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Article  |   September 2015
Global shape processing: A behavioral and electrophysiological analysis of both contour and texture processing
Author Affiliations
  • Vanessa K. Bowden
    University of Western Australia, School of Psychology, Perth, Western Australia, Australia
    vanessa.bowden@uwa.edu.au
  • J. Edwin Dickinson
    University of Western Australia, School of Psychology, Perth, Western Australia, Australia
    edwin.dickinson@uwa.edu.au
  • Allison M. Fox
    University of Western Australia, School of Psychology, Perth, Western Australia, Australia
    allison.fox@uwa.edu.au
  • David R. Badcock
    University of Western Australia, School of Psychology, Perth, Western Australia, Australia
    david.badcock@uwa.edu.au
Journal of Vision September 2015, Vol.15, 18. doi:10.1167/15.13.18
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      Vanessa K. Bowden, J. Edwin Dickinson, Allison M. Fox, David R. Badcock; Global shape processing: A behavioral and electrophysiological analysis of both contour and texture processing. Journal of Vision 2015;15(13):18. doi: 10.1167/15.13.18.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

The number of corners on the boundary of a closed contour is thought to be particularly critical for shape detection and discrimination. The aim of the current study was to examine the relative contribution of the number of corners and the angle between corners to shape discrimination in complex visual scenes as well as to determine the time course and neural substrates of global shape processing based on the presence or absence of these specific features. In Experiment 1, event-related potentials were recorded while participants discriminated between two radial frequency (RF) patterns with the same maximum local curvature defining corners but varying arrangements of those corners. The results showed that the angle separating corners was more critical than the overall number of corners for discrimination performance. An enhanced negativity (posterior N220) over the occipital lobe was elicited following the presentation of an RF with three modulation cycles (RF3) but not following a circle, suggesting that the posterior N220 is sensitive to variation in curvature on a contour. In Experiment 2, we confirm the primary effect of the presence of corners on the amplitude of the posterior N220 component and extend the stimuli to include shapes defined by texture. Source localization on the N170 and N220 components was conducted in Experiment 2, and a source in cortical area V4 was identified. These findings suggest that corners contain vital information for the discrimination of shapes. Additionally, this study shows that the perceptual characteristics and neuroanatomical substrates can be detected using electrophysiological measures.

Introduction
The human visual system is capable of efficiently processing the visual information in a scene to reliably recognize critical objects. The processing of local orientation information, critical for detecting shape boundaries, begins in area V1 of the visual cortex (Blakemore & Campbell, 1969; Ferster & Miller, 2000; Hubel & Wiesel, 1968; Loffler, 2008). The resulting visual representation is then processed through a hierarchy of cortical areas (Op de Beeck, Torfs, & Wagemans, 2008), each with increasing receptive field sizes (Felleman & Van Essen, 1991; Grill-Spector & Malach, 2004; Lennie, 1998; Wilson & Wilkinson, 2015). The representation continues through to size- and viewpoint-invariant representations of shape in higher cortical regions, such as the lateral occipital cortex (Grill-Spector, Kourtzi, & Kanwisher, 2001; Kourtzi & Kanwisher, 2000; Sawamura, Georgieva, Vogels, Vanduffel, & Orban, 2005; Silson et al., 2013) and inferior temporal cortex (Afraz & Cavanagh, 2009). The intermediate processes whereby discrete local elements are combined to form a global shape are not yet fully understood. 
Many shapes can be captured as deformations of a circular prototype (Bell, Gheorghiu, Hess, & Kingdom, 2011; Dumoulin & Hess, 2007; Loffler & Wilson, 2001; Wilkinson, Wilson, & Habak, 1998), and there is strong evidence to suggest that intermediate shape representations may be based in area V4 of the extrastriate cortex (Ungerleider, Galkin, Desimone, & Gattass, 2008). Single cell recordings in macaque V4 support this conclusion by showing that a significant proportion of V4 neurons are selective for concentric, as opposed to parallel or random, patterns (Gallant, Connor, Rakshit, Lewis, & Van Essen, 1996; Gallant, Shoup, & Mazer, 2000). Pasupathy and Connor (2001, 2002) also suggest a population code exists for V4 neurons, consistent with a circular prototype. In their model, shape is defined based on the specific deviations from circularity along the contour. They identified curvature (e.g., convex or concave) and the location of each feature with respect to the object's center as being key to shape construction (Connor, 2004; Kempgens, Loffler, & Orbach, 2013; Pasupathy & Connor, 2002). The number of points of maximum curvature (or corners) on the boundary of a closed contour is thought to be particularly critical for shape detection (Loffler, Wilson, & Wilkinson, 2003; Wang & Hess, 2005; Wilkinson et al., 1998). However, recent psychophysical evidence (Bell, Dickinson, & Badcock, 2008; Dickinson, Bell, & Badcock, 2013; Poirier & Wilson, 2010) also supports the view that the angle separating corners is very important, which would be consistent with the V4 model proposed by Pasupathy and Connor (2001, 2002). The first aim of this paper is to determine which of these two features, the number of corners or the angle between corners, is most important for intermediate shape processing. 
Most prior studies have presented single contours in otherwise empty fields (Bell et al., 2008; Loffler et al., 2003; Pasupathy & Connor, 2001, 2002) whereas shape discrimination is naturally performed in cluttered scenes. Therefore, in this study, we examine the contribution of these critical features to shape discrimination in more complex scenes. Fields of Gabor patches were used to create stimuli in which the average local orientation information remained approximately constant regardless of the shape formed by aligning a subset of elements (Wang & Hess, 2005). 
Similar Gabor field stimuli have previously been used to investigate contour integration mechanisms for collinear strings of elements that create a sinuous path in randomly oriented Gabor patches (Field, Hayes, & Hess, 1993; Hess, Hayes, & Field, 2003). Observers' detection of a closed collinear path is more likely due to global mechanisms than local ones (Schmidtmann, Gordon, Bennett, & Loffler, 2013) because contour closure (e.g., a circle compared to an “S” shape with the same curvature and number of elements) has a detection performance advantage both as a solitary path and in a field of noise (Mathes & Fahle, 2007). 
Radial frequency (RF) patterns are used here to define different shapes. RF patterns were originally used by Wilkinson et al. (1998) as precisely controlled stimuli for investigating sensitivity to global shape. An RF pattern is a sinusoidal modulation applied to the radius of a circle, with which the frequency of the function determines how many cycles of modulation would be required to cover the full extent of the circumference. RF patterns with fewer than 10 cycles of deformation have been shown to involve global processing whereas deformation in shapes with higher RF numbers is detected as local contour deviations (Bell & Badcock, 2009; Loffler et al., 2003). RF patterns have also been shown to be globally pooled when the contour is sampled by discrete Gabor patches instead of a solid, continuous contour (Dickinson, Han, Bell, & Badcock, 2010; Tan, Dickinson, & Badcock, 2013). 
In addition to employing behavioral measures in the current experiments, recordings of the brain's electrical activity elicited in response to presentations of different RF shapes are also used to assess the time course and cortical location of the response to the specific shape features identified. Mathes, Trenner, and Fahle (2006) previously measured the electrophysiological response to circular arcs, during which the contour was defined by aligning Gabor elements to form a path in a background of randomly oriented noise. They found that the presence of a shape was associated with an increased negativity approximately 150 ms after stimulus onset across the occipital and parietal electrodes (the N1 component in the event-related potential [ERP] waveform). In addition to this, a complete contour, such as a circle, produces a larger N1 compared to an incomplete contour at occipital electrodes (Tanskanen, Saarinen, Parkkonen, & Hari, 2008). These studies suggest that the N1 may be one of the earliest cortical indicators of global shape, and it might be used to determine whether a closed contour is present in randomly oriented noise. 
Similar studies have been conducted using stimuli in which shape is defined by texture rather than a contour. Coherent structure in a Glass pattern (fields of randomly placed dot stimuli in which dot pairs are oriented to form a coherent global structure; Glass, 1969) increases the N1 amplitude more than a pattern composed of randomly oriented elements at occipital electrode sites, and a concentric coherent arrangement elicits a larger amplitude than either radial or parallel arrangements (Ohla, Busch, Markus, & Herrmann, 2005; Ostwald, Lam, Li, & Kourtzi, 2008; Pei, Pettet, Vildavski, & Norcia, 2005; Swettenham, Anderson, & Thai, 2010). It is therefore likely that global orientation coherence in Glass pattern stimuli affects the N1 component despite a lack of connected or continuous contours. 
The posterior N220 component is a later negativity that peaks approximately 220 ms after stimulus presentation. This component has been linked to global processing by several studies that have demonstrated that the N220 is the first indicator of a divergence between global (whole shape) and local (components from which the shape is constructed) levels in object processing (Evans, Shedden, Hevenor, & Hahn, 2000; Heinze & Munte, 1993). Previous studies using contour closure to elicit global shape processing place the neural generator of the N220 in occipitotemporal regions corresponding to the intermediate shape area V4 (Doniger et al., 2000; Gallant et al., 1996; Pasupathy & Connor, 2001, 2002). If the N220 is an indicator of the shape integration processes occurring in area V4, then given Wilkinson et al.'s (1998) findings, it should show selectivity for intermediate shape features, such as curvature variation on a contour. 
In the current study, Experiment 1 examines the relative importance of two critical features on shape processing in the human visual system: the total number of corners on a contour and the angle separating the corners. In addition to behavioral performance measures, ERPs were recorded while participants discriminated between two RFs with the same local curvature but varying arrangements of corners. In Experiment 2, we confirm the primary effect of the presence of corners on the N1 and N220 components and extend the stimuli to include shapes defined by texture. Source localization on the N1 and N220 components was conducted in Experiment 2
Experiment 1
If the total number of corners is critical to shape representation, then behaviorally it should be harder to discriminate between shapes when the number of corners is the same but the angle between corners differs. If the angular difference between corners is also important (Bell et al., 2008; Dickinson et al., 2013), then shapes should be harder to tell apart when the angle between corners is the same—regardless of the total number of corners present. In addition to investigating the behavioral differences elicited by different shape comparisons, Experiment 1 also included an investigation of the electrophysiological differences elicited by these comparisons. 
In this first experiment, we predict that the presence of any global arrangement within a field of randomly oriented Gabor patches should lead to an enhanced N1 component because the N1 has been linked to the presence of a coherent structure (Ohla et al., 2005; Swettenham et al., 2010). Any effect of specific shape attributes, such as the number and placement of corners on the contour, would more likely be evident in later components, including the N220. These later components have been linked to more global processing of shape information (e.g., Evans et al., 2000; Heinze & Munte, 1993). 
Methods
Participants
Twenty-one participants aged between 19 and 46 years of age (mean 22.4) volunteered for Experiment 1. Nine participants were male, and one participant was left-handed. ERP data from four participants were excluded due to high impedances across several sites of interest. No reimbursement or payment was provided. A further 20 people aged between 18 and 46 years (mean 25.2) were recruited to participate in Experiment 2. Six participants were male, and three were left-handed. These participants received a small stipend to reimburse them for their time. EEG data from one participant were excluded due to high electrical impedances. 
All participants provided written informed consent, and these studies were approved by the Human Research Ethics Committee at the University of Western Australia in accordance with the Declaration of Helsinki. All participants reported normal or corrected-to-normal visual acuity. 
Stimuli
Shapes were constructed by aligning Gabor patches (a luminance-defined sinusoidal grating weighted by a Gaussian window; Daugman, 1984) according to an underlying contour embedded in a field of random elements. The spatial frequency of the carrier gratings in this experiment was 5.1 c/°, and all patches were in cosine phase. The diameter of the circular Gaussian window at the point of half contrast was 0.25° of visual angle. Equation 1 defines the RF patterns used to create the shape contours:  where r and θ are the radius and angle (expressed in radians) of the contour in polar coordinates, r0 is the mean radius of the shape, A is the amplitude of deformation expressed as a proportion of the mean radius, ω is the frequency of modulation (RF number), and φ is the phase (rotational orientation) of the shape. The rotation of each RF pattern was randomized by varying the phase. The amplitude used here was  This amplitude ensures that all noncircular shapes have the same curvature at each of the points of maximum curvature and no concavities between the corners (Dickinson, McGinty, Webster, & Badcock, 2012). Therefore, differences between shapes cannot be due to the local differences in peak curvature or the presence of indentations. Stimuli used here include RF3 (ω = 3), RF4 (ω = 4), and RF0 (ω = 0 or A = 0). For an RF3, the angle subtended by adjacent corners is 120°, and for an RF4 the angle is 90°.  
For shape stimuli with which the radial deformation was only applied to a fraction of the whole contour, a smoothing function was applied to avoid the sharp transition between deformed and nondeformed segments of the contour (see Figure 1 for an illustration of the construction of the RF path, including smoothing function). This smoothing function was introduced by Loffler et al. (2003), and it was applied to a continuous RF contour. Here, the smoothing function is applied to the position and orientations of Gabor patches along the implied contour. A first derivative of a Gaussian (D1) was fitted to the contour segment on the transition between deformation and the undeformed circular remainder. In shape conditions in which only a segment of contour was deformed, the pattern was defined as follows (Loffler et al., 2003):       where θcenter is the central location of the deformed segment of contour, and N is the number of cycles. The B and σ parameters of the D1 function were set to match the sine wave's maximum and minimum deviations from the base circle and its maximum slope. Equation 2 is defined for an odd number of cycles, and the angular phases for the D1 were  The pattern phase (φ) was set to create a zero crossing at θcenter:  Each shape was defined by 24 individual Gabor patches aligned to form a sampled RF contour with patches aligned tangentially to the path defined by the equations above. The contour was surrounded by randomly oriented noise patches, resulting in the appearance of a field of Gabor elements with an embedded contour (see Figure 2). The Gabor patches were arranged in a 15 × 15 element grid with 1° separating the centers of adjacent cells on the grid. The entire Gabor field thus subtended 15° with each patch located within a 1° square in the 225-element array. In experimental conditions in which a shape was present in the field, the 24 patches nearest to the patches representing the contour path were replaced by those contour elements. The position of individual noise Gabors was jittered within the square by up to half the width of the square to prevent the appearance of a regular grid. This constraint was introduced to ensure that there was no overlap between adjacent elements in the field.  
Figure 1
 
