Perception, 2014, volume 43, pages 1303 – 1315
doi:10.1068/p7746
The impact of stereoscopic depth on the Munker–White illusion Michael Kavšek
Department of Psychology, Unit of Developmental and Educational Psychology, University of Bonn, Kaiser-Karl-Ring 9, 53111 Bonn, Germany; e‑mail: [email protected] Received 11 March 2014, in revised form 27 October 2014, published online 9 December 2014 Abstract. The current study investigated the impact of stereoscopic depth information on adults’ perception of a coloured version of the Munker–White illusion. In one half of the illusory figure red patches were embedded in black stripes and flanked by yellow stripes. In the other half of the illusory figure red patches were embedded in yellow stripes and flanked by black stripes. The red patches either remained in the same depth plane as the black and yellow inducing stripes (zero horizontal disparity condition) or were shifted into the foreground (crossed horizontal disparity condition) or into the background (uncrossed horizontal disparity condition). According to the results, the illusory effect was robust across all viewing conditions. The illusion mainly consisted of a subjective darkening of the red patches superimposed on the yellow stripes, a perceived hue shift of the red patches superimposed on the black stripes toward yellow, and a subjective saturation decrease in both kinds of red patches. Moreover, the study established a partial confirmation of Anderson’s scission theory, according to which the Munker–White illusion should be largest in the crossed horizontal disparity condition, intermediate in the zero horizontal disparity condition, and smallest in the uncrossed horizontal disparity condition. Keywords: Munker–White illusion, stereoscopic depth, lightness illusion, visual illusion
1 Introduction The Munker–White illusion consists of a grating of alternating black and white bars or of bars with two different colours, some sections of which are replaced by mid-grey rectangles or by rectangles with a third colour. The black and white version of the illusion, White’s (1979, 2010) illusion, is depicted in figure 1. The figure induces a vivid lightness illusion. The grey rectangles placed on the black stripes appear lighter than the grey rectangles placed on the white stripes. Various attempts have been made to explain White’s illusion. These explanations assume either high-level or low-level processes. According to several prominent high-level theories, occlusion signals embedded in the illusory figure play a crucial role (eg Ross & Pessoa, 2000; Todorović, 1997; Zaidi, Spehar, & Shy, 1997). More specifically, our visual system extracts the local T-junction information which occurs at the intersections of the grey, black, and white areas (see figure 1). The stem of the junctions separates the grey rectangles and the bars on which they are superimposed. The top of the junctions runs along the adjacent bars. T-junctions specify the adjacent bars as occluding surfaces and the other two areas as occluded surfaces. As a consequence, the grey rectangles and the bars on which they are positioned are allocated the same layer, but the adjacent bars are allocated a different layer. This depth separation is consistent with a simultaneous contrast interpretation of the White illusion: the grey patches are darkened by the white bars on which they are superimposed but are unaffected by the lightness of the flanking black bars, and the grey patches are lightened by the black bars on which they are placed but are unaffected by the flanking white bars’ lightness. Anderson (1997, 2003), however, points out that this interpretation is incomplete because the White illusion is stronger than the illusory effect induced by simultaneous contrast displays. According to his perceptual scission theory, the grey elements of the White illusion are decomposed into a combination of light and dark. More specifically, based on a
1304
M Kavšek
Figure 1. In White’s illusion grey rectangles are superimposed on black and white bars. The grey rectangles embedded in the black stripes appear lighter than the grey rectangles embedded in the white stripes. In fact, the luminances of all grey rectangles are identical.
T-junction analysis, the grey patches are interpreted as semitransparent overlays (eg Watanabe & Cavanagh, 1993). As a consequence, the grey elements superimposed on the black bars appear lighter because some of their blackness is attributed to the subjacent black bars and is therefore subtracted from them. Similarly, our visual system assumes that some of the white of the grey elements positioned on the white bars belongs to these subjacent bars. Again, this amount of white is cancelled out of the grey elements, resulting in a darker appearance. Finally, according to Gilchrist et al. (1999), the T-junctions cause the grey elements to group with the embedding bars. The authors’ anchoring account states that the illusory effect consists mainly in an illusory lightening of the grey patches placed on the black stripes. Several studies have challenged these explanations. Howe (2005) demonstrated that the White illusion can be induced even without line junction information (see also Yazdanbakhsh, Arabzadeh, Babadi, & Fazl, 2002). Moreover, the White illusion is not always stronger than simultaneous contrast (eg Blakeslee, Pasieka, & McCourt, 2005; Li, Tavantzis, & Yazdanbakhsh, 2009). Low-level accounts refer to neurophysiological mechanisms. According to White (1981), the illusion is the result of three processes: lightness contrast, lightness assimilation occurring when the spatial frequency of the pattern is high, and lightness assimilation which is the result of ‘pattern-specific inhibition’ processes. Lightness contrast is a shift of a region’s lightness away from the lightness of the surrounding area. In contrast, lightness assimilation is the partial shift of a region’s lightness toward the lightness of the surrounding area. Blakeslee and McCourt (1999, 2004; Blakeslee et al., 2005) constructed a spatial filtering explanation for brightness phenomena such as the White effect. The parameters in this explanation reflect early stage cortical filtering operations. Later, Robinson, Hammon, and de Sa (2007) extended this model to account for a wider range of variants of the White illusion. Alternative low-level accounts have been suggested by Barkan, Spitzer, and Einav (2008) and by Otazu, Vanrell, and Párraga (2008).
