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Article  |   February 2016
The perception of three-dimensional contours and the effect of luminance polarity and color change on their detection
Author Affiliations
  • Sieu K. Khuu
    School of Optometry and Vision Science, The University of New South Wales, Sydney, Australia
    s.khuu@unsw.edu.au
  • Vanessa Honson
    School of Optometry and Vision Science, The University of New South Wales, Sydney, Australia
    v.honson@unsw.edu.au
  • Juno Kim
    School of Optometry and Vision Science, The University of New South Wales, Sydney, Australia
    juno.kim@unsw.edu.au
Journal of Vision February 2016, Vol.16, 31. doi:10.1167/16.3.31
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      Sieu K. Khuu, Vanessa Honson, Juno Kim; The perception of three-dimensional contours and the effect of luminance polarity and color change on their detection. Journal of Vision 2016;16(3):31. doi: 10.1167/16.3.31.

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

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Abstract

In the present study we investigated the detectability of three-dimensional (3D) cocircular contours defined by binocular disparity and established the influence of a number of stimulus factors to their perception. In Experiment 1 we examined the depth range over which local elements are grouped in depth, and whether contour detectability systematically changed with the degree to which they are oriented in depth. We found that increasing the orientation of curved contours in depth improved detection performance. In Experiment 2, we examined the degree to which contour detection was disrupted by varying their continuity in depth by jittering the local depth position of contour elements. Detection performance declined with the increasing displacement of local contour elements in depth away from the depth orientation of the contour. Experiments 3 and 4 ascertained whether a detection advantage is afforded to 3D contours defined by local variations in luminance polarity and color. Local color and polarity differences can disrupt the two-dimensional grouping of local contour elements on the basis of similarity, but we tested whether continuity in depth facilitates grouping of contour elements differing in polarity and color. We found no detection advantage for 3D contours defined by local color and polarity variations, suggesting binocular disparity does not facilitate grouping in depth when local elements differ in color and polarity. These findings further suggest the visual system uses binocular disparity to detect contours, but is likely to involve systems tuned to luminance polarity and color.

Introduction
An important task of the visual system is to identify luminance-defined contours in retinal images. Contours are a collection of spatially linked visual elements that in visual scenes frequently signify spatial layout, which is important for experiencing the definition of object boundaries and perceptual organization of the visual scene (see e.g., Braun, 1999; Field, Hayes, & Hess, 1993, 2000; Khuu, Moreland, & Phu, 2011; Kovacs & Julesz, 1993; Marr, 1982). The basis upon which contour elements are associated in the perception of contour structure has been proposed to largely reflect well-established grouping principles such as good continuation, smoothness, closure, and proximity that were central to the 20th century Gestalt movement in psychology (see Koffka, 1935; Wertheimer, 1938). 
The work of Field et al. (1993) has been instrumental in the development of a contour association-field model (governed by the Gestalt principle of good continuation) that specifies the optimal separation, placement, and relative orientation between local edge-elements most effective for contour grouping. The neural locus for contour integration is thought to be located in primary visual cortex in which the association-field is coded as a network of short- and long-range horizontal connections between local edge sensitive neurons (Bosking, Zhang, Schofield, & Fitzpatrick, 1997; Field, Hayes, & Hess, 1993; Hess & Field, 1999). Moreover, it is believed that the evolution of the neuro-circuitry governing contour processing and the perception of contours are largely constrained by the statistics of local orientation structure in natural images (see Cham, Khuu, & Hayes, 2007; Dumoulin & Hess, 2006; Elder & Goldberg, 2002; Geisler, Perry, Super, & Gallogly, 2001; Hayes, Cham, Khuu, & Brady, 2008; Sigman et al., 2001). 
Previous studies investigating contour integration and perception have typically done so under conditions in which contours are spatially arranged only in two–dimensional (2D) space, and well-developed models have been proposed to account for their perception (See Hess & Field, 1999). However, in natural scenes contours not only span 2D space, but also frequently extend in depth following a defined curved path through 3D space. For example, binocular fusion of the stereo pair shown in Figure 1 reveals the 3D contour profile of a flower defined by smooth and curved contours extending in depth. The abundance of 3D contours in daily scenes segues to the question of how they are detected by the visual system and what stimulus factors are important for this process. An expectation is that 3D contours might be simply detected from their 2D retinal projections, and associative principles that have been proposed to account for the analysis of 2D contours apply to the analysis of 3D contours. However, previous research has shown that 3D contours defined by binocular disparity are perceptible even when their 2D spatial profile is not immediately visible in the monocularly retinal images (see Hess & Field, 1995; Hess, Hayes, & Kingdom, 1997). These findings suggest that the visual system is selectively sensitive to the 3D configuration of contours. They also suggest that grouping principles such as good continuation and smoothness extend in depth, and that the detection of contours is not mediated solely by their 2D retinal representations (see Hess & Field, 1995). 
Figure 1
 
A stereo-pair when fused shows the 3D curved contour profile of a flower mutually extending in 2D space, and in depth.
Figure 1
 
