefore aware of the position of the circular boundary between signal and noise regions of the stimulus. In order to test whether this was a necessary condition for integration to be restricted to the signal area, five conditions were interleaved so that the observers would not know which condition would be presented in any single trial. In one of the interleaved conditions, the whole stimulus contained signal. In the four further conditions, signal was constrained to circles with 25% and 50% of the area of the whole stimulus and annuli with 25% and 50% of the total stimulus area. Areas external to the circular signal regions or internal to the annular signal regions contained noise. Figure 7 displays the thresholds for the conditions when using interleaved trials. The power functions that best describe these data have indices averaging 0.24 (95% C.I. = 0.1). This substantially lower index demonstrates that without prior knowledge of the signal area the observer's performance is substantially degraded in the conditions where signal was constrained to areas smaller than the whole stimulus. The observer defaults to integration over the whole stimulus area. 
Figure 7
 
Discrimination thresholds plotted against area of signal regions for interleaved stimuli with noise external to the signal regions. The indices of the fitted power functions are substantially smaller than those fitted to data from independent staircases (see Figure 4). This indicates that in the absence of prior knowledge of the size and topology of the signal region observers default to integrating signal and noise over the whole stimulus area.
Figure 7
 
Discrimination thresholds plotted against area of signal regions for interleaved stimuli with noise external to the signal regions. The indices of the fitted power functions are substantially smaller than those fitted to data from independent staircases (see Figure 4). This indicates that in the absence of prior knowledge of the size and topology of the signal region observers default to integrating signal and noise over the whole stimulus area.
Discussion
Glass patterns have been widely used to investigate the mechanisms responsible for the analysis of texture in visual stimuli. Conventionally, it has been assumed that such mechanisms operate over limited scales and that integration is obligatory within rigidly circumscribed circular areas. Our results show that the scale over which integration can occur is much larger than previously thought. Earlier studies have inferred maximum radii for region over which integration occurs no larger than 3° but we used stimuli with a maximum radius of 10° and saw no evidence for a drop in the efficiency of integration. We also demonstrate that the topology of the integration region can be more complex than simply circular. Integration can be restricted to annular regions of the visual field. Optimum sensitivity to the structure observed in Glass patterns is achieved through the application of an aperture of variable size and topology, which includes areas containing signal and excludes noise regions. The border between the noise and signal regions of the experimental stimuli is only defined by a change in signal level, and at discrimination, threshold cannot be perceived as an explicit boundary. We have demonstrated that in the absence of prior knowledge of the position of the boundary observers integrate information over the whole stimulus and therefore perform suboptimally. The aperture must therefore be modulated by attention and attention must be sustained. James (1890) first suggested the metaphor of a spotlight for attention illuminating areas of interest in the visual field and numerous psychophysical experiments have subsequently been used to test the veracity of the metaphor. The majority of such experiments have used a cue-probe paradigm. The onset of the cue draws attention to the cue position and the probe is then used to investigate performance at a position located relative to the cue. Reaction time to the onset of a probe in a cued position is reduced without a change in fixation (Eriksen & Hoffman, 1974). This effect can be observed with cue to probe times of as little as 50 ms. Away from the cued position reaction times are degraded (Posner, Snyder, & Davidson, 1980). This gradient in reaction times indicates a change in processing speed as attention is oriented to a particular point in the visual scene and indeed this change can be visualized as an illusion of motion (Hikosaka, Miyauchi, & Shimojo, 1993a, 1993b, 1993c; Kanizsa, 1951). If a cue is presented to elicit attention and a bar immediately presented adjacent and radial to the cue, the bar is not all simultaneously perceived. The end of the line closest to the cue is perceived first and the bar appears to grow from the cue outwards. It has been noted that this effect is predicted by motion energy and feature tracking models of motion detection (Zanker, 1997) but the effect has also been demonstrated using auditory and somatosensory cues to recruit attention (Hikosaka, Miyauchi, & Shimojo, 1996; Shimojo, Miyauchi, & Hikosaka, 1997). Moreover, further from the cue the direction of the illusion of motion is reversed indicating a radius beyond which processing speed declines upon presentation of the cue. This observation has been used to postulate a center surround spatial organization for attention (Steinman, Steinman, & Lehmkuhle, 1995). Experiments have produced varying estimates of the maximum radius for processing enhancement, but this is perhaps not surprising given the dynamic nature of the system under examination. Experiments comparing the effects of sustained and transient cues (Castiello, Badcock, & Bennett, 1999; Nakayama & Mackeben, 1989) have however suggested that attention itself can be dissociated into sustained and transient components. The transient component, it is suggested, is not subject to voluntary control and the ‘line motion’ illusion has been used to show that it supersedes the voluntary, sustained component of attention for around 300 ms (Hikosaka et al., 1996). The function of the transient component of attention may be to assign processing resources to the most salient objects in the visual scene. The visual system applies heuristic solutions to an inadequately constrained inverse problem in the reconstruction of a three-dimensional model of a scene from a two-dimensional projection. An early priority is the segregation of figures in the visual field from ground as this process orders objects in depth (Craft, Schütze, Niebur, & von der Heydt, 2007; Qiu, Sugihara, & von der Heydt, 2007; Rensink & Enns, 1998). The boundaries between shapes in the projection, identified through discontinuities in properties of the projected image, are defined by the nearer and typically most salient object. Parsing of the scene therefore requires that boundaries be assigned appropriately as the edges of objects. Psychophysical studies have shown that the completion of partially occluded objects can occur rapidly and in parallel (Rensink & Enns, 1998), but if the depth ordering of boundaries is subverted, objects can be recognized only with scrutiny (He & Nakayama, 1992). There is also psychophysical (Driver & Baylis, 1996) and neurophysiological (Qiu et al., 2007) evidence that the edge assignment is obligatory. Shapes in the image with assigned edges are processed preferentially, as figures, at the expense of unconstrained ground. The borders of discrete shapes are unambiguous and neurophysiological studies have shown that the response of cells stimulated by parts of such borders is not dependent on whether the particular figure is or is not the subject of the component of attention that is sustained (Qiu et al., 2007). A recent model proposed by Craft et al. (2007) and Qiu et al. (2007) suggests, however, that the mechanisms that facilitate the spontaneous segregation of figure from ground might also serve as a handle for selective attention. Their model is analogous to that of Wilson et al. (1997) in that it proposes summation of curvature information in cortical V4. The grouping cells of the model of Craft et al. though are required to sum information in the assignment of border ownership over linear scales of >20° (Zhou, Friedman, & von der Heydt, 2000) a much larger area that that suggested by Wilson et al. Our results demonstrate that summation of coherent orientation information can occur over areas with diameters of at least 20°. Also, consonant with our findings, the grouping cells proposed by Craft et al. have annular receptive fields. If such grouping cells do subserve selective attention, then they might be recruited in the analysis of texture within circular and annular regions of the visual field. As we have shown, noise external to circular and annular regions can be excluded from analysis, allowing much greater sensitivity to texture within the selectively attended region. 
Acknowledgments
This research was supported by Australian Research Council Grant DP0666206 to D.R.B. 
Commercial relationships: none. 
Corresponding author: J. Edwin Dickinson. 
Email: edwind@cyllene.uwa.edu.au. 
Address: School of Psychology, University of Western Australia, 35 Stirling Highway, CRAWLEY WA 6009, Australia. 
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Figure 1
 