The impact of stereoscopic depth on the Munker–White illusion
1305
A specific prediction of Anderson’s (1997, 2003) perceptual scission theory is that the White illusion should be enhanced by adding crossed horizontal disparity to the grey rectangles. Crossed horizontal disparity information shifts the grey rectangles into the foreground, thereby reinforcing the impression of a semitransparent overlay. Anderson (1997) compared the illusory effect of a two-dimensional version of the illusion with the illusory effects evoked by a figure, the rectangular regions in which were shifted to the front by adding crossed horizontal disparity, and a figure, the rectangular regions in which were moved into the background by adding uncrossed horizontal disparity. According to the perceptual scission theory, shifting of the rectangular regions into the background should diminish the illusion, because the regions can no longer be interpreted as floating above the white and black bars. Instead, when the grey rectangles are superimposed on the white stripes, both the grey regions and the white stripes seem to be shifted behind the black stripes, and when the grey rectangles are superimposed on the black bars, both the grey regions and the black stripes seem to be placed behind the white stripes. More specifically, in the first case the figure appears as a coherent grey surface on a white background with black stripes floating above these areas, while in the second case the figure appears as a coherent grey surface on a black background with white stripes partially occluding these areas. As a consequence, the illusory effect evoked by the display can be explained by simultaneous contrast evoked by the grey patches’ surrounding background. Anderson (1997) emphasizes that White’s illusion is stronger than simultaneous contrast effects. The illusion observed in the uncrossed horizontal disparity condition should therefore be smaller than the illusory effect observed in the no‑depth and crossed horizontal disparity conditions. According to Anderson’s (1997) results, the illusory effect was largest in the crossed horizontal disparity condition. Moreover, when comparing the uncrossed horizontal disparity condition with the two-dimensional no‑depth condition, five out of seven participants perceived a diminished or unaffected illusory effect and the remaining two participants perceived an enhanced illusory effect in the uncrossed horizontal disparity condition. Two additional studies have investigated the impact of stereoscopic depth information on the strength of White’s illusion. Taya, Ehrenstein, and Cavonius (1995) established an enhancement of the illusion under both crossed and uncrossed horizontal viewing conditions. The enhancement was smaller when the grey rectangles were moved to the back than when they were moved to the front. Ross and Pessoa (1995, 2000) found that the illusory effect was diminished under uncrossed horizontal disparity viewing, but was maintained under crossed horizontal disparity viewing. However, the viewing conditions created by Ross and Pessoa (eg 2000) were not comparable with those implemented by Anderson (1997), because they added horizontal disparity to both the grey rectangles and the stripes on which they were superimposed. Munker (1970) was amongst the first to describe a coloured version of the White illusion. For example, he placed red elements on blue and yellow stripes. The red elements appear slightly orange when placed on the blue stripes and slightly purplish when placed on the yellow stripes. Similar observations have been made by Anstis (2006), Clifford and Spehar (2003), Kitaoka (2010), Lingelbach, Neustadt, Schmidt, and Ehrenstein (2003), McCann (2002), and Yang, Kanazawa, and Yamaguchi (2010). Anstis (2006) points out that the induced colour of the superimposed elements is the result of both a shift toward the uninterrupted stripes’ colour (colour assimilation) and a shift toward the opposite of the interrupted stripes’ colour (colour contrast). Strength of the illusion and the relative contribution of assimilation and contrast depend on several factors. First, strength of the illusion is moderated by the stripes’ spatial frequency: the illusory effect increases, the higher the spatial frequency. Moreover, the contribution of assimilation correlates positively with spatial frequency (see also Clifford
1306
M Kavšek
& Spehar, 2003). According to Kitaoka (2010), the relative contribution of assimilation and contrast to the illusion varies across luminances. In particular, colour contrast is more effective than colour assimilation, if the luminance of the superimposed elements is intermediate and is close to the luminances of the inducing stripes. The current study investigated the illusory effect evoked by a coloured Munker–White illusion. In the illusory figure red elements were placed on black and yellow inducing stripes. Moreover, it was explored whether addition of uncrossed and crossed horizontal disparity to the red elements affected the illusory effect. Three versions of the illusion were created. In one version the illusory figure was a two-dimensional depiction. In the other two versions the red patches were shifted into either the background or the foreground. For each of the three versions of the illusion the participants’ task was to select those colours from the Natural Color System (NCS) most properly describing the perceived colours of the red patches. By comparing the colour selections made for the three versions of the illusion, it can be tested whether the illusory effect is largest for the figure containing crossed horizontal disparity and smallest for the figure containing uncrossed horizontal disparity, as predicted by the perceptual scission theory. Moreover, the illusory effects were quantified on the colour dimensions of hue, saturation, and lightness. As a consequence, the current study extended the previous stereoscopic experiments conducted by Anderson (1997), Ross and Pessoa (1995, 2000), and Taya et al. (1995): by using achromatic versions of the Munker–White illusion, these experiments focused solely on the lightness dimension. 