A stereo-pair when fused shows the 3D curved contour profile of a flower mutually extending in 2D space, and in depth.
To date, only a handful of studies have sought to understand this process by investigating how binocular disparity might contribute to the detection of contours. The work originally conducted by Uttal (1983) demonstrated that the visual system is capable of detecting contours by integrating dots across depth defined by binocular disparity. Similarly, Hess, and Field (1995) showed that oriented contour elements distributed across two depth-planes can be effectively integrated to reveal contours within a 3D field of randomly oriented local elements. Hess et al. (1997) further demonstrated that local contour elements that are systematically displaced through depth defined by binocular disparity (resembling the 3D contours in Figure 1) can be integrated and detected by the visual system. The findings of Uttal (1983) and Hess et al. (1997) are particularly noteworthy as they used nonoriented contour elements, which indicate that contour elements can be effectively grouped based primarily on the good/regular continuity of contour elements in depth. This assertion is consistent with the recent findings of Deas and Wilcox (2015), who demonstrated that the good disparity continuation of intermediate nonoriented contour elements decreased the perceived separation of end-elements of the contour in depth. However, they noted this effect was reduced when depth continuity was disrupted when intermediate dots were omitted or their depth positions randomly jittered. Additionally, they observed that contours defined by regular depth continuity were detected faster than discontinuous contours in a visual search task. Importantly, these findings collectively argue for the existence of specific depth grouping operations (reflecting the extension of Gestalt principles of continuity and smoothness in depth) that can be separable from those operating in 2D space. 
Beyond establishing that grouping of contour elements can occur in and through depth (defined by binocular disparity), little is known about this process and the stimulus factors that are important for the perception of 3D contour structure. The goal of the present study was to contribute to understanding how the visual system processes 3D contours by considering two important issues. First, we were interested in establishing whether the depth continuity of a 3D contour (i.e., the fact that elements are regularly displaced in depth) and the degree to which they extend in depth, might directly influence the detection of 3D contours. As noted above, the visual system is selectively sensitive to regular continuity of contours in depth; however, it is unclear whether this sensitivity is dependent on the degree to which contours extend through depth. It might be expected that 3D contours that extend further in depth are better detected, as the magnitude of depth continuity provides an additional means of grouping contour elements (see Uttal, 1983). Alternatively, it is possible that the contour integration process is tuned to depth, and at large depth separations, local contour elements might not be integrated. However, the spatial extent in depth over which this process occurs has yet to be established. We addressed these issues in Experiment 1 by quantifying the detection of 3D contours defined by different path angles, as a function of their depth orientation. In Experiment 2, we continue this investigation by examining how disrupting the regular depth continuity of a 3D contour affects its detection. Here, contour detection performance was measured using 3D contours that extended through depth, but local elements were alternately displaced in opposite directions in depth relative to the depth orientation of the contour (see Figure 2D). This local depth variation disrupted the 3D continuity of the contour, and we quantified the spatial limits over which this manipulation influenced 3D contour detection. Although previous studies have demonstrated that the visual system can rely on binocular disparity to group contour elements, it remains unclear the stimulus factors that might influence this process. Previous studies have established that local variations in luminance polarity and color (along the contour train) can disrupt the detectability of 2D contours (e.g., Field et al., 2000; McIlhagga & Mullen, 1996), presumably because local contour elements are more strongly grouped based on these 2D stimulus characteristics. However, it remains to be established how these factors might influence the ability of the visual system to group elements in depth. It is possible that 3D contours might be better detected than 2D contours because the regular continuity in depth provides a means of grouping contour elements despite their differences in color or luminance polarity. However, previous studies have demonstrated that disparity-tuned neurons in the primate visual cortex (e.g., in V2 and V4) are also selective for color (e.g., Hinkle & Connor, 2005; Tsao, Roe, & Gilbert, 2001) and luminance polarity (e.g., Ohzawa, DeAngelis, & Freeman, 1990; Tsao, Conway, & Livingstone, 2003) These physiological findings suggest that binocular disparity might be processed in separate independent color and luminance channels, and consequently, variations in color and luminance along the contour will disrupt 3D contour detection. We tested these predictions in Experiments 3 and 4 by examining whether variations in luminance contrast polarity and color of local contour elements (see Figures 2F and G) are important for the detection of 3D contours. 
Figure 2
 
Examples of contour stimuli used in the present study. Figure 2A provides a schematic representation of a contour following a constant angular path of 20°. In Figure 2B contours are oriented in depth given by σ (in degrees), while fusing the stereo pairs shown in Figure 2C provides a representation of this stimulus. Figure 2D is an example of a 3D contour in which the depth positions of local elements are jittered by displacing alternating contour elements in opposite directions away from the depth orientation of the contour (as in Experiment 2). Figure 2E shows a 3D contour embedded in noise, whereas Figures 2F and 2G are examples of 3D contours defined by local elements alternating in polarity and colour embedded in noise. The red dot in each stereo image provides an indication of the location of the contour visible through fusing the stereo image pair.
Figure 2
 
