Monocular and binocular edges enhance the perception of stereoscopic slant

VR 6817

No. of Pages 11, Model 5G

8 May 2014 Vision Research xxx (2014) xxx–xxx 1

Contents lists available at ScienceDirect

Vision Research journal homepage: www.elsevier.com/locate/visres 5 6

Monocular and binocular edges enhance the perception of stereoscopic slant

3 4 7 8 9 10 11 1 2 3 6 14 15 16 17 18 19 20 21 22 23 24 25

Q1

Susan G. Wardle a,⇑, Stephen Palmisano b, Barbara J. Gillam a a b

School of Psychology, The University of New South Wales, Sydney, Australia School of Psychology, University of Wollongong, Wollongong, Australia

a r t i c l e

i n f o

Article history: Received 21 November 2013 Received in revised form 22 April 2014 Available online xxxx Keywords: Binocular vision Stereoscopic slant Monocular regions 3D surface perception Depth matching Binocular disparity

a b s t r a c t Gradients of absolute binocular disparity across a slanted surface are often considered the basis for stereoscopic slant perception. However, perceived stereo slant around a vertical axis is usually slow and significantly under-estimated for isolated surfaces. Perceived slant is enhanced when surrounding surfaces provide a relative disparity gradient or depth step at the edges of the slanted surface, and also in the presence of monocular occlusion regions (sidebands). Here we investigate how different kinds of depth information at surface edges enhance stereo slant about a vertical axis. In Experiment 1, perceived slant decreased with increasing surface width, suggesting that the relative disparity between the left and right edges was used to judge slant. Adding monocular sidebands increased perceived slant for all surface widths. In Experiment 2, observers matched the slant of surfaces that were isolated or had a context of either monocular or binocular sidebands in the frontal plane. Both types of sidebands significantly increased perceived slant, but the effect was greater with binocular sidebands. These results were replicated in a second paradigm in which observers matched the depth of two probe dots positioned in front of slanted surfaces (Experiment 3). A large bias occurred for the surface without sidebands, yet this bias was reduced when monocular sidebands were present, and was nearly eliminated with binocular sidebands. Our results provide evidence for the importance of edges in stereo slant perception, and show that depth from monocular occlusion geometry and binocular disparity may interact to resolve complex 3D scenes. Ó 2014 Published by Elsevier Ltd.

27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

47 48

1. Introduction

49

Horizontal disparity arising from differences in perspective between the left and right eye’s views of the world gives rise to stereoscopic vision, which is an important source of information about depth and spatial structure for humans and other animals with overlapping visual fields. Absolute disparity of a single point is defined as the angular deviation of its left and right eye images from corresponding positions relative to the fixation point. However, the perceived depth of two points is based on their relative disparity (Erkelens & Collewijn, 1985; Gillam, Chambers, & Russo, 1988; Gogel, 1956; Westheimer, 1979). Relative disparity is the difference in angular separation between the two points in each eye’s view and does not change with fixation. For a slanted surface, absolute disparity increases across the surface as the first spatial

50 51 52 53 54 55 56 57 58 59 60 61

⇑ Corresponding author. Present address: Department of Cognitive Science, Macquarie University, Australian Hearing Hub, 16 University Avenue, Sydney, NSW 2109, Australia. E-mail address: [email protected] (S.G. Wardle).

derivative of disparity (i.e. the disparity gradient). Although a gradient of absolute disparity specifies stereo slant around a vertical axis, perceived slant is often significantly underestimated compared to geometric prediction (Gillam, Flagg, & Finlay, 1984; Mitchison & Westheimer, 1990; Pierce & Howard, 1997; van Ee & Erkelens, 1996), and can have a long latency after stereo fusion is achieved (Gillam, Chambers, & Russo, 1988; van Ee & Erkelens, 1996). Gillam, Chambers, and Russo (1988) attribute the ineffectiveness of absolute disparity in specifying stereoscopic slant to two factors. Firstly, that relative disparity is the critical stimulus for stereoscopic depth and secondly, that the relative disparity of successive pairs of equally spaced points on a slanted planar surface is constant across the surface and thus does not form a gradient. This proposal is supported by Gillam, Flagg, and Finlay’s (1984) and Gillam, Chambers, and Russo’s (1988) finding that stereo slant around a vertical axis is facilitated by introducing a gradient of relative disparity to the slanted surface. Slant is enhanced when a frontal plane surface is placed above the slanted surface in a ‘‘twist’’ configuration (similar to the situation depicted in Fig. 1a),

http://dx.doi.org/10.1016/j.visres.2014.04.012 0042-6989/Ó 2014 Published by Elsevier Ltd.