An illustration of the construction of the RF path. This path is an RF3 pattern with two cycles of modulation. The pattern comprises a single cycle of sinusoidal modulation with the two halves of a D1 (first derivative of a Gaussian) function concatenated to the two ends of the sinusoid. The D1 function matches the sine function in gradient at the point at which the two are joined (at zero crossings of the sinusoidal modulation) and in maximum amplitude. The D1 function thereby allows incomplete RF patterns with two or more cycles of sinusoidal modulation to be approximated while allowing for a smooth transition back into the circular remainder of the pattern. For RF patterns with the full complement of cycles of modulation, no smoothing function is required.
Figure 1
 
An illustration of the construction of the RF path. This path is an RF3 pattern with two cycles of modulation. The pattern comprises a single cycle of sinusoidal modulation with the two halves of a D1 (first derivative of a Gaussian) function concatenated to the two ends of the sinusoid. The D1 function matches the sine function in gradient at the point at which the two are joined (at zero crossings of the sinusoidal modulation) and in maximum amplitude. The D1 function thereby allows incomplete RF patterns with two or more cycles of sinusoidal modulation to be approximated while allowing for a smooth transition back into the circular remainder of the pattern. For RF patterns with the full complement of cycles of modulation, no smoothing function is required.
Figure 2
 
Sample stimuli presented across five experimental conditions. In each condition, the comparison shape (left) and the RF3 pattern (right) were presented with equal frequency.
Figure 2
 