Examples of contour stimuli used in the present study. Figure 2A provides a schematic representation of a contour following a constant angular path of 20°. In Figure 2B contours are oriented in depth given by σ (in degrees), while fusing the stereo pairs shown in Figure 2C provides a representation of this stimulus. Figure 2D is an example of a 3D contour in which the depth positions of local elements are jittered by displacing alternating contour elements in opposite directions away from the depth orientation of the contour (as in Experiment 2). Figure 2E shows a 3D contour embedded in noise, whereas Figures 2F and 2G are examples of 3D contours defined by local elements alternating in polarity and colour embedded in noise. The red dot in each stereo image provides an indication of the location of the contour visible through fusing the stereo image pair.
Experiment 1: The detection of curved contours in depth
In Experiment 1 we examined how binocular disparity might facilitate contour integration by examining the ability of the visual system to detect short contour fragments of no more than six elements displaced regularly in depth and embedded in a 3D volume of randomly placed Gaussian spots that were similar in appearance to contour elements (see Figure 2). To quantify contour detection performance, we adopted the methods of Field et al. (1993) in which observers were required to detect a 3D contour randomly embedded in a cube of randomly placed elements (see Figure 2). We specifically investigated whether the detection of curved/cocircular contours is dependent on the magnitude of the contour angle, and the degree to which they extend through depth. This differs from previous studies that have typically used long contour trains that follow an “open” or “jagged” pseudo random path (see Hess et al., 1997). Cocircular contours are trains of elements, which are placed at a fixed distance on a constantly changing angular/contour path. If the contour angle is 0°, elements are placed on a parallel path, and thus the contour is a straight line. The extent of the contour angle (which determines the extent of contour curvature) is indicated by magnitude of the constant angular offset of adjacent elements within the train. Figure 2A exemplifies how such contours can be generated by displacing successive Gaussian elements by 20°. We examined cocircular contours because they are more likely to correlate with salient objects (as in Figure 1), and the visual system might preferentially code cocircular contours (e.g., Elder & Zucker, 1993; Kovacs & Julesz, 1993; Mathes & Fahle, 2007; Pettet, 1999; Pettet, McKee, & Grzywacz, 1998). Indeed, previous studies have suggested that the visual system has a detection advantage for cocircular contours as they reflect Gestalt grouping principles of closure and smoothness as well as good continuation (see Kovacs & Julesz, 1993; Pettet, 1999; Poom, 2002; however, c.f. Tversky, Perry, & Geisler, 2004). Therefore, Experiment 1 determined how the detection of 3D cocircular contours differed across conditions in which the contour angle and depth orientation of the contour was systematically varied. This allowed for the determination of how these stimulus factors affected contour detection performance, particularly whether changing binocular disparity directly contributes to the integration of local contour elements. 
Methods
Observers
Five observers participated in the present study. All were experienced observers with normal or corrected-to-normal visual acuity. The relevant University of New South Wales Ethics committee gave ethics approval, and the observers gave informed consent prior to data collection with the research following the tenets of the Declaration of Helsinki. 
Stimuli
The stimulus was a stereogram showing a 14° × 14° square stimulus (See Figure 2) consisting of 240 nonoverlapping circular Gaussian elements of the form: G(x, y) = e –(x2 + y2) / 2s2 with the element size, s, set to a width of 0.25° of visual angle. Local elements were frontoparallel to the observer and not slanted in depth. The stimulus area was surrounded by a black square (luminance: 4 cd/m2, width: 0.2°) presented with 0° disparity. This configuration aided with the fusion of the stereo stimulus and minimized convergence. The stimulus background was set to midgray (41 cd/m2) and Gaussian elements were luminance increments and set to a Weber contrast of 0.75 at full height. 
Gaussian elements were assigned a random binocular disparity ranging between −36 and 36 arcmin, and when binocularly fused occupied random positions in depth (see Figure 2C). In our study, circular elements were used instead of oriented Gabor elements to prevent the observers from detecting 3D contours by a possible reliance on the local orientation of elements, making the latter evident in the monocular image. 
As mentioned, curved contours were a train of six Gaussian elements that was randomly placed within the stimulus volume (see Figure 2A through D). A pilot study demonstrated that contours were reliably detected by six elements under the stimulus conditions employed by the present study. Contours were created by initially assigning the first element of the contour a random 3D position within the stimulus area, and then assigning it a random path direction (0°–360°). Thus, contours could be oriented in any 2D direction. The second and subsequent Gaussian elements were placed a fixed 2D distance of 0.5° (Gaussian peak to peak) along the contour path direction given by contour angle θ (in degrees). Thus, the angular difference between contour elements was constant, producing a smooth contour with good continuation (see Figure 2A). If placement of contour elements resulted in any being outside the 3D stimulus area, the contour generation process was repeated. 
To create 3D contours, Gaussian elements along the contour train were successively displaced in depth by assigning them progressively larger binocular disparity values (by horizontally displacing corresponding elements in the stereo images in opposite directions), such that all elements fell on a particular oriented/slanted plane in depth, given by angle σ (in degrees); see Figures 2B and C. A σ of 0° indicates that the contour is 2D and all elements were assigned the same binocular disparity value. Systematic deviation from 0° rotated the contour in depth with the magnitude of the offset determining the deviation from 0° and the sign indicative whether the contour was oriented towards or away from the observer. Note that the contour could occupy any 3D spatial location within the stimulus area, which spanned equally across crossed and uncrossed directions. In the present study, we were only concerned with the absolute extent to which the contour extended in depth (which was specified by the absolute orientation of the depth plane: σ°). We did not consider whether the contour extended in crossed or uncrossed directions (i.e., positive or negative disparities), their 2D orientation, or their depth position relative to fixation. The manner in which we generated contours (as described above) randomly determined these stimulus parameters from trial to trial. After a 3D contour was generated, the stimulus area was filled with noise elements (which were perceptually identical to contour elements) that occupied random 3D positions (see Figure 2E). Accordingly, randomly positioned noise dots function to actively mask the curved contour embedded randomly in the 3D stimulus area. As evident in Figure 2E, the 3D contour is not immediately evident in each of the stereo image halves, but is readily detectable when viewed binocularly (its location indicated in Figure 2E by the red dot). A control study (see Supplementary Material) verified that the contour displays generated using the abovementioned procedures were not reliably detected in the individual stereo-image halves. Particularly, changing binocular disparity did not facilitate a noticeable 2D proximity cue that revealed the contour in each of the stereo-image halves. 
Stereo images of the contour stimulus were generated on a 15-inch Macbook Pro laptop using custom software in MATLAB (version 2014b) and displayed on a linearized 27-inch stereo monitor (TRUE3DI). This specialized monitor consists of two LCD panels with an occluding polarizing plate that alternately polarized at a rate of 1000 Hz. Stereo images were presented separately to the LCD panels, and observers viewed the stimulus through polarizing lenses to ensure dichoptic viewing of the stereo image pairs. Observers sat at a viewing distance of 80 cm from the monitor using a head and chin rest. 
Procedures
To quantify contour detection performance, we adopted the methods of Field et al. (1993) (see also Hess, et al. 1997) in which observers were required to detect a 3D contour randomly embedded in a cube of randomly placed elements (see Figure 2). Here, observers were presented with pairs of the abovementioned stereograms, and they were sequentially presented for 1s in a two interval forced choice task (2IFC). Both intervals were separated by an interstimulus interval of 0.5s in which the screen was blank with the exception of the black square framing the stimulus area. One interval contained a contour amongst randomly placed elements, while the other interval comprised only randomly placed elements. The task of the observer was to judge the interval containing the curved contour. The interval containing the contour was randomized from trial to trial. This judgment was repeated 40 times for conditions in which the contour angle (θ) was 0°, 10°, 20°, 30°, and 40° and this was repeated for absolute depth rotations of 0°, 15°, 30° ,and 60°. We avoided using larger depth rotations because the larger horizontal binocular disparities would result in noticeable deviations in the 2D shape of the contour (in each monocular image), which might reveal their locations in the stereo-image halves. Observers performed all conditions in a randomized order over two 1-hour sessions with sufficient breaks between conditions to minimize fatigue. 
Results and discussion
In Figure 3, we report Signal Detection Theory (d′) sensitivity values as a function of the contour angle for different depth orientations. d′ values were derived by converting the proportion of times in which observers correctly identified the interval containing the contour to z scores and multiplying them by the square root of 2. A two-way, repeated measures ANOVA revealed a main effect of both the contour angle, F(4, 60) = 23.05, p < 0.0001, and depth orientation, F(3, 60) = 9.42, p < 0.0001. Thus, changing the contour angle and depth rotation significantly affected curved contour perception. There was no significant interaction effect, F(12, 60) = 0.47, p = 0.9250, which suggests that the effect of changing contour angle on detection was the same for the different 3D orientations. 
Figure 3
 
Mean contour detection sensitivity represented as d′ values is plotted as a function of the contour angle (in degrees). Curved contours of different depth orientations are given by different symbols (see legend). Solid lines represent the line of best fit for each contour depth orientation (0°: Y = −0.03003 × X + 1.629; 15° Y = −0.03319 × X + 1.656; 30° Y = −0.03345 × X + 1.971; 60° Y = −0.04136 × X + 2.407).
 
In Figure 3B, contour detection performance is plotted for contours of different lengths (six and 12 elements) for depth orientations of 0° and 60°. In both A and B, points represent the averaged observer data and error bars represent 1 SEM.
Figure 3
 
Mean contour detection sensitivity represented as d′ values is plotted as a function of the contour angle (in degrees). Curved contours of different depth orientations are given by different symbols (see legend). Solid lines represent the line of best fit for each contour depth orientation (0°: Y = −0.03003 × X + 1.629; 15° Y = −0.03319 × X + 1.656; 30° Y = −0.03345 × X + 1.971; 60° Y = −0.04136 × X + 2.407).
 