Please cite this article in press as: Wardle, S. G., et al. Monocular and binocular edges enhance the perception of stereoscopic slant. Vision Research (2014), http://dx.doi.org/10.1016/j.visres.2014.04.012

62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81

VR 6817

No. of Pages 11, Model 5G

8 May 2014 2

S.G. Wardle et al. / Vision Research xxx (2014) xxx–xxx

Fig. 1. Schematic diagrams of the twist and hinge configurations. The axis of slant is shown by the vertical dashed line. The hinge configuration (b) contains only an absolute disparity gradient, while the twist configuration (a) produces a relative disparity gradient orthogonal to the axis of slant. (c) A variation on the hinge configuration in which the frontal plane surface is displaced in depth from the edge of the slanted surface produces relative disparity between the adjacent edges of the two surfaces.

82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132

which produces a gradient of relative disparity along the abutting surface edges. In contrast, when the second surface forms a ‘‘hinge’’ with the first (Fig. 1b), abutting the slanted surface on a side parallel to the axis of slant (Gillam, Blackburn, & Brooks, 2007; Gillam & Pianta, 2005), it does not produce a gradient of relative disparity or facilitate stereo slant perception. This demonstrates that the presence of a ‘‘reference surface’’ is not sufficient to facilitate stereoscopic slant. Interestingly, stereoscopic slant is increased in a variation of the ‘‘hinge’’ configuration (Fig. 1c) in which the frontal plane surface is displaced in depth from the edge of the slanted surface (Gillam, Blackburn, & Brooks, 2007). This supports the view that stereo slant perception is at least partly dependent on relative disparity at surface edges – what Gillam, Chambers, and Russo (1988) called the ‘‘boundary mode’’. However, the enhancement of perceived slant in this case is much less than that produced by the twist configuration (which in contrast provides a full gradient of relative disparity along the slanted surface – Fig. 1a). Gillam and Blackburn (1998) also showed that the presence of monocular regions at the edges of a stereoscopically slanted surface can enhance the perceived slant. Monocular regions occur with natural binocular viewing as a result of occlusion relationships between near and far objects in the two eyes, which produce regions of the 3D scene that are visible to only one eye. Importantly, these monocular regions do not introduce relative disparity, but can be seen in depth relative to a neighboring binocular surface Q2 based on occlusion geometry (Cook & Gillam, 2004; Gillam & Borsting, 1988; Nakayama & Shimojo, 1990; Wardle & Gillam, 2013a). The monocular regions in Gillam and Blackburn’s (1998) stimuli were regions of monocular texture (‘‘monocular sidebands’’) on the left and right side of a randomly textured binocular slanted surface. This would occur in a binocular view if a slanted surface passed through an aperture in the frontal plane. In the example shown in Fig. 2, the monocular sidebands are only visible to the right eye. The monocular sideband on the right is perceived to lie behind the slanted surface (hence it is occluded in the other eye’s view), and the monocular sideband on the left is x perceived as a continuation of the slanted surface. In order to account for the latter monocular sideband being invisible in the left eye, an illusory surface (a ‘‘phantom occluder’’) is perceived (see also: Wardle & Gillam, 2013b). The role of monocular sidebands in the enhancement of stereoscopic slant relative to or in addition to other forms of edge information about depth has not been investigated, and is a focus of this paper. Although a depth step due to a monocular region is based on occlusion geometry instead of relative disparity, it may be as effective as an equivalent binocular depth step in enhancing perceived slant. We use surfaces with a horizontal gradient of absolute disparity (consistent with slant around a vertical axis) to compare the effectiveness of monocular occlusion geometry and binocular disparity at surface edges in enhancing perceived slant. We con-