Sample stimuli presented across five experimental conditions. In each condition, the comparison shape (left) and the RF3 pattern (right) were presented with equal frequency.
Experimental conditions
Participants completed a single-interval, forced-choice reaction time task with separate data collated for each of the two choices. Task instructions were presented on the screen prior to starting each condition. Five experimental conditions were employed, and the participant's task was to identify which of two different stimuli selected from the set shown in Figure 2 had been presented. Within each of the experimental conditions, one of the two different stimuli presented was always an RF3. The second shape depended on the condition and is referred to here as the comparison stimulus. When a stimulus appeared on the screen, participants were asked to identify which of the two shapes was present by pressing one of two previously assigned keys on a standard keyboard as quickly as possible. Participants saw the RF3 and the comparison shape with equal probability within each block (equal numbers of either stimuli). 
In the first condition (RF3 vs. noise), the comparison stimulus consisted entirely of randomly oriented Gabor patches. A correct response required only the detection of any nonrandom arrangement of Gabor elements on the screen to distinguish between the two different stimuli (shape detection task). This was expected to be the simplest task behaviorally because only the earliest stages in the visual processing hierarchy would need to be accessed before a judgment could be reached (Machilsen & Wagemans, 2011). For example, a response could be made by detecting the presence of any approximately collinear Gabor patches in the stimulus when the collinearity has occurred with higher frequency than in the noise field—in which accidental alignment could still occur. 
The second condition (RF3 vs. circle) required a comparison between two stimuli that both contained a closed contour shape. In this condition, participants needed to engage in shape comparison to make the discrimination, as opposed to contour fragment detection in the RF3 versus noise comparison. The key difference between an RF3 and a circle is change in curvature due to variation in the radius along the implied contour. A circle has a constant rate of curvature, and an RF3 has three points of curvature maxima, so successful discrimination between these two stimuli could involve processing the contour curvature to detect any curvature variation. 
The remaining conditions were designed to assess the relative influences of the number of corners and the polar angle separating the corners on shape discrimination. In the third condition, the shapes presented (RF3 vs. RF4) differed both in the polar angle subtended by adjacent corners and also in the total number of corners present. This condition thus provided a performance baseline against which the subsequent two conditions, which independently vary the degree of angular separation and the number of corners, could be compared. In condition four, the number of corners was the same in both shapes whereas the degree of angular separation was varied. This was done by comparing the RF3 to an RF4 with only three of the corners present (three-cycle RF4). The angular separation between each point of maximum curvature in the three-cycle RF4 was 90°, and in the RF3 it was 120°. The fifth condition controlled for the angular difference between corners by comparing an intact RF3 with a two-cycle RF3. In this condition, the angular separation between corners was the same for both shapes (120°), but the total number of corners on the contour was different with three points of maximum curvature on the RF3 shape and two points of maximum curvature on the two-cycle RF3. If participants encoded angular separation as a more important feature than the number of corners in this shape discrimination task, we would expect this condition to be more difficult than condition four (RF3 vs. three-cycle RF4). 
Apparatus
Testing was completed in a darkened room (surfaces reflected <1 cd/m2) with participants seated 60 cm from an NEC MultiSync V500 CRT monitor with a 60-Hz refresh rate. The background luminance of the stimuli was 9.14 cd/m2, and the Michelson contrast was 0.967. Stimuli were displayed using Presentation (Neurobehavioral Systems version 14.5) on a PC, and participants responded via key press on a standard QWERTY keyboard. The PC was running an NVIDIA RIVA TNT2 Model 64 graphics card, and feedback tones were played using Auriga stereo speakers. 
Behavioral task and procedure for Experiments 1 and 2
Each trial commenced with a small white 500-ms fixation cross, following which the stimulus (RF3 or comparison) was presented for 160 ms. After the stimulus offset, the screen remained blank until a response key was pressed. Following the response, a 500-ms pause on the blank, mean luminance screen occurred before feedback to indicate either a correct (1000-Hz tone) or incorrect (500-Hz tone) choice. Within each condition, a total of 200 trials were presented, and the RF3 and comparison shape were presented 100 times each. The order of presentation was random. Self-paced breaks were available between each condition, and the order of conditions was randomized. Participants were instructed to respond with either a left (“Z”) or a right (“/”) key press, depending the shape presented. Both speed and accuracy were emphasized, and the keyboard allocation for the different stimuli was counterbalanced across participants. 
Median response times (RTs) for each participant, across each condition, were extracted to minimize the impact of skew in the RT distribution. An increase in RT would suggest that a particular comparison is more difficult and that either shape processing is slower or the representation needs to be processed further before a decision can be reached. 
Electrophysiological recording for Experiments 1 and 2
In Experiment 1, the EEG was recorded from electrodes positioned according to the International 10–20 system at sites Fp1, Fp2, F7, F3, Fz, F4, F8, FT7, FC3, FCz, FC4, FT8, T7, C3, Cz, C4, T8, TP7, CP3, CPz, CP4, TP8, P7, P3, Pz, P4, P8, O1, Oz, and O2 using a 32-channel EEG Quik-cap (Compumedics Neuroscan). Eye blinks were monitored with vertical electro-oculogram (VEOG) by electrodes placed two centimeters above and below the left eye. The ground electrode was placed at AFz, and continuous data were referenced to the linked mastoids with an averaged reference computed offline. The EEG was recorded with a Synamps 32-channel amplifier. 
A different cap and amplifier setup was used in Experiment 2. In Experiment 2, EEG was recorded from electrode sites positioned at sites Fp1, Fp2, F7, F3, Fz, F4, F8, FT9, FC5, FC1, FCz, FC2, FC6, FT10, T7, C3, Cz, C4, T8, TP9, CP5, CP1, CP2, CP6, TP10, P7, P3, P4, P8, PO9, O1, O2, PO10, and Iz using a 40-channel Easy Cap EC40 (EASYCAP GmbH, Herrsching-Breirbrun, Germany) and a Nuamps 40-channel amplifier. Eye blinks were monitored with VEOG, and continuous data were referenced to the right mastoid with an averaged reference computed offline. 
For both experiments, scalp electrode impedances were reduced below 5 kΩ prior to recording using saline gel. The signal was sampled at 250 Hz, and an online band-pass filter was applied with a low-frequency cutoff at 0.05 Hz (6 dB/octave roll-off) and a high-frequency cutoff at 30 Hz (24 dB/octave roll-off). In Experiment 1, an additional off-line band-stop filter (50–70 Hz, 96 dB/octave roll-off) was applied to the data to remove potential electrical interference from the monitor and the main power. 
Off-line analysis of the ERP waveform was completed in SCAN 4.3 (Compumedics Neuroscan, Charlotte, NC). The ERP epoch was defined as 100 ms prestimulus to 500 ms poststimulus and baseline corrected around the 100 ms prestimulus interval. Epochs in which the waveform was contaminated by eye blinks were corrected using the in-built algorithm. Artifact rejection was applied to exclude all epochs in which the voltage exceeded ±100 μV. 
ERP data analysis
ERP averages were calculated for all five conditions separately for both the RF3 and comparison shapes. Therefore, there are 10 different averages reported here (two different shapes for each of the five conditions). There were no systematic effects of behavioral accuracy on the stimulus-locked ERPs at any electrode sites, demonstrated by average intraclass correlations greater than 0.95 between the ERPs elicited in response to correct-only and incorrect-only trials. This suggests that the differences in behavioral accuracy are not affecting early perceptual processes in the ERP waveforms. The ERP analyses reported in this study therefore include all trials regardless of behavioral response accuracy. When sphericity was violated, a Greenhouse-Geisser correction was applied. 
Behavioral results
The response accuracy and RT elicited by both shapes in each of the five comparison conditions were compared. There was no significant effect of shape type (RF3 vs. comparison shape) on either accuracy or RT within any of the five conditions. Because there was no effect of shape type within conditions, the behavioral results reported here only use the response to the RF3 stimulus to make comparisons between conditions. Therefore, any differences observed between conditions are attributable to the type of comparison made within each condition and not to physical differences in the particular stimulus responded to. Summary statistics are presented in Figure 3. A one-way repeated-measures ANOVA found that there was a significant overall effect of condition on accuracy, F(4, 80) = 14.38, p < 0.01, partial η2 = 0.42. Bonferroni corrected, paired-samples t tests showed that accuracy for the two-cycle RF3 comparison condition was significantly lower than all other conditions. There were no differences in accuracy between any of the other conditions. 
Figure 3
 
Accuracy (lower) and RT (upper) means for the five conditions in response to the RF3 stimuli only; the y-axis labels indicate the comparison shape in each condition. 95% confidence intervals (between subjects) provided. One asterisk (*) indicates p < 0.05, and two asterisks indicate p < 0.01. Note that for the RT graph, all other stimuli conditions are slower than the RF3 versus noise condition.
Figure 3
 
Accuracy (lower) and RT (upper) means for the five conditions in response to the RF3 stimuli only; the y-axis labels indicate the comparison shape in each condition. 95% confidence intervals (between subjects) provided. One asterisk (*) indicates p < 0.05, and two asterisks indicate p < 0.01. Note that for the RT graph, all other stimuli conditions are slower than the RF3 versus noise condition.
A one-way repeated-measures ANOVA showed a significant overall effect of the comparison condition on RT as well, F(4, 80) = 34.38, p < 0.01, partial η2 = 0.69. Bonferroni corrected, paired-samples t tests (see Figure 3) indicated that participants were slower to respond when the comparison shape was a circle compared to noise. Participants were not significantly slower when responding to the three-cycle RF4 comparison condition compared to the RF4 comparison condition. Lastly, participants were slower again when responding to the two-cycle RF3 comparison condition than the three-cycle RF4 comparison condition. Because it was harder to discriminate between two shapes when the angle between corners was the same than it was to discriminate between shapes when the number of corners was the same (slower in the two-cycle RF3 comparison condition than the three-cycle RF4 comparison condition), it is suggested that the angular separation between corners is a more salient shape feature than the total number of corners. 
To confirm this, we conducted two paired-samples t tests comparing performance on the RF3 in the three-cycle RF4 and two-cycle RF3 conditions relative to the RF3 in the RF4 condition (baseline). As Figure 3 shows, there was a nonsignificant increase in RT relative to the RF4 baseline condition when participants had to discriminate the RF3 from a three-cycle RF4, t(20) = 2.03, p = 0.06, Cohen's d = 0.51. However, when they had to discriminate between the RF3 and two-cycle RF3, the increase in RT was significant, t(20) = 7.24, p < 0.01, Cohen's d = 1.55. These results show that the effect size is larger when the comparison stimuli are matched on angular separation instead of the number of corners. The accuracy data also supports this because the two-cycle RF3 condition yields significantly lower accuracy than the baseline, but the three-cycle RF4 is no different. 
Electrophysiological results
N1 component
The N1 component was the most negative amplitude between 130 and 170 ms (Herrmann & Bosch, 2001; Itier & Taylor, 2004; Ohla et al., 2005). The mean amplitudes of the N1 peak are summarized in Figure 4, and Figure 5 shows the averaged waveforms at occipital electrode sites for each of the five experimental conditions, superimposing the waveforms elicited by the RF3 stimulus (dashed line) and each comparison shape (solid line). 
Figure 4
 
Means and 95% confidence intervals (between subjects) for N1 peak amplitude in microvolts across all five conditions for both the RF3 and the comparison shape at electrodes O1, Oz, and O2.
Figure 4
 
Means and 95% confidence intervals (between subjects) for N1 peak amplitude in microvolts across all five conditions for both the RF3 and the comparison shape at electrodes O1, Oz, and O2.
Figure 5
 
Grand average waveforms at lateral occipital electrodes O1 and O2 and midline site Oz are presented. ERPs elicited in response to the presentation of RF3 stimuli are represented by the dotted line, and ERPs elicited in response to the comparison shape are represented by the solid line. The comparison shape varied depending on the condition, and the five comparison shapes are noise, circle, RF4, three-cycle RF4, and two-cycle RF3, respectively. The y-axis represents electrical activity in microvolts (in increments of 1 μV, ranging from +8 to −12 μV, negative up), and the x-axis represents time in milliseconds, starting 50 ms prior to the onset of the stimulus and extending to 350 ms poststimulus in increments of 100 ms.
Figure 5
 