2 Method 2.1 Participants In total, thirty-two adults participated in the experiment (sixteen females and sixteen males, mean age = 27 years, range = 20–42 years). An additional two participants (one female and one male) were excluded from the study due to defective colour vision. The participants gave informed consent before testing began. After the experiment, they were informed about the study. The study was approved by the ethics committee of the Department of Psychology at the University of Bonn (Germany). 2.2 Apparatus Each participant sat on a chair 70 cm from a 47.4 × 29.6 cm flat autostereoscopic threedimensional (3‑D) computer screen (SeeFront SF 2223). The screen could be seen through an aperture that was cut into the back of a 100 × 120-cm dull white wooden front panel. The centre of the screen was at the participant’s eye level. The front panel was mounted on a 50 cm high table. The floor below the table was hidden by a 100 × 51 cm black cloth. The room was dark except for light from a lamp behind the front panel and from the computer screens in the experimental room. A face-tracking camera was set into the monitor’s upper frame. The camera was connected to the software of the autostereoscopic monitor. The software was handled using an additional computer monitor, which also showed the shots of the face-tracking camera. Frames around the contour of the face, the eyes, and the nose signaled whether the face-tracking camera correctly captured the participant’s face. The frames disappeared as soon as the camera did not have sufficient information to detect the face. Lenticular lenses on top of the 3‑D screen split the image into two parts, one for the right eye and one for the left eye. Using the information from the face-tracking camera, the auto stereoscopic monitor’s software automatically determined the position of the participant’s face and adapted the half-images to that position. The autosteroscopic device needs about G 0.25 s to restore the stereoscopic effect after rapid head movements. The stereoscopic device may temporarily lose track of the face—for instance, if the face moves outside the scope of
The impact of stereoscopic depth on the Munker–White illusion
1307
the tracking camera or if the head is turned backwards. In this case, the device typically needs G 0.5 s to find the face again and restore the stereoscopic effect. The distance from the autostereoscopic monitor should be between 55 cm (minimum) and 120 cm (maximum). Within these distances, separation of the half-images is nearly perfect and interocular cross-talk is avoided. 2.3 Stimuli The participants were presented with computer animations depicting the stimuli (see http://munki.uni-bonn.de). In each animation the illusory figure was split into two parts, one in which red horizontal rectangular patches were superimposed on black horizontal stripes, and one in which red horizontal rectangular patches were superimposed on yellow horizontal stripes. One of the stimulus parts was situated on the left half of the computer screen, and the other one was situated on the right half of the screen. Distance between the two stimulus parts was 15.87 cm (12.94 deg). Each stimulus part consisted of 13 black (luminance, Y G 0.2 cd m–2 ) stripes, 13 yellow (x = 0.43, y = 0.51, Y = 163 cd m–2 ) stripes, and 13 red (x = 0.67, y = 0.33, Y = 49 cd m–2 ) stripes. Each black or yellow stripe measured 4 × 0.323 cm (3.27 × 0.26 deg); each red rectangular patch measured 2 × 0.323 cm (1.64 × 0.26 deg). Overall width of each stimulus part was 4 cm (3.27 deg), and the overall height was 8.4 cm (6.87 deg). The red patches were positioned in the middle of each stimulus part. They continuously moved back and forth in the horizontal plane. The movement’s path length from the left to the right or vice versa was 0.5 cm (0.41 deg). Speed of movement was 0.5 cm s–1. The red patches in the two stimulus parts moved in phase. The movement of the red patches was included because the stimuli were also used in an experiment with infants. Infants’ attention is highly attracted by motion. As a consequence, motion of the red patches might facilitate infants’ perception of the stimuli. The remaining parts of the computer screen were white. Participants were tested under three viewing conditions: a zero horizontal disparity condition, a crossed horizontal disparity condition, and an uncrossed horizontal disparity condition. In each condition two animations were shown. In one of the two animations the stimulus part with the red patches superimposed on the black stripes was shown on the left side of the screen, and the stimulus part with the red patches superimposed on the yellow stripes was shown on the right side of the screen. In the other animation the position of the two stimulus parts was exchanged. In the two zero disparity animations the red patches were situated in the same depth plane as the flanking and embedding stripes. In the two crossed disparity animations the red patches were shifted into the foreground by embedding them in a crossed horizontal disparity of 0.393 cm (0.32 deg). In the two uncrossed disparity animations the red patches were shifted into the background by embedding them in an uncrossed horizontal disparity of 0.393 cm. Participants assessed the perceived colour of the red patches using the 15 × 14.5 mm, semimatt colour samples of the Natural Color Atlas (Swedish Standards Institute, 2008). The NCS is a perceptual system, the colours in which are defined by three properties: hue, blackness, and chromaticness (Hård, Sivick, & Tonnquist, 1996a, 1996b). The colour system has been developed to have equal visual steps within these scales (eg Kuehni, 2000). Hue is specified in terms of similarity to the basic chromatic sensations: yellow, red, blue, and green. Blackness specifies how dark the colour is, and chromaticness specifies how saturated the colour is. Values for blackness and chromaticness are percentages. The value for hue is a percentage score between two of the colours: yellow, red, blue, and green. For example, ‘S 0585–Y80R’ denotes a colour with 5% perceived blackness, 85% perceived chromaticness, 80% perceived red (R), and the remaining 20% perceived yellow (Y).