Fig. 2. Scene geometry for viewing a slanted surface with monocular regions (aerial view). The monocular sidebands (shown in red) are only visible to the right eye. For the left eye, the right sideband is occluded by the far edge of the slanted surface, and the left sideband is occluded by a phantom surface. The depth of the phantom surface is precisely determined at the depth of the center of the slant axis. The left sideband is perceived as a continuation of the slanted surface, and the right sideband is perceived behind the slanted surface, but is compatible with a range of depths within the depth constraint region. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

sider four forms of relative depth information at the surface edges; relative disparity between opposite edges of a single surface (Experiment 1), and three forms of relative depth between a slanted surface and contextual surfaces. These are (a) the relative disparity gradient between abutting surfaces separated vertically (Experiments 2 and 3), (b) relative depth at the sides of the slanted surfaces from monocular occlusion geometry (Experiments 1–3) and (c) relative depth between the sides of the slanted surfaces and proximal binocular surfaces in the frontal plane (Experiments 2 and 3). In Experiment 1, we used stimuli of different widths to test whether relative disparity at opposite sides of a single binocular surface is used to derive stereo slant. If this is the case, we should find greater perceived slant for narrower surfaces than for

Please cite this article in press as: Wardle, S. G., et al. Monocular and binocular edges enhance the perception of stereoscopic slant. Vision Research (2014), http://dx.doi.org/10.1016/j.visres.2014.04.012

133 134 135 136 137 138 139 140 141 142 143 144 145

VR 6817

No. of Pages 11, Model 5G

8 May 2014 S.G. Wardle et al. / Vision Research xxx (2014) xxx–xxx

155

wider ones with the same disparity gradient. We also compared the effects of adding monocular sidebands to surfaces of different widths. In Experiment 2 we compared the effects of binocular and monocular edge information on the perception of stereo slant, using a slant-matching task. Finally, in Experiment 3 we measured the degree to which stereo slant is underestimated in stimuli with different forms of edge information by using a measure of bias. To preview the results, we find that the quality and precision of edge information relates directly to the magnitude of the perceived stereoscopic slant.

156

2. Experiment 1

157

The aim of Experiment 1 was to test whether the width of an isolated stereoscopic surface slanted around a vertical axis affects the magnitude of perceived slant. It is possible that perceived slant of a single surface could be based on the relative disparity between its near and far edges, with interpolation of the intervening slant. This should be more effective when the slanted surface is narrower, since the edges will be closer together. It is known that the stereo threshold for detecting the depth difference between two lines increases with target separation (Fahle & Westheimer, 1988; Gogel & Harker, 1955; Hirsch & Weymouth, 1948; Marlow & Gillam, 2011; Rady & Ishak, 1955; Wright, 1951). Conversely, the relative disparity of the edges of a surface with a given slant increases with the width of the surface, and this may compensate for the disadvantage of greater separation. A further consideration is that wider surfaces have better specified gradients of vertical disparity. Vertical disparity is a major factor in the scaling of horizontal disparity gradients for both distance and azimuth, and if vertical disparity is more constrained, this should lead to more accurate estimates of surface slant for larger surfaces (Backus et al., 1999). Experiment 1 was designed to evaluate these conflicting predictions about the effect of surface width on stereoscopic slant. In addition,as monocular regions increase perceived slant (Gillam & Blackburn, 1998), we compared the effect of surface width on slant for surfaces both with and without monocular regions to determine whether the effects are independent.

146 147 148 149 150 151 152 153 154

158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181

182

2.1. Method

183

2.1.1. Observers Twelve observers naive to the experimental hypotheses participated. Observers had normal or corrected-to-normal vision and normal stereovision as assessed by the Stereo Titmus test (Stereo Optical, Chicago, IL, USA). All experiments were conducted in accordance with the ethical guidelines in the Declaration of Helsinki and informed consent was obtained prior to participation.