Grand average waveforms at lateral occipital electrodes O1 and O2 and midline site Oz are presented. ERPs elicited in response to the presentation of RF3 stimuli are represented by the dotted line, and ERPs elicited in response to the comparison shape are represented by the solid line. The comparison shape varied depending on the condition, and the five comparison shapes are noise, circle, RF4, three-cycle RF4, and two-cycle RF3, respectively. The y-axis represents electrical activity in microvolts (in increments of 1 μV, ranging from +8 to −12 μV, negative up), and the x-axis represents time in milliseconds, starting 50 ms prior to the onset of the stimulus and extending to 350 ms poststimulus in increments of 100 ms.
A three-factor, repeated-measures ANOVA was conducted to determine the effects of condition (five comparison conditions), shape (two shapes: RF3 and comparison), and site (three levels: O1, O2, Oz electrodes) on the N1 peak amplitude. There was no main effect of condition or shape, suggesting that the comparison between different shapes did not affect amplitude. There was an effect of site, F(1.50, 32) = 10.41, p < 0.01, partial η2 = 0.39, with the largest peak reported at the midline electrode Oz. There were no significant interactions. It can be concluded from this that the N1 peak amplitude does not appear to differ as a function of either the underlying shape or number of curvature maxima on the comparison stimulus. 
Posterior N220 component
As with the N1, the posterior N220 component is evident at occipital electrodes. Figure 5 shows that the N220 lacks a clear peak; therefore, the mean amplitude is used instead of the peak amplitude. The latency range over which mean amplitudes were measured was identified by analyzing difference waveforms across conditions (Guthrie & Buchwald, 1991), and the N220 was quantified as a mean amplitude from 200 to 228 ms (summarized in Figure 6). 
Figure 6
 
Means and 95% confidence intervals (between subjects) for posterior N220 mean in microvolts across all five conditions for both the RF3 and the comparison shape at electrodes O1, Oz, and O2.
Figure 6
 
Means and 95% confidence intervals (between subjects) for posterior N220 mean in microvolts across all five conditions for both the RF3 and the comparison shape at electrodes O1, Oz, and O2.
A three-factor, repeated-measures ANOVA was conducted with the factors condition (five levels), shape (two levels: RF3 and comparison), and site (three levels: O1, O2, Oz electrodes). As with the N1, the N220 was largest at Oz, F(2, 32) = 3.27, p = 0.051, partial η2 = 0.17. Unlike the N1, there was a significant main effect of shape type, F(1, 16) = 28.25, p < 0.01, partial η2 = 0.64, on mean amplitude. The main effect of shape suggests that the N220 can be used to distinguish between different shapes present in the Gabor field. There was also an interaction between condition and shape, F(2.44, 64) = 8.47, p < 0.01, partial η2 = 0.35, but no main effect of the condition. Because of this, post hoc two-factor, repeated-measures ANOVAs were conducted for each condition with site and shape as factors. 
In the RF3 versus noise condition, there was a main effect of shape on the N2 amplitude, F(1, 16) = 48.81, p < 0.01, partial η2 = 0.75, with the RF3 stimuli eliciting a significantly larger negative amplitude than the noise array. There was no effect of site or interaction between site and shape. There was also a significant main effect of shape in the RF3 versus circle condition, F(1, 16) = 13.33, p < 0.01, partial η2 = 0.46, with the RF3 eliciting a significantly larger N220 amplitude than the circle. This provides electrophysiological evidence for the N220 being sensitive to the specific shape arrangement within the Gabor field. There was also a main effect of site, F(2, 32) = 6.17, p < 0.01, partial η2 = 0.28, with the largest peak again occurring at the midline electrode Oz. There was no interaction between shape and site for the RF3 versus circle condition. There were no significant effects of either site or shape for any of the remaining three comparison conditions (RF4, three-cycle RF4, and two-cycle RF3). 
Experiment 1 discussion
The aim of the first experiment was to determine the relative significance of points of maximum curvature and the separation in polar angle to the internal representation of global shape and to then identify the electrophysiological correlates in the human brain using ERPs. The behavioral results support the conclusion that, once the corners are defined, a critical shape feature is the angular separation between points of maximum curvature (corners) on the boundary of a shape. We have demonstrated that RTs for discriminating between two shapes with the same number of corners but different angular separation between those corners were quicker than for two shapes with the same angular separation and a different number of corners. In other words, once the angle between corners has been matched, discriminating between two shapes becomes much more difficult. This supports recent work by Dickinson et al. (2013) who showed, using different methods, that that the discrimination of RF patterns is based on the periodicity of corners. 
The current findings support existing behavioral research that demonstrates points of maximum curvature are critical for shape construction in both threshold discrimination (Loffler et al., 2003) and suprathreshold (Attneave, 1954) experiments. Specifically, we show that the polar angle separating the points of maximum curvature on a closed contour is more important for discriminating between basic suprathreshold shapes than the number of corners. This is consistent with the argument suggesting polar coding of shape information (Bell et al., 2008; Dickinson et al., 2013; Dickinson et al., 2010; Pasupathy & Connor, 2001). 
It is unlikely that local differences between stimuli contributed to this effect. RF patterns with modulation frequencies less than this number have been shown to be globally pooled with detection thresholds well within the range of hyperacuity (Bell & Badcock, 2009; Hess, Wang, & Dakin, 1999; Loffler et al., 2003; Wilkinson et al., 1998). Therefore, the specific RF patterns used in this study (RF3s and RF4s) should all be processed within the global range. Although Schmidtmann et al. (2013) have argued that partial contours are not processed globally, several other recent studies have demonstrated global processing of sampled RF contours similar to those used here (Dickinson et al., 2010; Tan et al., 2013). 
There was also no difference in the peak curvature contained in the corners of the Gabor-sampled RF contours used here because the local curvature maxima were the same across all noncircular patterns used, including those with different RFs. In addition to this, all the contours were constructed from the same number of identical Gabor elements, so there was no variation in the average path luminance or contrast. The length of the implied underlying path to which the Gabor patches were aligned varied slightly depending on the shape presented, but the pattern of changes observed was inconsistent with the pattern of results observed here (the component amplitude effects did not correlate with path length). Based on this, it can be concluded that the local image attributes are unlikely to be responsible for the effects reported here. 
The behavioral results support the argument that corners are a critical shape feature and suggest that the angle between corners is most relevant. Although the ERP results were not able to distinguish between shapes with varying arrangements of corners (e.g., RF3 vs. RF4), they did provide evidence that, in addition to an enhanced N220 for the presence of global structure in an array, the N220 also differentiates between shapes with corners and those without. The novel finding of an enhanced N220 component provides electrophysiological evidence for the key role of corners more broadly in the cortical representation of shape. V4 is an excellent candidate region for the integration of local orientation information in RF patterns to form a basic representation of shape (see Gallant et al., 1996; Pasupathy & Connor, 2002, for primate studies and Gallant et al., 2000, for a human comparison). Experiment 2 investigates the source of the N220 component and extends the range of stimuli used to define shape to include textures. 
Experiment 2
Aligning Gabor patches to form a path is not the only way to form a shape; they can also be formed by illusory contours (Herrmann & Bosch, 2001; Murray et al., 2002; Seghier & Vuilleumier, 2006) or textures (Kurki & Saarinen, 2004; Tan, Bowden, Dickinson, & Badcock, 2015; Wilson, Wilkinson, & Asaad, 1997). Glass patterns (Glass, 1969) are texture stimuli that can be used to represent many different shape structures (Dickinson & Badcock, 2007). Glass patterns with circular structures have lower coherence detection thresholds than patterns in which the structure is parallel (Achtman, Hess, & Wang, 2003). Because of this difference, it has been suggested that there is a global processing advantage for circular structures in texture-defined shapes. 
ERP research using Glass pattern stimuli has demonstrated that the N220 component is selective for circular structure as opposed to radial or parallel structure (Tanskanen, Saarinen, Parkkonen, & Hari, 2008). Experiment 2 sought to address whether the same N220 enhancement, which occurs in response to shapes containing corners, exists when shape is defined by organized texture. This is of interest because it is not yet clear whether the N220 is only sensitive to shapes defined by a single contour or if implied curvature discontinuities in a texture also affect N220 amplitude. Experiment 2 also sought to identify where in the visual cortex global shape is processed. To do this, we attempted to localize the sources of both the N1 and N220 components. 
In this study, we determined whether the results reported in Experiment 1 (N1 not affected by the presence of corners on a contour, but N220 significantly enhanced by the presence of corners) could be replicated. It was predicted that the N1 and N220 would localize to extrastriate regions of the visual cortex, such as area V4 or V3a, which have been shown to be selective for the curvature information on a basic shape contour (Caplovitz & Tse, 2007; Mannion & Clifford, 2011; Pasupathy & Connor, 2002; Smith, Bair, & Movshon, 2002). 
Methods
Stimuli
The physical descriptions and mathematical parameters for the single, aligned contour stimuli used in this experiment are described in Experiment 1. In the current experiment, only the noise, circle, and RF3 stimuli were used because ERP results from Experiment 1 revealed no differences in the other comparison conditions. In addition to these single-contour shapes, texture-defined stimuli were also used. These stimuli were the same as the single-contour stimuli except that, instead of being aligned to a path, the orientation of every Gabor in the field was aligned tangentially to an underlying RF structure (see Tan et al., 2015). However, unlike the single-contour shapes, the position of all the elements was spatially jittered, again by up to half the width and height of the cell. As a result, there was no discernible path in the oriented Gabor field pattern (spatial misalignment caused by jitter significantly degrades path detection; Hayes, 2000). The lack of a path allowed the center of the patterns to be jittered by up to 200′ (3.33°) from the center of the screen to minimize the utility of monitoring local regions of the pattern because there was no longer a risk that part of the path could move beyond the array. 
Experimental conditions
There were two different shape comparison conditions and two different types of array used (single contour and texture), creating a total of four experimental conditions (see Figure 7). In the shape detection comparison, the stimulus presented either contained an RF3 or noise. In the shape discrimination comparison, participants had to identify the specific shape presented based on the presence or absence of corners and of a defined internal polar angle (RF3 vs. circle). The shape detection task makes it possible to assess the effect of the presence of a global structure in an array on the ERP response, and the shape discrimination task allows for the influence of curvature variation and the presence of corners to be measured. 
Figure 7
 