In Figure 3B, contour detection performance is plotted for contours of different lengths (six and 12 elements) for depth orientations of 0° and 60°. In both A and B, points represent the averaged observer data and error bars represent 1 SEM.
Two findings are evident in Figure 3A. First, increasing the contour angle reduced contour detectability. To provide an indication of how detection performance systematically changed with the contour angle, linear regression was fitted to the data: The line of best fit is shown in Figure 3A, and the fit values reported in the figure caption. As evident in the figure, contours with small angles are generally more detectable than contours with larger angles. Increasing the contour angle generally reduced detection, as seen by a reduction in sensitivity values d′, by approximately 0.2–0.3 over the range of contour angles examined in the present study; this effect was the same regardless of the depth orientation. 
These findings are consistent with previous studies that have examined the perception of cocircular contours (see General discussion in Pettet et al., 1998; Cham, et al., 2007; Yang & Purves, 2003a) and consistent with a condition of the association field model in which local elements that largely differ in orientation are less likely to be linked to form a contour (see also Yen & Finkel, 1998). Second, increasing depth orientation, such that the contour extended further in depth, significantly improved contour detection sensitivity d′ values. Improvements in detection from when the contour was 2D (i.e., depth rotation of 0°) to when it was oriented 60° in depth was small but consistent and were on average 0.1–0.15 over the range of contour angles. These findings provide evidence that the visual system is sensitive to binocular disparity, and this cue directly facilitates the integration and grouping of local contour elements. 
The findings of Experiment 1, though in agreement with the abovementioned studies, differ from Hess et al. (1997) who observed that 2D “open” contours were better detected than those extending through depth. A possible explanation for this is that the contour stimuli used by Hess et al. were much longer than those adopted in the present study. Contours employed by Hess et al. comprised 12 contour elements whereas those used in the present study were only six elements long. A noteworthy observation is that the 2D contours used by Hess et al. (1997) spanned almost the entire length (75%) of the stimulus area. Longer contours might provide a detection advantage simply because more contour elements (which are visually unoccluded) are localized to a particular depth plane, and this offers an effective means to perceptually segment the contour from the background noise. Note that varying the contour length does not have the same effect on the detection of 3D contours, because contour elements are distributed in depth, and at each depth position contour elements are effectively surrounded in 3D space by noise elements. Importantly, the use of long contours might mask/override any subtle perceptual grouping effects primarily facilitated by good binocular disparity continuation. 
It is possible that a detection advantage for 2D contours was not found in the present study because our contours were much shorter (spanning a maximum length of 20% (depending on the contour angle of curvature) of the 2D stimulus area), and below which is necessary to perceptually segment the contour from the noise background. Note that the short contour length might result in greater 2D position uncertainty, as the contour can be randomly located to a larger range of positions in the 3D stimulus area. Accordingly, our 2D contour stimulus was not immediately obvious in the stimulus, as its length does not immediately provide a cue to the location of the contour. Importantly, the advantage of using shorter contours is that its detection cannot be accounted for by its length, but rather performance might reflect specific grouping processes that are dependent on the 3D profile of the contour. 
To investigate the impact of contour length on the detection of 2D and 3D contours, we conducted a supplementary experiment (using the same procedures and observers as Experiment 1) in which contour detection performance was measured in separate conditions for contours comprising of six and 12 elements, and this was repeated for depth orientations of 0° and 60°. Only a contour angle of 20° was examined as Experiment 1 showed that the effect of depth orientation was the same for different contour angles (i.e., no significant interaction effect). The results (averaged across observers) of this experiment are shown in Figure 3B. Here contour detection sensitivity (representing the ability of the observers to correctly identify the interval containing the contour) is plotted as a function of their contour length for different depth orientations. Paired t tests, two-tailed, corrected for multiple comparisons (Holm-Sidak, assuming an alpha of 0.05), were performed to compare the difference in mean detection performance between different conditions. When contours comprised six elements, 3D contours were detected better than 2D contours, as originally noted in Experiment 1, t(4) = 4.814, p = 0.0086. However, increasing the length (from six to 12 elements) of a 2D contour significantly improved contour detection with performance improving, t(4) = 5.857, p = 0.0042. However, increasing the contour length of a 3D contour did not improve detection performance, t(4) = 0.5545, p = 0.6088. Replicating the results of Hess et al. (1997), the detection of 2D contours was superior to 3D contours when it consisted of 12 elements, t(4) = 4.501, p = 0.0108. Importantly, these findings confirm that the contour length can differentially affect the detection of 2D and 3D contours, and that longer contours might provide a detection advantage for 2D contours. Importantly, the use of shorter contour fragments in the present study avoided this effect, and we argue that our results provide a better indication of how binocular disparity facilitates the grouping of elements through depth. Particularly, the detection advantage observed for 3D reflects the addition of binocular disparity grouping. 
Finally, we note that the present study employed cocircular contours while Hess et al. (1997) used contours that were open in structure. It has been reported that the visual system selectively processes cocircular contours (leading to better contour detection as compared to open contours) as their detection, in addition to continuity, is facilitated by Gestalt grouping principles of closure and smoothness. We argue that grouping based on these principles also occur for our 3D contours, and the addition of binocular disparity continuity serves to additionally highlight the profile of the contour. 
Experiment 2: 3D contour detection: The effect of local depth variations
In Experiment 1 we showed that the visual system can effectively detect contours that extend in depth. Note that the contours examined in the previous experiment comprised elements that were regularly displaced in depth along a particular oriented depth plane. In Experiment 2 we examined whether disrupting this regular depth continuity by displacing local elements away from their depth orientation plane affected contour detection performance. In particular, we quantified the perception of contours that globally extended through depth along a particular depth orientation (as in Experiment 1), but consisted of alternating local elements that, across different conditions, were systematically displaced in depth in opposite directions (see Figure 2D). In Experiment 2, we established the effective depth range over which local elements continue to be grouped in the perception of 3D contours. 
Methods
The same observers as in Experiment 1 participated in Experiment 2. Stimuli were similar to those used in Experiment 1, except contour angles of 10° and 30° were examined, and contours were oriented in depth along three directions of 0°, 30°, and 60°. As in Experiment 1, contours comprised six Gaussian elements that extended in depth, but across separate conditions alternating elements were additionally displaced in depth in opposite directions by 1, 2, 4, and 8 arcmin in the stereo images. As in Experiment 1, observers were required to identify which of two sequentially presented intervals contained the contour. Observers repeated this judgement 40 times for each of the 24 stimulus conditions (2 curved contours × 3 depth orientations × 4 element depth offsets). The order in which the different stimulus conditions were performed was randomized for each observer, and sufficient breaks were provided to avoid fatigue. 
Results and discussion
Figure 4 plots contour detection sensitivity as a function of the absolute depth displacement of local elements for contours of different depth orientations. Left and right panels of Figure 4 plot the results for contour angles of 10° and 30° respectively. Repeated-measures ANOVAs performed separately for the two contour angles observed a main effect of both depth orientation [10° contour: F(2, 32) = 7.467, p = 0.0022; 30° contour: F(2, 32) = 4.579, p = 0.0178] as well as the displacement of local elements [10° contour: F(3, 16) = 6.810, p = 0.0036; 30° contour: F(3, 16) = 14.74, p < 0.0001], but no significant interaction effects for both contour angles were observed (ps > 0.9215). A number of findings are evident. First, replicating the findings of Experiment 1, detection performance was superior for contours oriented in depth, compared with contours oriented at 0°. Second, contour detection performance decreased when local elements were increasingly displaced in depth. Note that performance approached chance levels for certain conditions (e.g., contours with an angle of 30°) when local elements were maximally displaced by 8 arcmin; thus, large displacements in depth disrupted the grouping of local contour elements. 
Figure 4
 