184 185 186 187 188 189

190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205

2.1.2. Stimuli and procedure The stereoscopic stimuli were pseudo-random line patterns of even density (see Fig. 3), constructed according to the method detailed in Gillam and Blackburn (1998). Stimuli were generated on a Pentium computer and displayed stereoscopically via a Cambridge Research Systems D300 dual-point plotter (16-bit resolution D/A converters) on a pair of Kikusui COS1161 X–Y oscilloscopes (P31 phosphor). The stimuli were viewed from a distance of 70 cm through a Wheatstone stereoscope, which presented separate images to the left and right eye. Stereoscopic slant around the vertical axis (with either the left or right side nearer) was produced by horizontal magnification of the texture in one eye’s image, which was either 4% or 8%. These magnifications correspond to slants of 22 and 39 deg respectively, at the 70 cm viewing distance used. The conversion of magnification to slant (h) is shown in Eq. (1) (Ogle, 1950), where M is the magnifi-

3

Fig. 3. Example of the stimuli for Experiment 1, with monocular sidebands (bottom) and without sidebands (top).

cation (in the form e.g. 1.04 for 4%), d is the viewing distance (70 cm) and a is half the interocular distance (6.5/2 = 3.25 cm). The stimuli were ellipses 3.8 deg in height, and three different widths were used: 2.4 deg (thin), 3.8 deg (medium), and 5.1 deg (wide). Stimuli with monocular regions had extra regions of texture added to the left and right sides of the non-magnified eye’s image, which equated the image widths in the two eyes. The monocular region for each width on the near side of the surface coincided with the occlusion zone for that degree of stereo slant for a surface at the depth of the slant axis (Fig. 2 shows the equivalent situation for rectangular stimuli as used in Experiments 2 and 3). On the far side, the monocular region was consistent with occlusion and produced a phantom occluder at the depth of the slant axis (Gillam & Blackburn, 1998; Wardle & Gillam, 2013b).

a

ð1Þ

206 207 208 209 210 211 212 213 214 215 216 217 218 219 220

221 223

Observers matched the perceived slant on each trial using a mechanical comparator constructed from a Meccano pulley wheel attached to a potentiometer, which could be rotated about the vertical axis (for details see Gillam & Blackburn, 1998). Observers rotated the comparator wheel to match the apparent slant of the elliptical surface on each trial. The 2  2  3  2 factorial design of magnification (4% or 8%), direction of slant (left or right), stimulus width (thin, medium, wide), and monocular regions (present or absent) produced a total of 24 conditions. Each condition was repeated 4 times, for a total of 96 trials per observer.

224

2.2. Results and discussion

234

The group means for Experiment 1 are shown in Fig. 4. Note that data for the left and right directions of slant are averaged together in the graph as there was no significant main effect of slant direction. The data were analyzed in a repeated measures ANOVA with the following factors: monocular sidebands (absent

235

Please cite this article in press as: Wardle, S. G., et al. Monocular and binocular edges enhance the perception of stereoscopic slant. Vision Research (2014), http://dx.doi.org/10.1016/j.visres.2014.04.012

225 226 227 228 229 230 231 232 233

236 237 238 239

VR 6817

No. of Pages 11, Model 5G

8 May 2014 4

S.G. Wardle et al. / Vision Research xxx (2014) xxx–xxx

(b) 8% magnication

(a) 4% magnication

no sidebands monocular sidebands

50

matched slant (deg)

matched slant (deg)

50 40 30 20 10 0

40 30 20 10

N = 12

0 2.4

3.8

5.1

width of surface (deg)

2.4

3.8

5.1

width of surface (deg)

Fig. 4. Average comparator settings for each condition in Experiment 1 (N = 12) for (a) 4% magnification and (b) 8% magnification. The dashed line on each graph shows the predicted slant for that magnification [from Eq. (1)]. Error bars are between-subjects SEM.