Examples of test stimuli. Stimuli were Glass patterns comprised of pairs of dots. Signal dot pairs were oriented coherently (concentrically in examples A and B, and radially in C and D). Noise dot pairs were oriented at random. Signal regions were circular (A and B) or annular (C and D). The outer radius of the circular signal region and the inner radius of the annular signal region were varied across conditions. The circular signal region could be surrounded by noise (B) or not (A). Similarly, the annular signal region could surround noise (D) or not (C). The signal regions of all of these examples have 50% of their dot pairs coherently oriented (180 of 360 dot pairs). Examples B, C, and D have dot pairs extending to the maximum outer radius of 10° and can be used as a scale. The circular signal regions of A and B have radii of 6°. The inner radii of the annular signal regions of examples C and D are 8°.
Figure 1
 
Examples of test stimuli. Stimuli were Glass patterns comprised of pairs of dots. Signal dot pairs were oriented coherently (concentrically in examples A and B, and radially in C and D). Noise dot pairs were oriented at random. Signal regions were circular (A and B) or annular (C and D). The outer radius of the circular signal region and the inner radius of the annular signal region were varied across conditions. The circular signal region could be surrounded by noise (B) or not (A). Similarly, the annular signal region could surround noise (D) or not (C). The signal regions of all of these examples have 50% of their dot pairs coherently oriented (180 of 360 dot pairs). Examples B, C, and D have dot pairs extending to the maximum outer radius of 10° and can be used as a scale. The circular signal regions of A and B have radii of 6°. The inner radii of the annular signal regions of examples C and D are 8°.
Figure 2
 
Discrimination thresholds plotted against area of a circular signal region for a constant number of dot pairs. All stimuli in this set of conditions contained 250 dot pairs and so dot pair density varied with circle radius. The regions of the stimuli external to the signal region were empty. Reported thresholds and error bars for each condition, for this and subsequent figures, are the means and standard deviations of five staircases. Power functions fitted to the data have indices consistent with zero showing that discrimination thresholds are independent of area when the total number of dot pairs is constant. The errors quoted for the indices of the power functions in these and subsequent graphs are the 95% confidence intervals.
Figure 2
 