Contour detection sensitivity (d′) is plotted as a function of the depth displacement of local elements for different depth orientations (different symbols). Error bars represent 1 SEM.
Figure 4
 
Contour detection sensitivity (d′) is plotted as a function of the depth displacement of local elements for different depth orientations (different symbols). Error bars represent 1 SEM.
In summary, we showed that jittering the depth positions of local contour elements affected the ability to detect 3D contours. This finding suggests that disrupting the regular depth continuity of local contour elements prevented their grouping in depth; in the present study we have established the spatial range over which this occurs for the stimulus conditions employed in Experiment 2. Finally, our observations suggest that contour grouping in depth might involve the linking of a number of depth selective mechanisms that are tuned for a range of binocular disparities. This is similar to Hess and Field (1995),and to Khuu and Hayes (2005), who showed that the integration of local orientations occurs over large depth separations in the perception of global form in Glass patterns. 
Experiment 3: The effect of luminance polarity on the perception of 3D curved contours
In Experiment 3 we examined the degree to which local polarity affects the ability of the visual system to detect 3D contours (see Figure 2F). Previous studies have shown that polarity differences along the train of contour elements disrupt the detectability of form/shape by disrupting the integration of local elements (Badcock, Clifford, & Khuu, 2005; Field et al., 2000; Guidi, Parlangeli, Bettella, & Roncato, 2011; Roncato, 2014; Wilson & Wilkinson, 1998). Note that whereas polarity change might disrupt the ability to detect 2D contours, for 3D contours the regular depth continuity of local elements might provide an additional means through which local elements are grouped. Accordingly, it might be expected that 3D contours consisting of local polarity differences might be better detected (than 2D contours) owing to the continuation of its profile in depth which is unaffected by polarity variations. As shown in Experiments 1 and 2, the visual system is able to associate local contour elements in depth, and therefore binocular disparity might provide an aid to detecting 3D contours. Alternatively, much like the processing of 2D contours, the visual system might analyze 3D contour elements separately based on their luminance polarity, which is consistent with the physiological responses of disparity-tuned mechanisms in the primate visual cortex (e.g., Cumming & Parker, 2003; Ohzawa et al., 1990). Under these circumstances the visual system independently determines the depth profile of opposite polarity elements, and does not combine opposite polarity elements to detect the contour. In Experiment 3 we determined which of these two outcomes characterized the detection of 3D contours. 
Methods
The same observers as in Experiments 1 and 2 participated in the present study. The stimulus conditions and procedures were similar to the previous experiments, and the detectability of curved contours with angles of 10° and 30° were examined at depth orientations of 0° and 60° only. As before, the stimulus comprised six Gaussian elements, but alternating elements differed in luminance polarity—odd numbered elements were fixed to a Weber contrast of 1 (at full height), while in different conditions even numbered Gaussians were set to Weber contrast of 1, 0.5, 0.25, −0.25, −0.5, and −1. As in Experiments 1 and 2, contour detection was measured using a 2IFC procedure and the observer had to indicate the interval containing the 3D contour. This judgment was repeated 40 times for each of the 24 stimulus conditions. Observers performed these conditions in a randomized order with sufficient breaks between conditions to avoid fatigue. 
Results and discussion
In Figure 5, contour detection sensitivity is plotted as a function of the polarity of even numbered contour elements for depth orientations of 0° and 60° (circles and squares respectively). Results for contour angles of 10° and 30° are plotted in separate left and right panels respectively. Generally, as previously demonstrated, contours with a smaller contour angle of 10° were better detected than with an angle of 30°. A two-way, repeated measures ANOVA performed separately for the two curved contour angles both revealed no significant interaction effects (ps > 0.3292), but main effects of depth orientation [10° contour: F(1, 30 = 9.288, p = 0.0048; 30° contour: F(1, 30) = 5.173, p = 0.0303] and the local element contrast [10° contour: F(5, 30) = 23.85, p < 0.0001; 30° contour: F(5, 30) = 32.33, p < 0.0001]. Consistent with the findings of the previous experiments, contours oriented in depth (60°) were generally better detected than 2D contours (depth orientation of 0°), but this effect is only evident for same-sign (polarity) contrast values. 
Figure 5
 
Contour detection sensitivity (d′) plotted as a function of the Weber contrast of even-numbered contour elements; note that odd-numbered elements were fixed to a contrast of 1. Error bars represent 1 SEM. The results for contours with different depth orientations are shown as different symbols.
Figure 5
 