The top three figures show the stimuli used in the two texture conditions, and the bottom three figures are the single-contour stimuli. The comparison stimulus in the shape detection task is noise, and the comparison stimulus in the shape discrimination task is a circle. In the texture conditions, the orientations (but not positions) of all elements are consistent with the shape. In the single-contour conditions, both the position and orientation of 24 patches is aligned according to the underlying shape structure, and the remaining elements are randomized.
Figure 7
 
The top three figures show the stimuli used in the two texture conditions, and the bottom three figures are the single-contour stimuli. The comparison stimulus in the shape detection task is noise, and the comparison stimulus in the shape discrimination task is a circle. In the texture conditions, the orientations (but not positions) of all elements are consistent with the shape. In the single-contour conditions, both the position and orientation of 24 patches is aligned according to the underlying shape structure, and the remaining elements are randomized.
Behavioral results
Shape detection (RF3 vs. noise) and shape discrimination (RF3 vs. circle) data were analyzed separately (see Figure 8). Inspection of the Q-Q normal distribution plots (probability plots comparing two probability distributions by plotting their quantiles against each other) revealed that the median RTs and the accuracy data were approximately normally distributed. First, to determine if there was an effect of shape detection, the response accuracies (percentage) and reaction times (milliseconds) for the RF3 versus noise conditions were analyzed. Two-factor, repeated-measures ANOVAs were conducted on both the accuracy and response time data with array type (two levels: single contour and texture) and shape (two levels: RF3 and noise) as factors. 
Figure 8
 
Accuracy (lower) and RT (upper) means for the two conditions in response to the RF3 stimuli only; the y-axis labels indicate the comparison shape in each condition and 95% confidence intervals (between subjects) provided.
Figure 8
 
Accuracy (lower) and RT (upper) means for the two conditions in response to the RF3 stimuli only; the y-axis labels indicate the comparison shape in each condition and 95% confidence intervals (between subjects) provided.
Overall, participants maintained a high degree of accuracy, comparable to Experiment 1. There was a significant main effect of shape presence on response accuracy, F(1, 19) = 10.31, p < 0.05, partial η2 = 0.35, as participants were more accurate when responding to the noise than the RF3 stimuli. There was no effect of the array type on accuracy and also no significant interaction between the two factors. The RT ANOVA results indicated no significant main effects of either shape presence or array type in the detection task. Again, there was no interaction between shape presence and array type. 
In order to assess the effects of shape and array type in the shape discrimination task, in which participants were required to discriminate between an RF3 and a circle, two-factor, repeated-measures ANOVAs were again conducted. The factors were array type (two levels: single contour and texture) and shape (two levels: RF3 and circle). There was a significant effect of shape type on the response accuracy, F(1, 19) = 8.88, p < 0.05, partial η2 = 0.32, as participants were more accurate responding to the circle than to the RF3. There was also a main effect of the array type on the accuracy, F(1, 19) = 6.53, p < 0.05, partial η2 = 0.26, as responses to the single-contour stimuli were significantly more accurate than to the texture. There was no significant interaction between the two factors. The RT ANOVA results indicated significant main effects of both shape type and array type, F(1, 19) = 14.74, p < 0.05, partial η2 = 0.44; F(1, 19) = 14.00, p < 0.05, partial η2 = 0.42, respectively. RTs for the circle stimuli were consistently faster than responses to the RF3, and the responses to the single-contour stimuli were also significantly faster than to the texture stimuli. Again, there was no interaction between shape and array type. The behavioral results for the shape discrimination task show that participants were faster and more accurate when identifying the circle compared to the RF3 stimuli. They were also significantly quicker and more accurate when the shape was constructed from a single contour of aligned Gabor patches compared to the same shape represented by a texture. 
Electrophysiological results
The early negativities associated with the N1 and N220 were maximal at posterior sites, so electrodes O1, Iz, and O2 were therefore selected to be analyzed in further detail (see Figure 9 for ERP waveforms). Further analyses were conducted to determine whether there were any significant differences both within and between the different conditions. 
Figure 9
 
Grand average waveforms at lateral occipital electrodes O1 and O2 and midline site Iz are presented. ERPs elicited in response to the presentation of RF3 stimuli are represented by the dotted line, and ERPs elicited in response to the comparison shape are represented by the solid line. Shapes were defined by either a texture (aligning the orientation of all elements to form a texture) or a single contour (aligning 24 elements according to a single contour). The comparison shape varied depending on the condition, and the two comparison shapes were noise and circle. The y-axis represents electrical activity in microvolts (in increments of 1 μV, ranging from +8 to −12 μV, negative up), and the x-axis represents time in milliseconds, starting 50 ms prior to the onset of the stimulus and extending to 350 ms poststimulus in increments of 100 ms.
Figure 9
 
Grand average waveforms at lateral occipital electrodes O1 and O2 and midline site Iz are presented. ERPs elicited in response to the presentation of RF3 stimuli are represented by the dotted line, and ERPs elicited in response to the comparison shape are represented by the solid line. Shapes were defined by either a texture (aligning the orientation of all elements to form a texture) or a single contour (aligning 24 elements according to a single contour). The comparison shape varied depending on the condition, and the two comparison shapes were noise and circle. The y-axis represents electrical activity in microvolts (in increments of 1 μV, ranging from +8 to −12 μV, negative up), and the x-axis represents time in milliseconds, starting 50 ms prior to the onset of the stimulus and extending to 350 ms poststimulus in increments of 100 ms.
N1 component
To determine whether shape presence in the detection task affected the amplitude of the N1 component, a three-factor, repeated-measures ANOVA was conducted. The three factors included electrode site (three levels: O1, O2, and Iz), array type (two levels: single contour and texture), and shape (two levels: RF3 and noise). The ANOVA results are presented in Table 1
Table 1
 
Three-factor, repeated-measures ANOVA results for the N1, including F value, degrees of freedom, and partial eta squared. Notes: *p < 0.05.
Table 1
 
Three-factor, repeated-measures ANOVA results for the N1, including F value, degrees of freedom, and partial eta squared. Notes: *p < 0.05.
There was a significant main effect of the electrode site, where the amplitude of the N1 was largest at electrodes Iz and O2 (see Figure 10 for means). Electrode site interacted significantly with both array type and shape, and there was also a three-way interaction present between array type, shape, and site. There were significant main effects of both the array type and shape presence on the N1 peak amplitude. The N1 response to the texture array was larger than the response to the single-contour array, and the RF3 stimuli elicited a greater negativity than the noise. 
Figure 10
 
Means and 95% confidence intervals (between subjects) for N1 peak in microvolts across two conditions for both the RF3 and the comparison shape at electrodes O1, Iz, and O2. Shapes were defined by either a texture (bars on the right) or a single contour (bars on the left).
Figure 10
 
Means and 95% confidence intervals (between subjects) for N1 peak in microvolts across two conditions for both the RF3 and the comparison shape at electrodes O1, Iz, and O2. Shapes were defined by either a texture (bars on the right) or a single contour (bars on the left).
Because there was a significant three-way interaction, further post hoc analyses were conducted to clarify the nature of this effect. ANOVAs with shape as a factor were run separately for each array type. There was a significant effect of shape presence on the N1 for the texture array condition at electrode sites O1 and O2, respectively, F(1, 18) = 46.97, p < 0.05, partial η2 = 0.72; F(1, 18) = 18.43, p < 0.05, partial η2 = 0.51. There was no significant effect of shape presence in either array condition at electrode site Iz, and there was also no effect on N1 amplitude when the array type was a single contour. These results suggest that the effect of shape presence was dependent on the shape being presented in a texture array. The N1 was largest at Iz and O2, but the shape presence effect was evident only at electrodes O1 and O2, suggesting different topographies. It is possible that the modulation due to shape presence is not affecting the N1 per se but might be related to another component overlapping with the N1. 
To determine whether there was a significant effect of shape discrimination between an RF3 and a circle on the N1, a second three-factor, repeated-measures ANOVA was conducted (see Table 1 for results). The factors were electrode site (three levels: O1, O2, and Iz), array type (two levels: single contour and texture), and shape (two levels: RF3 and circle). There was a significant effect of electrode site, as the N1 amplitude at O2 and Iz was again larger than at O1 (see Figure 10 for means). There was also a significant effect of array type with the texture array eliciting a greater N1 amplitude. There was no effect of shape type on the amplitude of the N1 component, and the only significant interaction was between site and array type. 
Overall, the N1 results show that the presence of a coherent global structure in a texture array (but not in a single-contour array) enhanced the peak amplitude of the N1 component. However, this component did not provide an indicator of the type of shape presented because there was no effect of shape type (RF3 vs. circle) in the discrimination condition, at least for the shapes used in this experiment. This finding is consistent with the single-contour results presented in Experiment 1, which also showed no effect of the presence of corners on the N1 peak amplitude. 
Posterior N220 component
Because the posterior N220 overlapped with the descending slope of the N1, the mean amplitude was used to measure the N220 component. The latency range identified for the N220 component in Experiment 1 was 200–228 ms. The latency range here was determined for both the texture and single-contour conditions separately. In the texture condition, the difference was only significant between 220 and 280 ms, and in the single-contour condition, it was significant from 196 to 268 ms. Because the ranges identified for texture and single contours were different, we used the 60-ms interval with the largest difference to ensure that the same length interval was used. For the single-contour condition, the N220 latency became 200–260 ms, and the onset matched the equivalent single-contour condition from Experiment 1. The texture condition latency remained unchanged. 
As with the N1 component, both shape detection (RF3 vs. noise) and shape discrimination (RF3 vs. circle) conditions were assessed to determine the effect of array type and shape on the mean amplitude of the N220 component (see Figure 9 for ERP waveforms). For shape detection, the factors included electrode site (three levels: O1, O2, and Iz), array type (two levels: single contour and texture), and shape (two levels: RF3 and noise). All ANOVA results are presented in Table 2. The electrode site had a significant effect on the N220 amplitude for shape detection (RF3 vs. noise), and the component was more negative at the midline site Iz than either O1 or O2. Electrode site significantly interacted with both array type and shape. There was also a three-way interaction present between electrode site, shape, and array type. 
Table 2
 