1308
M Kavšek
2.4 Procedure Each participant was tested individually. The participant was seated comfortably in front of the computer screen. First, a practice trial was run to make him or her familiar with the stereoscopic device, the visual stimuli, and the experimental task. Afterwards, the participant was shown the six animations depicting the zero, the crossed disparity, and the uncrossed disparity stimuli on separate trials. The two animations for each viewing condition were presented on successive trials. As a consequence, each viewing condition consisted of two trials which differed with respect to the position of the two parts of the illusory figure. The three viewing conditions can be combined into six orders. Each of these six orders of three viewing conditions was conducted twice to obtain 12 experimental trials. The six sequences of 12 trials were randomly assigned to the thirty-two participants such that each sequence occurred approximately equally often. The position of the stimulus part (red patches superimposed on the black stripes shown on the left versus right side of the screen) alternated from trial to trial. Three out of the six sequences of 12 trials started with an animation in which the red patches on the black stripes were positioned on the left side of the screen; the other three sequences started with an animation in which the red patches on the black stripes were positioned on the right side of the screen. Since each (zero disparity, crossed disparity, and uncrossed disparity) version of the illusory figure was presented 2 (positions of the stimulus parts) × 2 (repetitions) times, an overall number of 384 judgments was made by the thirty-two participants (3 versions × 4 presentations × 32 participants). On each trial the participant was instructed to select and point at the two NCS colour samples best describing perceived colours of the red patches in the two halves of the illusory figure. A short break was taken after the sixth experimental trial. The experiment took about 20 to 30 min. 2.5 Results The participants selected NCS blackness values between 5% and 25% in 5% increments, NCS chromaticness values between 60% and 85% in 5% increments, and NCS hue values between 50% and 90% in 10% increments. Values for hues indicated the amount of perceived red with the difference to 100% indicating the amount of perceived yellow. In the first step the deviation of both the subjective colour of the red patches on the yellow stripes and the subjective colour of the red patches on the black stripes from the subjective red tone used in the illusory figure was examined. More specifically, five adult participants were presented with the red tone in isolation—that is, without the context of the black and yellow inducing stripes. The participants’ task was to find the NCS colour sample that was most similar to the red tone. The red tone was presented on the 3‑D computer monitor. It was surrounded by a white background. All participants uniformly selected the colour sample ‘S 0585–Y80R’, the colour sample with 5% perceived blackness, 85% perceived chromaticness, 80% perceived red, and 20% perceived yellow. One-sample t‑tests were conducted to compare the empirical means with these values. First, deviation of mean percentage of perceived blackness of both the red patches on the yellow stripes and the red patch on the black stripes from 5% perceived blackness was tested for each of the three viewing conditions. Mean percentages of perceived blackness for each of the three viewing conditions are summarized in figure 2. The two-tailed B–Y (Benjamini & Yekutieli, 2001; Narum, 2006) corrected 0.05 level of significance for a total of six comparisons is p = 0.02041. All two-tailed scores of p resulting from the t‑tests for the red patches on the yellow stripes were lower than 0.02041, indicating that the patches were perceived as significantly darker than 5% perceived blackness. To examine whether this result was moderated by the viewing condition variable, pairwise comparisons between the deviations of mean percentage of perceived blackness of the red patches on the yellow
The impact of stereoscopic depth on the Munker–White illusion
1309
stripes from 5% were conducted across the three viewing conditions. Paired t‑tests showed that the deviation score for the crossed disparity condition was significantly higher than the deviation score for the uncrossed disparity condition ( p 0.02727). The perceived hue of the red patches superimposed on the yellow stripes was significantly ( p
doi:10.1068/p7746
The impact of stereoscopic depth on the Munker–White illusion Michael Kavšek
Department of Psychology, Unit of Developmental and Educational Psychology, University of Bonn, Kaiser-Karl-Ring 9, 53111 Bonn, Germany; e‑mail: [email protected] Received 11 March 2014, in revised form 27 October 2014, published online 9 December 2014 Abstract. The current study investigated the impact of stereoscopic depth information on adults’ perception of a coloured version of the Munker–White illusion. In one half of the illusory figure red patches were embedded in black stripes and flanked by yellow stripes. In the other half of the illusory figure red patches were embedded in yellow stripes and flanked by black stripes. The red patches either remained in the same depth plane as the black and yellow inducing stripes (zero horizontal disparity condition) or were shifted into the foreground (crossed horizontal disparity condition) or into the background (uncrossed horizontal disparity condition). According to the results, the illusory effect was robust across all viewing conditions. The illusion mainly consisted of a subjective darkening of the red patches superimposed on the yellow stripes, a perceived hue shift of the red patches superimposed on the black stripes toward yellow, and a subjective saturation decrease in both kinds of red patches. Moreover, the study established a partial confirmation of Anderson’s scission theory, according to which the Munker–White illusion should be largest in the crossed horizontal disparity condition, intermediate in the zero horizontal disparity condition, and smallest in the uncrossed horizontal disparity condition. Keywords: Munker–White illusion, stereoscopic depth, lightness illusion, visual illusion