Contour detection sensitivity (d′) plotted as a function of the Weber contrast of even-numbered contour elements; note that odd-numbered elements were fixed to a contrast of 1. Error bars represent 1 SEM. The results for contours with different depth orientations are shown as different symbols.
When the polarity of even numbered Gaussian elements was the same sign (i.e., light increment) as odd numbered Gaussian elements (which was fixed to a Weber contrast of 1), observers were able to detect contours, but decreasing the contrast value reduced detection performance. These findings are consistent with those of McIlhagga and Mullen (1996), who showed that 2D contours consisting of local same sign contrast variations remain detectable by the visual system, and reduced as the luminance difference between contour elements increased. When the contrast polarity of even numbered Gaussian elements was negative (i.e., light decrement and below the background luminance) and opposite to odd numbered elements, observers were unable to detect the contour and performed at chance level regardless of the contrast value. One-sample t tests indicated that contour detection at −1,−0.5, and −0.25 contrast levels were not significantly different from chance performance (i.e., d′ of 0) for both depth orientations of 0° and 60° and contour angles of 10° (ps > 0.1081) and 30° (s > 0.5063). This indicates that 3D contours comprising of opposite polarity elements are not detectable despite the fact that they are additionally defined by regular depth continuity. The findings of Experiment 3 indicated that the visual system is unable to use binocular disparity as a means of associating local contour elements of opposite polarity, and that polarity grouping must predominantly mediate the processing of 3D contours. These results agree with physiological findings that have shown that disparity-tuned units in the visual cortex are selective for luminance polarity (see Cumming & Parker, 1997; Ohzawa, DeAngelis, & Freeman, 1990) and their activation is inhibited by visual stimuli of the opposite polarity. Polarity-dependent depth effects much like those observed in Experiment 3 have also been noted by Anderson and Nakayama (1994), who observed that elements of the same polarity are usually matched when resolving the depth profile (defined by binocular disparity) of occluded contours. 
Experiment 4: Color grouping and its effect on 3D contour perception
In the final experiment, we determined the degree to which 3D contours defined by color variations are detected by the visual system. Mullen, Beaudot, and McIlhagga (2000) have shown that varying the color of local elements along the contour (i.e., alternating elements were of different colors) disrupted 2D contour detection. These findings suggest that color information interferes with the integration of contours, and in Experiment 4 we examined the degree to which color variations affect the detection of 3D contours. While Experiment 3 showed that the visual system is unable to group different luminance polarity elements in depth, it is possible that the regular depth continuity of differently coloured contour elements might facilitate their grouping and therefore contour detection. However, color selective depth mechanisms have been reported in the visual cortex (e.g., Tsao et al., 2003), which suggests that depth might occur separately in different color channels. In Experiment 4 we tested these assumptions by requiring observers to detect red-green 3D contours of different depth orientations and compared performance to when the contour was achromatic. 
Methods
Observers were the same as those who participated in the previous experiments. The stimulus and procedures were similar to those used in Experiment 3, but all contour elements were light increment and set to a nominal Weber contrast of (0.375); however, alternating elements were differently coloured red and green. Thus, 3D contours used in Experiment 4 were defined by both luminance and color contrasts. The contour was embedded in a field of randomly placed Gaussian elements that were also luminance defined and similarly coloured red or green (see Figure 2F). Color was defined using the Derrington, Krauskopf, and Lennie (DKL; see Derrington, Krauskopf, & Lennie, 1984) color space. DKL space is represented in 3D dimensions (derived from the chromaticity diagram) with different colors specified by spherical coordinates in which the azimuth specifies the hue, the elevation specifies deviation from the isoluminant plane, and the amplitude determines the color contrast as a fraction of the maximum modulation along the cardinal axis. The chromaticity is defined in the horizontal plane along two axes of L-M and S-(L+M) which represents the modulations of color mechanisms, with cardinal directions of 0°–180° and 90°–270° representing exclusive modulation/excitation along L-M and S-(L+M) cone systems. According to this nomenclature an azimuth of 0° is red and 180° is green. We employed these colors, and 3D contour elements were alternately coloured red and green (see Figure 2G). 
Hetereochromatic flicker photometry was employed to ensure that contour elements were perceptually equiluminant with each other. Here a single Gaussian element (radius of 2°) was presented centrally that alternated in color from red to green at 20 Hz. The intensity of the red stimulus was held constant, and observers adjusted the intensity of the green stimulus (using Method of Adjustment) until perceptual flicker was minimized. This process was repeated at least three times for each observer. Because our stimulus comprised many Gaussian elements distributed over a large spatial area, precise isoluminance at all spatial points could not be ensured. To further minimize luminance artefacts, the luminance of each element was randomly permutated within the range −8 to 8 cd/m2. This approach is similar to that adopted by pseudoisochromatic stimuli such as the well-known Ishihara Plates and the Cambridge Color Test (e.g., Regan, Reffin, & Mollon, 1994) to minimize luminance artefacts when using coloured stimuli. As shown in Experiment 3 (and also shown by McIlhagga & Mullen, 1996) small variations in luminance of the same polarity did not prevent contour detection. 
As in the previous experiment, contour detection performance was measured using a 2IFC procedure, and observers were required to indicate the interval containing the contour; as in Experiment 3 contours were 2D (i.e., 0°) or rotated in depth by 60°. Detection of curved contours was repeated for two contour angles of 10° and 30° and repeated for color amplitudes/contrasts of 0, 0.2, and 0.4 for each color. These values in DKL space are arbitrary and represent the relative output of our testing monitor relative to its maximum output. Thus, there were 12 stimulus conditions in total, and each condition was repeated at least 30 times for each condition. Observers performed each condition in a randomized order. 
Results and discussion
The results of Experiment 4 are shown in Figure 6 in which contour sensitivity (d′) is plotted as a function of the color contrast. A repeated measures, two-way ANOVA (performed separately for both contour angles) revealed no significant interaction effects (regardless of the contour angle, ps > 0.3427), but did reveal a main effect of color contrast [10°: F(2, 12) = 21.61, p < 0.0001; 30°: F(2, 12) = 5.75, p = 0.0181]. A main effect of depth orientation was observed for the 10° curve, F(1, 12) = 6.284, p = 0.0276, but this did not reach significance for the 30° contour (p = 0.1568). 
Figure 6
 
Contour detection sensitivity (oriented 0°—circles—and 60°—squares—in depth) is plotted as a function of the colour contrast for 10° and 30° contour. Error bars represent 1 SEM.
Figure 6
 