Discrimination thresholds plotted against area of a circular signal region for a constant number of dot pairs. All stimuli in this set of conditions contained 250 dot pairs and so dot pair density varied with circle radius. The regions of the stimuli external to the signal region were empty. Reported thresholds and error bars for each condition, for this and subsequent figures, are the means and standard deviations of five staircases. Power functions fitted to the data have indices consistent with zero showing that discrimination thresholds are independent of area when the total number of dot pairs is constant. The errors quoted for the indices of the power functions in these and subsequent graphs are the 95% confidence intervals.
Figure 3
 
Discrimination thresholds plotted against area of signal regions for stimuli with circular and annular signal regions and no dot pairs outside these regions. Icons have been added to two of the graphs illustrating the sizes and shapes of the regions containing dot pairs. The positions on the graphs where examples A and C in Figure 1 would lie are also marked. All data sets are well represented by power functions. The top row of graphs display thresholds for stimuli with circular and the bottom row annular signal areas. The dashed lines in the bottom row are the fits to the data of the top row. The indices of the power functions do not differ significantly.
Figure 3
 
Discrimination thresholds plotted against area of signal regions for stimuli with circular and annular signal regions and no dot pairs outside these regions. Icons have been added to two of the graphs illustrating the sizes and shapes of the regions containing dot pairs. The positions on the graphs where examples A and C in Figure 1 would lie are also marked. All data sets are well represented by power functions. The top row of graphs display thresholds for stimuli with circular and the bottom row annular signal areas. The dashed lines in the bottom row are the fits to the data of the top row. The indices of the power functions do not differ significantly.
Figure 4
 
Discrimination thresholds plotted against area of signal regions for stimuli with noise dot pairs outside the signal regions. In the icons illustrating the stimuli, the regions including signal and noise dot pairs are dark gray and the regions containing only noise are light gray. The positions on the graphs where examples B and D in Figure 1 would lie are marked. All data sets are again well represented by power functions with similar indices.
Figure 4
 
Discrimination thresholds plotted against area of signal regions for stimuli with noise dot pairs outside the signal regions. In the icons illustrating the stimuli, the regions including signal and noise dot pairs are dark gray and the regions containing only noise are light gray. The positions on the graphs where examples B and D in Figure 1 would lie are marked. All data sets are again well represented by power functions with similar indices.
Figure 5
 
Comparison of data from this study with those of Mandelli and Kiper (2005) and Wilson et al. (1997). Coherence thresholds (as a percentage of the total number of dot pairs within the critical radius) are plotted against the critical radius. All data shown are for concentric patterns with circular signal areas. The signal areas in the stimuli of Wilson et al. (1997) were surrounded by a region containing noise dot pairs while those of Mandelli and Kiper (2005) were not. The corresponding data from this study are also plotted. A power function is a good fit to the data over the whole range of radii.
Figure 5
 
Comparison of data from this study with those of Mandelli and Kiper (2005) and Wilson et al. (1997). Coherence thresholds (as a percentage of the total number of dot pairs within the critical radius) are plotted against the critical radius. All data shown are for concentric patterns with circular signal areas. The signal areas in the stimuli of Wilson et al. (1997) were surrounded by a region containing noise dot pairs while those of Mandelli and Kiper (2005) were not. The corresponding data from this study are also plotted. A power function is a good fit to the data over the whole range of radii.
Figure 6
 
Discrimination thresholds plotted against area of signal regions: Signal constrained to sectors of an annulus. The signal regions for these conditions were four sectors of an annulus with an inner radius of 6°. The sectors represented 100%, 50%, or 25% of the annulus. Icons on the graph illustrate the signal and noise distribution within the stimuli. Dark-colored regions of the icons contain signal and noise dot pairs, the light-colored regions contained noise pairs only. The dashed lines are the fits to the thresholds for the annular stimuli reported in Figure 4. The indices of the fitted power functions are small indicating almost perfect integration of signal and noise around the annulus.
Figure 6
 
Discrimination thresholds plotted against area of signal regions: Signal constrained to sectors of an annulus. The signal regions for these conditions were four sectors of an annulus with an inner radius of 6°. The sectors represented 100%, 50%, or 25% of the annulus. Icons on the graph illustrate the signal and noise distribution within the stimuli. Dark-colored regions of the icons contain signal and noise dot pairs, the light-colored regions contained noise pairs only. The dashed lines are the fits to the thresholds for the annular stimuli reported in Figure 4. The indices of the fitted power functions are small indicating almost perfect integration of signal and noise around the annulus.
Figure 7
 
Discrimination thresholds plotted against area of signal regions for interleaved stimuli with noise external to the signal regions. The indices of the fitted power functions are substantially smaller than those fitted to data from independent staircases (see Figure 4). This indicates that in the absence of prior knowledge of the size and topology of the signal region observers default to integrating signal and noise over the whole stimulus area.
Figure 7
 
Discrimination thresholds plotted against area of signal regions for interleaved stimuli with noise external to the signal regions. The indices of the fitted power functions are substantially smaller than those fitted to data from independent staircases (see Figure 4). This indicates that in the absence of prior knowledge of the size and topology of the signal region observers default to integrating signal and noise over the whole stimulus area.
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