1 Introduction The Munker–White illusion consists of a grating of alternating black and white bars or of bars with two different colours, some sections of which are replaced by mid-grey rectangles or by rectangles with a third colour. The black and white version of the illusion, White’s (1979, 2010) illusion, is depicted in figure 1. The figure induces a vivid lightness illusion. The grey rectangles placed on the black stripes appear lighter than the grey rectangles placed on the white stripes. Various attempts have been made to explain White’s illusion. These explanations assume either high-level or low-level processes. According to several prominent high-level theories, occlusion signals embedded in the illusory figure play a crucial role (eg Ross & Pessoa, 2000; Todorović, 1997; Zaidi, Spehar, & Shy, 1997). More specifically, our visual system extracts the local T-junction information which occurs at the intersections of the grey, black, and white areas (see figure 1). The stem of the junctions separates the grey rectangles and the bars on which they are superimposed. The top of the junctions runs along the adjacent bars. T-junctions specify the adjacent bars as occluding surfaces and the other two areas as occluded surfaces. As a consequence, the grey rectangles and the bars on which they are positioned are allocated the same layer, but the adjacent bars are allocated a different layer. This depth separation is consistent with a simultaneous contrast interpretation of the White illusion: the grey patches are darkened by the white bars on which they are superimposed but are unaffected by the lightness of the flanking black bars, and the grey patches are lightened by the black bars on which they are placed but are unaffected by the flanking white bars’ lightness. Anderson (1997, 2003), however, points out that this interpretation is incomplete because the White illusion is stronger than the illusory effect induced by simultaneous contrast displays. According to his perceptual scission theory, the grey elements of the White illusion are decomposed into a combination of light and dark. More specifically, based on a
1304
M Kavšek
Figure 1. In White’s illusion grey rectangles are superimposed on black and white bars. The grey rectangles embedded in the black stripes appear lighter than the grey rectangles embedded in the white stripes. In fact, the luminances of all grey rectangles are identical.
T-junction analysis, the grey patches are interpreted as semitransparent overlays (eg Watanabe & Cavanagh, 1993). As a consequence, the grey elements superimposed on the black bars appear lighter because some of their blackness is attributed to the subjacent black bars and is therefore subtracted from them. Similarly, our visual system assumes that some of the white of the grey elements positioned on the white bars belongs to these subjacent bars. Again, this amount of white is cancelled out of the grey elements, resulting in a darker appearance. Finally, according to Gilchrist et al. (1999), the T-junctions cause the grey elements to group with the embedding bars. The authors’ anchoring account states that the illusory effect consists mainly in an illusory lightening of the grey patches placed on the black stripes. Several studies have challenged these explanations. Howe (2005) demonstrated that the White illusion can be induced even without line junction information (see also Yazdanbakhsh, Arabzadeh, Babadi, & Fazl, 2002). Moreover, the White illusion is not always stronger than simultaneous contrast (eg Blakeslee, Pasieka, & McCourt, 2005; Li, Tavantzis, & Yazdanbakhsh, 2009). Low-level accounts refer to neurophysiological mechanisms. According to White (1981), the illusion is the result of three processes: lightness contrast, lightness assimilation occurring when the spatial frequency of the pattern is high, and lightness assimilation which is the result of ‘pattern-specific inhibition’ processes. Lightness contrast is a shift of a region’s lightness away from the lightness of the surrounding area. In contrast, lightness assimilation is the partial shift of a region’s lightness toward the lightness of the surrounding area. Blakeslee and McCourt (1999, 2004; Blakeslee et al., 2005) constructed a spatial filtering explanation for brightness phenomena such as the White effect. The parameters in this explanation reflect early stage cortical filtering operations. Later, Robinson, Hammon, and de Sa (2007) extended this model to account for a wider range of variants of the White illusion. Alternative low-level accounts have been suggested by Barkan, Spitzer, and Einav (2008) and by Otazu, Vanrell, and Párraga (2008).