Contour detection sensitivity (oriented 0°—circles—and 60°—squares—in depth) is plotted as a function of the colour contrast for 10° and 30° contour. Error bars represent 1 SEM.
A number of findings are evident in Figure 6. First, note that contours were both luminance and color defined. Were it that contour detection was primarily dependent on luminance, it is expected that performance would be the same as the achromatic stimulus (i.e., color contrast of 0) and increasing color contrast would leave performance unchanged. However, increasing the color contrast affected its detection with performance decreasing with greater color contrast. This finding is consistent with those of McIIhagga and Mullen (1996) and argues that continuity of color is an important requirement for the detection of contours, as it serves as an important cue in identifying the borders of objects independent of luminance variations, which might be attributed to local changes in lighting in natural scenes (see also Long, Yang, & Purves, 2006). Second, the fact that no significant interaction effect (between depth orientation and color contrast) was observed indicated that the effect of changing color contrast on contour detection performance was the same for curved contours oriented 0° and 60° in depth. Accordingly, there is no advantage for detecting coloured 3D contours, and binocular disparity is not used to facilitate the grouping of different colored elements. 
In Experiment 4 we noted that while increasing color contrast decreased contour detection performance, observers were nevertheless able to detect them as performance was above chance level. This finding is consistent with the observation made by Mullen et al. (2000), who noted that (in the case of 2D contours), integration does not exclusively occur in separate color channels (e.g., Shapley & Hawken, 2011), but rather operates by combining different colors. However, this process is not optimal compared to when the contour is achromatic. As mentioned, disparity-tuned mechanisms are also selective for color (e.g., Tsao et al., 2001), and our finding suggests that the outputs of such neural mechanisms are also not optimally integrated in the detection of 3D contours. Alternatively, above chance contour detection performance reported in the present study and Mullen et al. (2000) might be accounted through contour grouping by other means. For example, in the study by Mullen et al., contours comprised of coloured elements that were additionally oriented, while in the present study elements were additionally luminance defined. It is possible that these local features might contribute to the perceptual grouping of contour elements. 
The dependency of depth processing on color, as demonstrated in the present study, is consistent with the observations of Domini, Blaser, and Cicerone (2000) who noted a depth aftereffect that is contingent on the color of the test and adapting stimulus. In their study, observers viewed and adapted to two distributions of red and green dots separated in depth (defined by binocular disparity). When the adapting stimulus was comprised of green dots in front, this resulted in the perceptual displacement in depth of only red dots in the test stimulus. On the other hand, adaptation to red dots in front selectively altered the perceived depth of green dots in the test stimulus. This color-contingent depth effect and the findings of the present study support the possibility that the processing of depth information is largely mediated by functionally separable color systems. 
General discussion
The aim of the present study was to examine the detectability of 3D curved contours, and the stimulus factors contributing to their perception. In Experiment 1, we characterized the impact of changing depth orientation on the detectability of contours with different contour angles. Cocircular contours were particularly investigated as they are likely to represent salient objects that have smooth and closed contour profiles such as fruits and faces. We find that increasing contour angle decreased detection performance, and 3D contours that were oriented in depth were more accurately detected than 2D contours. The latter finding suggests that the visual system is sensitive to the depth profile of the contour, which provides a detection advantage over 2D contours. In Experiment 2, we demonstrated that contour integration can occur when local elements are displaced in depth to disrupt the continuity of the contour. Systematically increasing the displacement of elements (away from the contour depth orientation) disrupted detection performance. In Experiments 3 and 4 we examined whether variations in the contrast polarity and color of local elements affected the perception of 3D curved contours. In particular, we questioned whether the regular depth continuity of the contour can aid in the detection of contours characterized by local polarity and color variations. Interestingly, we find that binocular information does not facilitate the grouping of local elements with variations in luminance and color. 
The findings of the present study are significant as they build upon existing studies that have directly demonstrated that binocular disparity can be effectively used to group contour elements. Both Hess and Field (1995) and Hess et al. (1997) demonstrated better contour detection for contours with local elements displaced in depth and contours that traverse depth. In the present study, we further demonstrated this effect for contour detection over a range of depth orientations and local depth displacements. Our findings suggests that the visual system actively represents the 3D profile of contours, and this representation is likely to be mediated by disparity-tuned cells known to exist in the visual cortex. The locus of contour integration is believed to reside in primary visual cortex with the association field network emulated in the horizontal cell linking between orientation-tuned detectors (e.g., Bosking et al., 1997). Such detectors are also tuned for binocular disparity (see Cumming & Parker, 1997; Tsao et al., 2003), and are therefore capable of associating contour elements in depth. Indeed the range of binocular disparities, over which local contour elements are associated, are within the tuning bandwidths of disparity-tuned mechanisms that have been identified in the primary visual cortex (e.g., Ohzawa et al., 1990). The results of the present study (and those of Hess and colleagues, 1997) are significant as they provide conclusive behavioral evidence for the existence of depth detectors that facilitate the detection of 3D scene structure and call for a revision of the association field model to extend contour grouping in depth. 
Our observation that contrast polarity changes affected the detection of 3D contours suggests these low-level features must initially mediate contour detection and that depth processing occurs independently within systems that are selective for different contrast polarity differences. The observations made in Experiment 3 are likely to reflect independent processing by functional pathways that operate separately to recover different luminance polarities, and their outputs are not combined at the stage of contour analysis. Our findings are consistent with physiological studies that have reported the existence of disparity detectors in V1 and V2 which are also selective for contrast polarity (e.g., Cumming & Parker, 2003; Ohzawa et al., 1990). As our contours comprised six alternating elements of either different contrast polarity, these different polarity systems provide an estimate of only half of the contour (i.e., contour fragments of three elements). Within each system estimates, the depth of local elements are also determined, but the outputs of each system is insufficient to identify the whole 3D contour due to masking by surrounding noise elements in the stimulus. Note that a pilot study established that six elements was the minimum number of contour elements required for the contour to be optimally detected; below this, contours are detected at chance levels as indicated by our findings. 
Cham et al. (2007) raised the possibility that cocircular contour detection performance might be related to their statistics in natural images. Cham et al. measured the frequency of occurrence of cocircular contours with different contour angles, and observed that contours without or with small contour angles were most frequently occurring; contours defined by larger angular change occurred less frequently in natural images. They argued that the visual system capitalizes on this natural image statistic such that detection is optimally tuned to detecting curved contours with shallower curves. This assertion agrees with the findings of the present study. 
By extension, it is possible that cocircular contours that are oriented in depth are also more frequently occurring in natural images, which might account for their superior detection as reported by the present study. Whereas only a handful of studies have sought to characterize the statistics of surfaces in natural images (e.g., Hibbard, 2008; Yang & Purves, 2003a, 2003b), the findings of Yang and Purves (2003b) suggest that such a relationship might exist. In a comprehensive study, Yang and Purves sought to characterize the properties (e.g., roughness, slant, and tilt) of local planar surfaces in natural scenes using a laser range scanner. In regards to depth slant (i.e., the degree to which the surface extends in depth), they observed that the occurrence probability of a local planar surface increases with depth slant, peaking at a value of approximately 57°, though this is most evident for horizontal and vertical 2D tilts. Moreover, in natural scenes the orientation (i.e., slant and tilt) of nearby local surfaces is strongly correlated when they are closely spaced (and less than 10°). Thus, in natural scenes there is a tendency for local surfaces to be oriented in depth, and adjacent surfaces are continuous in depth. As the contours employed in the present study comprised of contour elements that regularly extended through depth (see Figure 2), our findings are in agreement with these surface statistics, as we find better detection performance for contours 3D contours. In addition, Yang and Purves noted that occurrence of 3D curved surfaces in natural images decreases with the degree of 3D curvature. We observe a similar effect such that the detection of 3D contours decreased with increasing contour angle. However, it is important to note that further studies are required to directly establish the relationship between contour detection and scene statistics. While our findings and those of Yang and Purves show a degree of similarity, data describing the statistics of the 3D scene have been analyzed without direct and specific reference to contour structure. Future studies might wish to extend the current study to specifically examine the relationship between human contour detection and natural images and consider the relative importance of other contour scene characteristics such as 2D tilt and smoothness, which have been shown to be contributing factors in the occurrence probability of surfaces. 
Our observation that changes in contrast polarity and color affects contour perception is of note in regards to considerations regarding the effectiveness of camouflage, in which the contour profile/shape of an object is broken up by random textures of different sizes, color, and luminance polarity. Note that the 3D profile of camouflaged objects is unaffected by these variations, and accordingly, might provide a means for detection by a visual sensitive system sensitive to binocular disparity. Our findings suggest this 3D profile does not provide an effective cue for contrast detection, and that variations in contrast polarity and color are sufficient to reduce overall contour detectability. The present study demonstrates the effectiveness of camouflage because it also disrupts the recovery of the global depth profile of objects. Depth grouping is seen to be most effective between similar polarity and coloured elements, and the visual system does not optimally combine information from separate (polarity and color) systems to detect the object contour. 
In conclusion, the present study demonstrated that observers are able to detect 3D curved contours. Particularly, the visual system is able to integrate across a broad range of depths, but varying luminance polarity and color along the contour train affects 3D contour detection. The present findings serve to confirm the importance of these visual factors in the grouping of elements in depth. 
Acknowledgments
We thank the two anonymous reviewers whose comments and suggestions have improved the reported studies. This work was supported by the Australian Research Council project grant (DP11010471) to S Khuu, and an ARC Future Fellowship (FT140100535) awarded to J. Kim. V. Honson was supported by an Australian Postgraduate Award. 
Commercial relationships: none. 
Corresponding author: Sieu Khuu. 
Email: s.khuu@unsw.edu.au. 
Address: School of Optometry and Vision Science, The University of New South Wales, Sydney, Australia. 
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Figure 1
 