Three-factor, repeated-measures ANOVA results for the N220, including F value, degrees of freedom, and partial eta squared. Notes: *p < 0.05.
Table 2
 
Three-factor, repeated-measures ANOVA results for the N220, including F value, degrees of freedom, and partial eta squared. Notes: *p < 0.05.
There was an effect of shape presence in the array on the mean amplitude of the N220 component, where the N220 was enhanced in response to the RF3 relative to noise stimuli (see Figure 11 for means). There was also a significant effect of the array type on the N220 component, where the texture array elicited a significantly larger (more negative) N220 than the single-contour array. There was no interaction between the array type and shape in the shape detection analysis. 
Figure 11
 
Means and 95% confidence intervals (between subjects) for the posterior N2 mean amplitude in microvolts across two conditions for both the RF3 and the comparison shape at electrodes O1, Iz, and O2. Shapes were defined by either a texture (bars on the right) or a single contour (bars on the left).
Figure 11
 
Means and 95% confidence intervals (between subjects) for the posterior N2 mean amplitude in microvolts across two conditions for both the RF3 and the comparison shape at electrodes O1, Iz, and O2. Shapes were defined by either a texture (bars on the right) or a single contour (bars on the left).
For the shape discrimination condition, the N220 amplitude was analyzed using a three-factor, repeated-measures ANOVA with electrode site, array type, and shape (two levels: RF3 and circle) included. There was a significant main effect of electrode site on amplitude with Iz again eliciting the largest negativity. There was also a large main effect of the specific shape presented in the array (RF3 or circle) on the amplitude of the N220 component as the N220 was reduced for the circle stimulus. This finding is consistent with the results from Experiment 1, in which we also showed that the N220 amplitude was reduced in response to the circle compared to the RF3 stimuli in a single-contour array only. As with the shape detection condition, there was a significant main effect of the array type on the mean N220 amplitude. A larger N220 was elicited when the shape was presented in a texture array rather than as a single contour. Electrode site interacted significantly with shape but not with array type, and there was a significant three-way interaction between the factors. 
Because there was a significant three-way interaction present, several post hoc ANOVAs were conducted to determine the nature of this effect. These ANOVAs had shape as a factor and were conducted separately for each array type and electrode site. The results revealed a significant effect of shape type for both single-contour and texture arrays at all three electrode sites. Further inspection of the N220 means showed that the interaction was due to a larger difference between RF3 and circle stimuli for the single-contour compared to the texture condition. Therefore, although the RF3 elicits a significantly larger negativity than the circle regardless of the array type used to construct the shape, the effect of corners on the N220 is greater in the single-contour array than it was in the texture array, which does not contain precisely aligned contours. 
To summarize, when shape was constructed by aligning the orientations of all local elements in an array (texture), the N220 amplitude was larger than when the shape was constructed from a single path of 24 elements. The mean amplitude of the N220 was always larger when the shape presented was an RF3 as opposed to a circle, and this difference was largest when the shape was represented by an aligned path. 
Source localization
Figure 12 shows the scalp topographies of the N1 and the N220 difference waveforms for all experimental conditions. Using BESA 5.1.2 software, the sources of the N1 and N220 components were localized. A four-shell spherical head model was used to obtain the solution (Scherg, 1992). Localization used the difference waveforms for each of the array types—texture and single contour—for both RF3 minus noise and RF3 minus circle conditions. The ascending slope of the difference waveform at the N1 and N220 latencies identified previously was used to specify the interval over which localization was conducted. To determine the source of the peak in each difference waveform, a single pair of symmetrical dipoles was used. 
Figure 12
 
Scalp topography maps for difference waveforms (RF3 minus comparison pattern). The upper half shows the top-down topography for the texture patterns; the N1 is shown at 152 ms, and the N220 is shown at 252 ms. The bottom half shows the top-down topography for single-contour patterns; the N1 is shown at 152 ms, and the N220 is shown at 220 ms. Note that the N220 peak was later for the texture compared to single-contour patterns. Electrical activity in microvolts, ranging from +4 to −4 μV, is indicated by the scale on the right.
Figure 12
 
Scalp topography maps for difference waveforms (RF3 minus comparison pattern). The upper half shows the top-down topography for the texture patterns; the N1 is shown at 152 ms, and the N220 is shown at 252 ms. The bottom half shows the top-down topography for single-contour patterns; the N1 is shown at 152 ms, and the N220 is shown at 220 ms. Note that the N220 peak was later for the texture compared to single-contour patterns. Electrical activity in microvolts, ranging from +4 to −4 μV, is indicated by the scale on the right.
Sources were localized in standard x, y, z Talairach coordinates (Talairach & Tournoux, 1988), and the coordinates are presented in Table 3. The Talairach atlas defines and catalogues the structure of the human brain in addition to providing a consistent terminology for labeling brain regions (Lancaster et al., 2000). We used Talairach Daemon (Lancaster et al., 1997; Lancaster et al., 2000) to determine which cortical structures were associated with the coordinates generated here. The N1 (RF3 minus noise waveform) was localized to the Brodmann area 18 region in the occipital lobe for both the texture and single-contour arrays (see red and blue markers in Figure 13). The bilateral sources identified for the texture array were in the lingual gyrus and accounted for 96.7% of the variance in the data. The sources for the single-contour array were located in the middle occipital gyrus and accounted for 96.3% of the variance data. There was no significant improvement in the residual variance accounted for when more dipoles were added. 
Table 3
 
Talairach coordinates (in millimeters) for foci across conditions forming the N1 (RF3 vs. noise) and N220 (RF3 vs. circle) components. Notes: Bilateral sources are indicated.
Table 3
 
Talairach coordinates (in millimeters) for foci across conditions forming the N1 (RF3 vs. noise) and N220 (RF3 vs. circle) components. Notes: Bilateral sources are indicated.
Figure 13
 
Source localization of the difference potentials for shape detection (N1, RF3 minus noise) and shape discrimination (N220, RF3 minus circle) conditions. Difference potentials obtained are mapped against a standard MRI template image to represent the locations of the sources identified; the red marker indicates the left hemisphere source, and the blue marker indicates the right hemisphere source when viewed from the front.
Figure 13
 