The impact of stereoscopic depth on the Munker–White illusion
1305
A specific prediction of Anderson’s (1997, 2003) perceptual scission theory is that the White illusion should be enhanced by adding crossed horizontal disparity to the grey rectangles. Crossed horizontal disparity information shifts the grey rectangles into the foreground, thereby reinforcing the impression of a semitransparent overlay. Anderson (1997) compared the illusory effect of a two-dimensional version of the illusion with the illusory effects evoked by a figure, the rectangular regions in which were shifted to the front by adding crossed horizontal disparity, and a figure, the rectangular regions in which were moved into the background by adding uncrossed horizontal disparity. According to the perceptual scission theory, shifting of the rectangular regions into the background should diminish the illusion, because the regions can no longer be interpreted as floating above the white and black bars. Instead, when the grey rectangles are superimposed on the white stripes, both the grey regions and the white stripes seem to be shifted behind the black stripes, and when the grey rectangles are superimposed on the black bars, both the grey regions and the black stripes seem to be placed behind the white stripes. More specifically, in the first case the figure appears as a coherent grey surface on a white background with black stripes floating above these areas, while in the second case the figure appears as a coherent grey surface on a black background with white stripes partially occluding these areas. As a consequence, the illusory effect evoked by the display can be explained by simultaneous contrast evoked by the grey patches’ surrounding background. Anderson (1997) emphasizes that White’s illusion is stronger than simultaneous contrast effects. The illusion observed in the uncrossed horizontal disparity condition should therefore be smaller than the illusory effect observed in the no‑depth and crossed horizontal disparity conditions. According to Anderson’s (1997) results, the illusory effect was largest in the crossed horizontal disparity condition. Moreover, when comparing the uncrossed horizontal disparity condition with the two-dimensional no‑depth condition, five out of seven participants perceived a diminished or unaffected illusory effect and the remaining two participants perceived an enhanced illusory effect in the uncrossed horizontal disparity condition. Two additional studies have investigated the impact of stereoscopic depth information on the strength of White’s illusion. Taya, Ehrenstein, and Cavonius (1995) established an enhancement of the illusion under both crossed and uncrossed horizontal viewing conditions. The enhancement was smaller when the grey rectangles were moved to the back than when they were moved to the front. Ross and Pessoa (1995, 2000) found that the illusory effect was diminished under uncrossed horizontal disparity viewing, but was maintained under crossed horizontal disparity viewing. However, the viewing conditions created by Ross and Pessoa (eg 2000) were not comparable with those implemented by Anderson (1997), because they added horizontal disparity to both the grey rectangles and the stripes on which they were superimposed. Munker (1970) was amongst the first to describe a coloured version of the White illusion. For example, he placed red elements on blue and yellow stripes. The red elements appear slightly orange when placed on the blue stripes and slightly purplish when placed on the yellow stripes. Similar observations have been made by Anstis (2006), Clifford and Spehar (2003), Kitaoka (2010), Lingelbach, Neustadt, Schmidt, and Ehrenstein (2003), McCann (2002), and Yang, Kanazawa, and Yamaguchi (2010). Anstis (2006) points out that the induced colour of the superimposed elements is the result of both a shift toward the uninterrupted stripes’ colour (colour assimilation) and a shift toward the opposite of the interrupted stripes’ colour (colour contrast). Strength of the illusion and the relative contribution of assimilation and contrast depend on several factors. First, strength of the illusion is moderated by the stripes’ spatial frequency: the illusory effect increases, the higher the spatial frequency. Moreover, the contribution of assimilation correlates positively with spatial frequency (see also Clifford
1306
M Kavšek
& Spehar, 2003). According to Kitaoka (2010), the relative contribution of assimilation and contrast to the illusion varies across luminances. In particular, colour contrast is more effective than colour assimilation, if the luminance of the superimposed elements is intermediate and is close to the luminances of the inducing stripes. The current study investigated the illusory effect evoked by a coloured Munker–White illusion. In the illusory figure red elements were placed on black and yellow inducing stripes. Moreover, it was explored whether addition of uncrossed and crossed horizontal disparity to the red elements affected the illusory effect. Three versions of the illusion were created. In one version the illusory figure was a two-dimensional depiction. In the other two versions the red patches were shifted into either the background or the foreground. For each of the three versions of the illusion the participants’ task was to select those colours from the Natural Color System (NCS) most properly describing the perceived colours of the red patches. By comparing the colour selections made for the three versions of the illusion, it can be tested whether the illusory effect is largest for the figure containing crossed horizontal disparity and smallest for the figure containing uncrossed horizontal disparity, as predicted by the perceptual scission theory. Moreover, the illusory effects were quantified on the colour dimensions of hue, saturation, and lightness. As a consequence, the current study extended the previous stereoscopic experiments conducted by Anderson (1997), Ross and Pessoa (1995, 2000), and Taya et al. (1995): by using achromatic versions of the Munker–White illusion, these experiments focused solely on the lightness dimension. 