A stereo-pair when fused shows the 3D curved contour profile of a flower mutually extending in 2D space, and in depth.
Figure 1
 
A stereo-pair when fused shows the 3D curved contour profile of a flower mutually extending in 2D space, and in depth.
Figure 2
 
Examples of contour stimuli used in the present study. Figure 2A provides a schematic representation of a contour following a constant angular path of 20°. In Figure 2B contours are oriented in depth given by σ (in degrees), while fusing the stereo pairs shown in Figure 2C provides a representation of this stimulus. Figure 2D is an example of a 3D contour in which the depth positions of local elements are jittered by displacing alternating contour elements in opposite directions away from the depth orientation of the contour (as in Experiment 2). Figure 2E shows a 3D contour embedded in noise, whereas Figures 2F and 2G are examples of 3D contours defined by local elements alternating in polarity and colour embedded in noise. The red dot in each stereo image provides an indication of the location of the contour visible through fusing the stereo image pair.
Figure 2
 
Examples of contour stimuli used in the present study. Figure 2A provides a schematic representation of a contour following a constant angular path of 20°. In Figure 2B contours are oriented in depth given by σ (in degrees), while fusing the stereo pairs shown in Figure 2C provides a representation of this stimulus. Figure 2D is an example of a 3D contour in which the depth positions of local elements are jittered by displacing alternating contour elements in opposite directions away from the depth orientation of the contour (as in Experiment 2). Figure 2E shows a 3D contour embedded in noise, whereas Figures 2F and 2G are examples of 3D contours defined by local elements alternating in polarity and colour embedded in noise. The red dot in each stereo image provides an indication of the location of the contour visible through fusing the stereo image pair.
Figure 3
 
Mean contour detection sensitivity represented as d′ values is plotted as a function of the contour angle (in degrees). Curved contours of different depth orientations are given by different symbols (see legend). Solid lines represent the line of best fit for each contour depth orientation (0°: Y = −0.03003 × X + 1.629; 15° Y = −0.03319 × X + 1.656; 30° Y = −0.03345 × X + 1.971; 60° Y = −0.04136 × X + 2.407).
 
In Figure 3B, contour detection performance is plotted for contours of different lengths (six and 12 elements) for depth orientations of 0° and 60°. In both A and B, points represent the averaged observer data and error bars represent 1 SEM.
Figure 3
 
Mean contour detection sensitivity represented as d′ values is plotted as a function of the contour angle (in degrees). Curved contours of different depth orientations are given by different symbols (see legend). Solid lines represent the line of best fit for each contour depth orientation (0°: Y = −0.03003 × X + 1.629; 15° Y = −0.03319 × X + 1.656; 30° Y = −0.03345 × X + 1.971; 60° Y = −0.04136 × X + 2.407).
 
In Figure 3B, contour detection performance is plotted for contours of different lengths (six and 12 elements) for depth orientations of 0° and 60°. In both A and B, points represent the averaged observer data and error bars represent 1 SEM.
Figure 4
 
Contour detection sensitivity (d′) is plotted as a function of the depth displacement of local elements for different depth orientations (different symbols). Error bars represent 1 SEM.
Figure 4
 
Contour detection sensitivity (d′) is plotted as a function of the depth displacement of local elements for different depth orientations (different symbols). Error bars represent 1 SEM.
Figure 5
 
Contour detection sensitivity (d′) plotted as a function of the Weber contrast of even-numbered contour elements; note that odd-numbered elements were fixed to a contrast of 1. Error bars represent 1 SEM. The results for contours with different depth orientations are shown as different symbols.
Figure 5
 
Contour detection sensitivity (d′) plotted as a function of the Weber contrast of even-numbered contour elements; note that odd-numbered elements were fixed to a contrast of 1. Error bars represent 1 SEM. The results for contours with different depth orientations are shown as different symbols.
Figure 6
 
Contour detection sensitivity (oriented 0°—circles—and 60°—squares—in depth) is plotted as a function of the colour contrast for 10° and 30° contour. Error bars represent 1 SEM.
Figure 6
 
Contour detection sensitivity (oriented 0°—circles—and 60°—squares—in depth) is plotted as a function of the colour contrast for 10° and 30° contour. Error bars represent 1 SEM.
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