Source localization of the difference potentials for shape detection (N1, RF3 minus noise) and shape discrimination (N220, RF3 minus circle) conditions. Difference potentials obtained are mapped against a standard MRI template image to represent the locations of the sources identified; the red marker indicates the left hemisphere source, and the blue marker indicates the right hemisphere source when viewed from the front.
Based on the definitions for visual areas taken from Hasnain, Fox, and Woldorff (1998), who produced mean locations of areas V1 to V5 using fMRI data from human participants, the dipole pair generated in the texture array for the RF3 minus noise difference waveform (shape detection) is within ±1 mm of the center of the area defined as V4. The dipole generated in the single-contour array for RF3 minus noise is within ±3 mm of the center of the area defined as V3. 
Source localization was also attempted for the shape discrimination data to determine a source of the activation specific to the presence of corners. The N220 (RF3 minus circle waveform) in the single-contour array produced a source accounting for 96% of the variance. This source was in the declive located in the posterior lobe, which is within ±1 mm of the area defined as V4 by Hasnain et al. (1998). Unfortunately, the difference waveforms between the RF3 and circle stimuli did not yield a reliable source for the texture array condition. Localization attempts were therefore not able to reduce the level of residual variance below 10% and obtain a reliable source for the texture array condition. 
Experiment 2 discussion
The aim of this second experiment was to determine the electrophysiological parallels to behavioral judgments of shapes defined by textures and to identify the potential locations of the cortical regions responsible for those judgments. The N1 was found to be modulated by the presence of a global RF3 structure in the texture condition but not in the single-contour condition. The N220 was larger for shapes containing corners and defined internal polar angles between the corners compared to those without as predicted regardless of the type of array used to represent the shape (texture or single contour). Interestingly, the overall magnitude of the N220 component was larger for textures, suggesting differential processing of shapes defined by contours compared to textures. Source localization was also conducted in an attempt to clarify the cortical regions associated with shape detection and shape discrimination. It should be noted here that the source localization conducted only provides an estimate of the source model. 
The global processing associated with Glass patterns has previously been localized to areas external to the primary visual cortex (Ohla et al., 2005; Vreven & Berge, 2007) with a recent high-density MEG study suggesting a generator in area V3a (Swettenham et al., 2010). Mannion and Clifford (2011) have shown that both V3 and V4 were involved in processing global arrangements in Glass patterns. V4 has also been identified as an area of importance for processing global shape defined by a continuous contour (Gallant et al., 2000), particularly when that processing involves curvature information (Carlson, Rasquinha, Zhang, & Connor, 2011; Gustavsen & Gallant, 2003). Wilkinson et al. (2000) have demonstrated V4 involvement in the processing of multiringed concentric RF patterns, and fMRI also shows area V3a is sensitive to the curvature information on a closed contour (Caplovitz & Tse, 2007). 
For the current data, sources were successfully obtained for the shape detection (RF3 minus noise) difference waveform with a peak difference close to or in V4 for the texture-defined stimuli and V3 for the single contour–defined stimuli. Localizing the difference between specific shapes was more difficult because the overall magnitude of the difference was smaller. However, V4 was identified as the source of the difference between a single-contour shape with corners and one without. This supports the V4 coding system based on the presence and arrangement of curvature discontinuities suggested by Pasupathy and Connor (2001, 2002) and Wilson and Wilkinson (2015). However, it is acknowledged that it is difficult to discriminate between V3 and V4 and V1 and V2 because they lie very close together (Ales, Yates, & Norcia, 2010; Hasnain et al., 1998). The conclusion is not made here that V4 is the only region involved; simply that it might be one of the earlier regions involved in global shape processing. 
Overall, the results suggest that texture-defined shape has a similar reliance on the presence of corners as aligned contours. However, the presence of differences between textures and single contours in the ERPs may imply the existence of separate global mechanisms for integrating the two stimuli (Badcock, Almeida, & Dickinson, 2013). 
General discussion
The experiments reported here provide evidence for the critical importance of corners in basic shape processing as well as demonstrating which specific aspect of corners is most relevant. In Experiment 1, we showed that the angle separating corners was more critical than the overall number of corners for discrimination performance. This fits well with polar models of RF encoding (Bell et al., 2008), recent work examining the ability to discriminate between RF patterns at threshold (Badcock, Haley, & Dickinson, 2015; Dickinson et al., 2013), and neural population models in which basic shape is defined by the curvature variation around a closed contour (Carlson et al., 2011; Gallant et al., 1996; Pasupathy & Connor, 2001, 2002). We also presented electrophysiological evidence in Experiments 1 and 2 that supported the importance of changes in curvature for shape processing. Although the ERP results were not able to distinguish between shapes with varying arrangements of corners, an enhanced negativity over the occipital lobe following the presentation of an RF3 but not following a circle was demonstrated in shapes defined by either an aligned contour or a texture. We suggest that this early cortical response (the N220, which occurs approximately 220 ms poststimulus) is sensitive to variation in curvature on a contour. 
Although the results reported here show that the curvature-specific N220 response occurs regardless of whether a shape is defined by a diffuse texture or an aligned contour, there were however some differences between the electrophysiology of the texture and single-contour shapes with respect to the relative size of their elicited components. The overall amplitudes of both the N1 and N220 were larger (more negative) when the stimuli were defined by a texture rather than a single aligned contour. One possible explanation for this relates to the difficulty in discriminating between the shapes represented by each type of array. Previous research has shown that the amplitude of the N220 component is increased with increasing discrimination difficulty in a visual task (Brodeur, Lepore, & Debruille, 2006; Shedden & Nordgaard, 2001). The enhanced N220 for texture patterns in the current study could possibly be the result of an increased difficulty discriminating the structure in the texture patterns compared to the single-contour patterns (see work by Schmidtmann et al., 2013). 
Increased discrimination difficulty can be demonstrated by comparing RTs and accuracies between conditions. Speed of processing is affected by discrimination difficulty in Glass patterns (RTs increase when structure in a Glass pattern is harder to detect; Tanskanen et al., 2008). Participants in the current study were also slower and less accurate when responding to textures than to single contours, although only in the shape discrimination (RF3 vs. circle) task. This partially supports the argument that the enhanced N220 amplitude is due to increased difficulty because the N220 was largest in the condition in which the behavioral performance was poorest. 
Taken together, these results suggest that increased task difficulty could account for the enhanced N220 elicited by texture patterns in the shape discrimination condition. However, Senkowski and Herrmann (2002) have clearly demonstrated that task difficulty in a visual discrimination task affects the amplitude of the N220 component but not the N1. So although task difficulty could potentially explain some of the N220 differences, the larger N1 amplitude elicited when responding to texture stimuli still remains unaccounted for. 
A possible reason for the enhanced N1 when viewing texture-defined shapes is a change in the dynamic allocation of attention. It has been argued that attention can work as a kind of “zoom lens” focused on an attended region or stimuli (Eriksen & St James, 1986). Luck et al. (1994) found that the N1 was larger in response to attended, as opposed to unattended, stimuli in a visual discrimination task. Incongruent distractors in a face discrimination task are also associated with a larger N1 because they are thought to be competing for resources and attracting more attention (Sreenivasan & Jha, 2007). Therefore, a smaller attentional window would seem to be associated with a smaller N1 component. This conclusion is supported by ERP studies in which larger attended areas led to larger N1 amplitudes (Korth & Nguyen, 1997; Torriente, Valdes-Sosa, Ramirez, & Bobes, 1999). A larger attentional window would help to detect the organization of a texture field (Dickinson, Broderick, & Badcock, 2009). 
Because there is a large quantity of redundant information in the visual world, a system that focuses on identifying the points of change in an image is one that would be particularly efficient (Simoncelli & Olshausen, 2001). In such a system, the most salient features are enhanced and receive preferential processing—such as the edges for boundary detection (Lamme, Rodriguez-Rodriguez, & Spekreijse, 1999) or the areas with abrupt changes in curvature (Heitger, Rosenthaler, Vonderheydt, Peterhans, & Kubler, 1992). As the image representation progresses from V1 through to V4, the irrelevant information is discarded, allowing the visual system to remain sensitive to the information that is most relevant (Gardner et al., 2005). 
The information contained in corners is particularly relevant when it comes to forming an object representation. We know this because occluding or disrupting corners substantially impairs detection performance on a threshold task (Loffler et al., 2003). A classic study by Attneave (1954) also shows that when people are asked to draw dots on the contour to represent a shape, they overwhelmingly draw dots at the corners. Identification of common objects is impaired more when contour removal is concentrated on the vertices instead of the midsegments (Biederman, 1987). We conclude that corners, or curvature maxima, appear to contain particularly vital information for the formation of shapes and therefore objects. 
Conclusion
The behavioral results reported here provide support for the hypothesis that the angle separating corners, and not the total number of corners, is a key defining characteristic for shape. Analysis of the ERPs elicited from human participants introduces the N220 component as an indicator of the presence of corners on a shape contour or of implied contours in a texture field. Previous research using ERPs has only been able to show cortical selectivity for the presence of any global arrangement in a visual stimulus, but this work shows a modulation of the critical ERP components dependent on the specific shape variations employed. The research reported here expands the current knowledge of human visual perception by demonstrating what specific characteristics of shape are critical and by providing an electrophysiological marker for this characteristic that has not previously been demonstrated. The localization of this critical shape difference suggests a neural generator in or around cortical area V4. 
Acknowledgments
This work was supported by Australian Research Council grants DP-0666206, DP-110105443, and DP-1097003 to DRB and DP-0665616 to AMF. Funding was also provided to VKB by the School of Psychology, University of Western Australia, and technical support was provided by John Love. 
Commercial relationships: none. 
Corresponding author: Vanessa K. Bowden. 
Email: vanessa.bowden@uwa.edu.au. 
Address: University of Western Australia, School of Psychology, Perth, Western Australia, Australia. 
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Figure 1
 
An illustration of the construction of the RF path. This path is an RF3 pattern with two cycles of modulation. The pattern comprises a single cycle of sinusoidal modulation with the two halves of a D1 (first derivative of a Gaussian) function concatenated to the two ends of the sinusoid. The D1 function matches the sine function in gradient at the point at which the two are joined (at zero crossings of the sinusoidal modulation) and in maximum amplitude. The D1 function thereby allows incomplete RF patterns with two or more cycles of sinusoidal modulation to be approximated while allowing for a smooth transition back into the circular remainder of the pattern. For RF patterns with the full complement of cycles of modulation, no smoothing function is required.
Figure 1
 
An illustration of the construction of the RF path. This path is an RF3 pattern with two cycles of modulation. The pattern comprises a single cycle of sinusoidal modulation with the two halves of a D1 (first derivative of a Gaussian) function concatenated to the two ends of the sinusoid. The D1 function matches the sine function in gradient at the point at which the two are joined (at zero crossings of the sinusoidal modulation) and in maximum amplitude. The D1 function thereby allows incomplete RF patterns with two or more cycles of sinusoidal modulation to be approximated while allowing for a smooth transition back into the circular remainder of the pattern. For RF patterns with the full complement of cycles of modulation, no smoothing function is required.
Figure 2
 
Sample stimuli presented across five experimental conditions. In each condition, the comparison shape (left) and the RF3 pattern (right) were presented with equal frequency.
Figure 2
 