2 Method 2.1 Participants In total, thirty-two adults participated in the experiment (sixteen females and sixteen males, mean age = 27 years, range = 20–42 years). An additional two participants (one female and one male) were excluded from the study due to defective colour vision. The participants gave informed consent before testing began. After the experiment, they were informed about the study. The study was approved by the ethics committee of the Department of Psychology at the University of Bonn (Germany). 2.2 Apparatus Each participant sat on a chair 70 cm from a 47.4 × 29.6 cm flat autostereoscopic threedimensional (3‑D) computer screen (SeeFront SF 2223). The screen could be seen through an aperture that was cut into the back of a 100 × 120-cm dull white wooden front panel. The centre of the screen was at the participant’s eye level. The front panel was mounted on a 50 cm high table. The floor below the table was hidden by a 100 × 51 cm black cloth. The room was dark except for light from a lamp behind the front panel and from the computer screens in the experimental room. A face-tracking camera was set into the monitor’s upper frame. The camera was connected to the software of the autostereoscopic monitor. The software was handled using an additional computer monitor, which also showed the shots of the face-tracking camera. Frames around the contour of the face, the eyes, and the nose signaled whether the face-tracking camera correctly captured the participant’s face. The frames disappeared as soon as the camera did not have sufficient information to detect the face. Lenticular lenses on top of the 3‑D screen split the image into two parts, one for the right eye and one for the left eye. Using the information from the face-tracking camera, the auto stereoscopic monitor’s software automatically determined the position of the participant’s face and adapted the half-images to that position. The autosteroscopic device needs about G 0.25 s to restore the stereoscopic effect after rapid head movements. The stereoscopic device may temporarily lose track of the face—for instance, if the face moves outside the scope of
The impact of stereoscopic depth on the Munker–White illusion
1307
the tracking camera or if the head is turned backwards. In this case, the device typically needs G 0.5 s to find the face again and restore the stereoscopic effect. The distance from the autostereoscopic monitor should be between 55 cm (minimum) and 120 cm (maximum). Within these distances, separation of the half-images is nearly perfect and interocular cross-talk is avoided. 2.3 Stimuli The participants were presented with computer animations depicting the stimuli (see http://munki.uni-bonn.de). In each animation the illusory figure was split into two parts, one in which red horizontal rectangular patches were superimposed on black horizontal stripes, and one in which red horizontal rectangular patches were superimposed on yellow horizontal stripes. One of the stimulus parts was situated on the left half of the computer screen, and the other one was situated on the right half of the screen. Distance between the two stimulus parts was 15.87 cm (12.94 deg). Each stimulus part consisted of 13 black (luminance, Y G 0.2 cd m–2 ) stripes, 13 yellow (x = 0.43, y = 0.51, Y = 163 cd m–2 ) stripes, and 13 red (x = 0.67, y = 0.33, Y = 49 cd m–2 ) stripes. Each black or yellow stripe measured 4 × 0.323 cm (3.27 × 0.26 deg); each red rectangular patch measured 2 × 0.323 cm (1.64 × 0.26 deg). Overall width of each stimulus part was 4 cm (3.27 deg), and the overall height was 8.4 cm (6.87 deg). The red patches were positioned in the middle of each stimulus part. They continuously moved back and forth in the horizontal plane. The movement’s path length from the left to the right or vice versa was 0.5 cm (0.41 deg). Speed of movement was 0.5 cm s–1. The red patches in the two stimulus parts moved in phase. The movement of the red patches was included because the stimuli were also used in an experiment with infants. Infants’ attention is highly attracted by motion. As a consequence, motion of the red patches might facilitate infants’ perception of the stimuli. The remaining parts of the computer screen were white. Participants were tested under three viewing conditions: a zero horizontal disparity condition, a crossed horizontal disparity condition, and an uncrossed horizontal disparity condition. In each condition two animations were shown. In one of the two animations the stimulus part with the red patches superimposed on the black stripes was shown on the left side of the screen, and the stimulus part with the red patches superimposed on the yellow stripes was shown on the right side of the screen. In the other animation the position of the two stimulus parts was exchanged. In the two zero disparity animations the red patches were situated in the same depth plane as the flanking and embedding stripes. In the two crossed disparity animations the red patches were shifted into the foreground by embedding them in a crossed horizontal disparity of 0.393 cm (0.32 deg). In the two uncrossed disparity animations the red patches were shifted into the background by embedding them in an uncrossed horizontal disparity of 0.393 cm. Participants assessed the perceived colour of the red patches using the 15 × 14.5 mm, semimatt colour samples of the Natural Color Atlas (Swedish Standards Institute, 2008). The NCS is a perceptual system, the colours in which are defined by three properties: hue, blackness, and chromaticness (Hård, Sivick, & Tonnquist, 1996a, 1996b). The colour system has been developed to have equal visual steps within these scales (eg Kuehni, 2000). Hue is specified in terms of similarity to the basic chromatic sensations: yellow, red, blue, and green. Blackness specifies how dark the colour is, and chromaticness specifies how saturated the colour is. Values for blackness and chromaticness are percentages. The value for hue is a percentage score between two of the colours: yellow, red, blue, and green. For example, ‘S 0585–Y80R’ denotes a colour with 5% perceived blackness, 85% perceived chromaticness, 80% perceived red (R), and the remaining 20% perceived yellow (Y).
1308
M Kavšek
2.4 Procedure Each participant was tested individually. The participant was seated comfortably in front of the computer screen. First, a practice trial was run to make him or her familiar with the stereoscopic device, the visual stimuli, and the experimental task. Afterwards, the participant was shown the six animations depicting the zero, the crossed disparity, and the uncrossed disparity stimuli on separate trials. The two animations for each viewing condition were presented on successive trials. As a consequence, each viewing condition consisted of two trials which differed with respect to the position of the two parts of the illusory figure. The three viewing conditions can be combined into six orders. Each of these six orders of three viewing conditions was conducted twice to obtain 12 experimental trials. The six sequences of 12 trials were randomly assigned to the thirty-two participants such that each sequence occurred approximately equally often. The position of the stimulus part (red patches superimposed on the black stripes shown on the left versus right side of the screen) alternated from trial to trial. Three out of the six sequences of 12 trials started with an animation in which the red patches on the black stripes were positioned on the left side of the screen; the other three sequences started with an animation in which the red patches on the black stripes were positioned on the right side of the screen. Since each (zero disparity, crossed disparity, and uncrossed disparity) version of the illusory figure was presented 2 (positions of the stimulus parts) × 2 (repetitions) times, an overall number of 384 judgments was made by the thirty-two participants (3 versions × 4 presentations × 32 participants). On each trial the participant was instructed to select and point at the two NCS colour samples best describing perceived colours of the red patches in the two halves of the illusory figure. A short break was taken after the sixth experimental trial. The experiment took about 20 to 30 min. 2.5 Results The participants selected NCS blackness values between 5% and 25% in 5% increments, NCS chromaticness values between 60% and 85% in 5% increments, and NCS hue values between 50% and 90% in 10% increments. Values for hues indicated the amount of perceived red with the difference to 100% indicating the amount of perceived yellow. In the first step the deviation of both the subjective colour of the red patches on the yellow stripes and the subjective colour of the red patches on the black stripes from the subjective red tone used in the illusory figure was examined. More specifically, five adult participants were presented with the red tone in isolation—that is, without the context of the black and yellow inducing stripes. The participants’ task was to find the NCS colour sample that was most similar to the red tone. The red tone was presented on the 3‑D computer monitor. It was surrounded by a white background. All participants uniformly selected the colour sample ‘S 0585–Y80R’, the colour sample with 5% perceived blackness, 85% perceived chromaticness, 80% perceived red, and 20% perceived yellow. One-sample t‑tests were conducted to compare the empirical means with these values. First, deviation of mean percentage of perceived blackness of both the red patches on the yellow stripes and the red patch on the black stripes from 5% perceived blackness was tested for each of the three viewing conditions. Mean percentages of perceived blackness for each of the three viewing conditions are summarized in figure 2. The two-tailed B–Y (Benjamini & Yekutieli, 2001; Narum, 2006) corrected 0.05 level of significance for a total of six comparisons is p = 0.02041. All two-tailed scores of p resulting from the t‑tests for the red patches on the yellow stripes were lower than 0.02041, indicating that the patches were perceived as significantly darker than 5% perceived blackness. To examine whether this result was moderated by the viewing condition variable, pairwise comparisons between the deviations of mean percentage of perceived blackness of the red patches on the yellow
The impact of stereoscopic depth on the Munker–White illusion
1309
stripes from 5% were conducted across the three viewing conditions. Paired t‑tests showed that the deviation score for the crossed disparity condition was significantly higher than the deviation score for the uncrossed disparity condition ( p 0.02727). The perceived hue of the red patches superimposed on the yellow stripes was significantly ( p