Sample stimuli presented across five experimental conditions. In each condition, the comparison shape (left) and the RF3 pattern (right) were presented with equal frequency.
Figure 3
 
Accuracy (lower) and RT (upper) means for the five conditions in response to the RF3 stimuli only; the y-axis labels indicate the comparison shape in each condition. 95% confidence intervals (between subjects) provided. One asterisk (*) indicates p < 0.05, and two asterisks indicate p < 0.01. Note that for the RT graph, all other stimuli conditions are slower than the RF3 versus noise condition.
Figure 3
 
Accuracy (lower) and RT (upper) means for the five conditions in response to the RF3 stimuli only; the y-axis labels indicate the comparison shape in each condition. 95% confidence intervals (between subjects) provided. One asterisk (*) indicates p < 0.05, and two asterisks indicate p < 0.01. Note that for the RT graph, all other stimuli conditions are slower than the RF3 versus noise condition.
Figure 4
 
Means and 95% confidence intervals (between subjects) for N1 peak amplitude in microvolts across all five conditions for both the RF3 and the comparison shape at electrodes O1, Oz, and O2.
Figure 4
 
Means and 95% confidence intervals (between subjects) for N1 peak amplitude in microvolts across all five conditions for both the RF3 and the comparison shape at electrodes O1, Oz, and O2.
Figure 5
 
Grand average waveforms at lateral occipital electrodes O1 and O2 and midline site Oz are presented. ERPs elicited in response to the presentation of RF3 stimuli are represented by the dotted line, and ERPs elicited in response to the comparison shape are represented by the solid line. The comparison shape varied depending on the condition, and the five comparison shapes are noise, circle, RF4, three-cycle RF4, and two-cycle RF3, respectively. The y-axis represents electrical activity in microvolts (in increments of 1 μV, ranging from +8 to −12 μV, negative up), and the x-axis represents time in milliseconds, starting 50 ms prior to the onset of the stimulus and extending to 350 ms poststimulus in increments of 100 ms.
Figure 5
 
Grand average waveforms at lateral occipital electrodes O1 and O2 and midline site Oz are presented. ERPs elicited in response to the presentation of RF3 stimuli are represented by the dotted line, and ERPs elicited in response to the comparison shape are represented by the solid line. The comparison shape varied depending on the condition, and the five comparison shapes are noise, circle, RF4, three-cycle RF4, and two-cycle RF3, respectively. The y-axis represents electrical activity in microvolts (in increments of 1 μV, ranging from +8 to −12 μV, negative up), and the x-axis represents time in milliseconds, starting 50 ms prior to the onset of the stimulus and extending to 350 ms poststimulus in increments of 100 ms.
Figure 6
 
Means and 95% confidence intervals (between subjects) for posterior N220 mean in microvolts across all five conditions for both the RF3 and the comparison shape at electrodes O1, Oz, and O2.
Figure 6
 
Means and 95% confidence intervals (between subjects) for posterior N220 mean in microvolts across all five conditions for both the RF3 and the comparison shape at electrodes O1, Oz, and O2.
Figure 7
 
The top three figures show the stimuli used in the two texture conditions, and the bottom three figures are the single-contour stimuli. The comparison stimulus in the shape detection task is noise, and the comparison stimulus in the shape discrimination task is a circle. In the texture conditions, the orientations (but not positions) of all elements are consistent with the shape. In the single-contour conditions, both the position and orientation of 24 patches is aligned according to the underlying shape structure, and the remaining elements are randomized.
Figure 7
 
The top three figures show the stimuli used in the two texture conditions, and the bottom three figures are the single-contour stimuli. The comparison stimulus in the shape detection task is noise, and the comparison stimulus in the shape discrimination task is a circle. In the texture conditions, the orientations (but not positions) of all elements are consistent with the shape. In the single-contour conditions, both the position and orientation of 24 patches is aligned according to the underlying shape structure, and the remaining elements are randomized.
Figure 8
 
Accuracy (lower) and RT (upper) means for the two conditions in response to the RF3 stimuli only; the y-axis labels indicate the comparison shape in each condition and 95% confidence intervals (between subjects) provided.
Figure 8
 
Accuracy (lower) and RT (upper) means for the two conditions in response to the RF3 stimuli only; the y-axis labels indicate the comparison shape in each condition and 95% confidence intervals (between subjects) provided.
Figure 9
 
Grand average waveforms at lateral occipital electrodes O1 and O2 and midline site Iz are presented. ERPs elicited in response to the presentation of RF3 stimuli are represented by the dotted line, and ERPs elicited in response to the comparison shape are represented by the solid line. Shapes were defined by either a texture (aligning the orientation of all elements to form a texture) or a single contour (aligning 24 elements according to a single contour). The comparison shape varied depending on the condition, and the two comparison shapes were noise and circle. The y-axis represents electrical activity in microvolts (in increments of 1 μV, ranging from +8 to −12 μV, negative up), and the x-axis represents time in milliseconds, starting 50 ms prior to the onset of the stimulus and extending to 350 ms poststimulus in increments of 100 ms.
Figure 9
 
Grand average waveforms at lateral occipital electrodes O1 and O2 and midline site Iz are presented. ERPs elicited in response to the presentation of RF3 stimuli are represented by the dotted line, and ERPs elicited in response to the comparison shape are represented by the solid line. Shapes were defined by either a texture (aligning the orientation of all elements to form a texture) or a single contour (aligning 24 elements according to a single contour). The comparison shape varied depending on the condition, and the two comparison shapes were noise and circle. The y-axis represents electrical activity in microvolts (in increments of 1 μV, ranging from +8 to −12 μV, negative up), and the x-axis represents time in milliseconds, starting 50 ms prior to the onset of the stimulus and extending to 350 ms poststimulus in increments of 100 ms.
Figure 10
 
Means and 95% confidence intervals (between subjects) for N1 peak in microvolts across two conditions for both the RF3 and the comparison shape at electrodes O1, Iz, and O2. Shapes were defined by either a texture (bars on the right) or a single contour (bars on the left).
Figure 10
 
Means and 95% confidence intervals (between subjects) for N1 peak in microvolts across two conditions for both the RF3 and the comparison shape at electrodes O1, Iz, and O2. Shapes were defined by either a texture (bars on the right) or a single contour (bars on the left).
Figure 11
 
Means and 95% confidence intervals (between subjects) for the posterior N2 mean amplitude in microvolts across two conditions for both the RF3 and the comparison shape at electrodes O1, Iz, and O2. Shapes were defined by either a texture (bars on the right) or a single contour (bars on the left).
Figure 11
 
Means and 95% confidence intervals (between subjects) for the posterior N2 mean amplitude in microvolts across two conditions for both the RF3 and the comparison shape at electrodes O1, Iz, and O2. Shapes were defined by either a texture (bars on the right) or a single contour (bars on the left).
Figure 12
 
Scalp topography maps for difference waveforms (RF3 minus comparison pattern). The upper half shows the top-down topography for the texture patterns; the N1 is shown at 152 ms, and the N220 is shown at 252 ms. The bottom half shows the top-down topography for single-contour patterns; the N1 is shown at 152 ms, and the N220 is shown at 220 ms. Note that the N220 peak was later for the texture compared to single-contour patterns. Electrical activity in microvolts, ranging from +4 to −4 μV, is indicated by the scale on the right.
Figure 12
 
Scalp topography maps for difference waveforms (RF3 minus comparison pattern). The upper half shows the top-down topography for the texture patterns; the N1 is shown at 152 ms, and the N220 is shown at 252 ms. The bottom half shows the top-down topography for single-contour patterns; the N1 is shown at 152 ms, and the N220 is shown at 220 ms. Note that the N220 peak was later for the texture compared to single-contour patterns. Electrical activity in microvolts, ranging from +4 to −4 μV, is indicated by the scale on the right.
Figure 13
 
Source localization of the difference potentials for shape detection (N1, RF3 minus noise) and shape discrimination (N220, RF3 minus circle) conditions. Difference potentials obtained are mapped against a standard MRI template image to represent the locations of the sources identified; the red marker indicates the left hemisphere source, and the blue marker indicates the right hemisphere source when viewed from the front.
Figure 13
 
Source localization of the difference potentials for shape detection (N1, RF3 minus noise) and shape discrimination (N220, RF3 minus circle) conditions. Difference potentials obtained are mapped against a standard MRI template image to represent the locations of the sources identified; the red marker indicates the left hemisphere source, and the blue marker indicates the right hemisphere source when viewed from the front.
Table 1
 
Three-factor, repeated-measures ANOVA results for the N1, including F value, degrees of freedom, and partial eta squared. Notes: *p < 0.05.
Table 1
 
Three-factor, repeated-measures ANOVA results for the N1, including F value, degrees of freedom, and partial eta squared. Notes: *p < 0.05.
Table 2
 
Three-factor, repeated-measures ANOVA results for the N220, including F value, degrees of freedom, and partial eta squared. Notes: *p < 0.05.
Table 2
 
Three-factor, repeated-measures ANOVA results for the N220, including F value, degrees of freedom, and partial eta squared. Notes: *p < 0.05.
Table 3
 
Talairach coordinates (in millimeters) for foci across conditions forming the N1 (RF3 vs. noise) and N220 (RF3 vs. circle) components. Notes: Bilateral sources are indicated.
Table 3
 
Talairach coordinates (in millimeters) for foci across conditions forming the N1 (RF3 vs. noise) and N220 (RF3 vs. circle) components. Notes: Bilateral sources are indicated.
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