240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289

or present), stimulus width (thin, medium, wide), magnification (4% or 8%), and slant direction (left or right). Mauchly’s test indicated that the sphericity assumption was violated for the main effect of width (v2(2) = 8.699, p < .05), so the Greenhouse–Geisser correction was applied to the degrees of freedom. There was a significant main effect of width on perceived slant (F(1.265, 13.915) = 32.169, p < .01). Planned contrasts with the error rate controlled at p < .05 for multiple comparisons using the Bonferroni correction were carried out for the effect of width. Greater slant was perceived for the thinnest stimulus width compared to both the medium sized (F(1, 11) = 36.093, p < .05), and wider (F(1, 11) = 33.605, p < .05) stimuli. However, there was no difference in perceived slant for the medium sized and wide stimuli (F(1, 11) = 0.817, p > .05). Overall, greater slant was perceived for the larger 8% magnification than 4% (F(1, 11) = 26.650, p < .01), as expected from geometric predictions. There was no difference in the slant perceived for the left and right directions (F(1, 11) = 3.611, p > .05). Significantly greater slant was perceived for the stimuli with monocular sidebands (F(1, 11) = 66.034, p < .01). There was a significant interaction between magnification and sidebands (F(1, 11) = 6.362, p < .05), as adding monocular regions produced a greater enhancement of slant for the larger magnification. However, the interaction between sidebands and width was not significant (F(1.475, 16.220) = 1.863, p > .05), indicating that the enhancement of slant with sidebands did not differ across the different stimulus widths. Thus the addition of sidebands enhanced the perception of slant by a constant amount, suggesting that its effect on slant is independent of that of stimulus width. Slant was generally underestimated relative to the geometric predictions (in all but one condition: 4% magnification, width = 2.4 deg), but observers perceived considerably greater slant for the narrowest ellipse compared to the two wider ellipses. This is consistent with the hypothesis that observers are able to use the relative disparity of the surface’s opposite edges when they are not too far apart. The results are not consistent with the alternative hypothesis that the greater disparity of the edges of wider surfaces compensates for the increase in separation, nor with the hypothesis that the wider surface should be better specified stereoscopically because of an increase in the range of the vertical disparity gradient, which is important for scaling. Perceived slant for the two wider ellipses did not differ from each other, suggesting that the relative disparity of the surface edges is only useful for narrow figures. The addition of monocular sidebands increased perceived slant under all conditions. Since their addition equalized the left and right eye’s image widths, their magnitude was always equal to the angular difference at the edges of the binocular part of the ellipses, whether resulting from magnification or from width. Although the effect of monocular sidebands was independent of

the width of the surface, it was not independent of the degree of magnification, and there was a greater enhancement of slant from monocular sidebands for the larger magnification. This can be explained as follows: Although doubling the width of the ellipse and doubling the magnification (without altering the width of the ellipse), would have had similar effects in terms of the disparity at the edge (i.e. they would generate monocular sidebands of the same width), edge-based depth signals in the former case would be more separated from each other (due to the greater width of the ellipse). In Experiments 2 and 3 we investigate the enhancement of slant from monocular sidebands further by comparing it to equivalent binocular information at the surface edges.

290

3. Experiment 2

303

Gillam and Blackburn (1998) previously showed that monocular sidebands enhance stereoscopic slant (also demonstrated in Experiment 1). Here we measured whether this enhancement is comparable to that produced when binocular discontinuity information is provided at the surface’s near and far edges. Gillam, Blackburn, and Brooks (2007) reported that greater slant is perceived for surfaces in a hinge configuration when the edges of the adjoining surfaces are separated in depth, although slant was still underestimated compared to the twist configuration (see Fig. 1). This suggests that depth discontinuities at surface edges influence the perception of stereoscopic slant, although to a lesser extent than a continuous gradient of depth discontinuities, e.g. from the relative disparities in the twist stimulus. The effects of monocular and binocular forms of depth discontinuity at the edges of slanted surfaces have not yet been directly compared. In Experiment 2, monocular sidebands were added to a randomly-textured stimulus stereoscopically slanted around a vertical axis. The texture of the sidebands was created in the same way as that on the surface itself. The sidebands were consistent with occlusion of or by the slanted surface at its vertical edges (Fig. 2). We used this particular surface layout, which involves a slanted surface partially occluded on one side by a nearer surface and partially occluding another farther surface on the other side, because we were interested in following-up the accidental discovery that slant is greatly increased with monocular sidebands in this case (Gillam & Blackburn, 1998). Pilot experiments in our lab indicate that other arrangements of monocular regions are not as effective in enhancing slant as those used by Gillam and Blackburn (1998). Thus we compared the effect on perceived slant of this form of monocular edge information to the effect of binocular edge information, using an ordinary stereoscopic slant stimulus (which contained no edge information) as a control. Observers matched the slant of the three different types of surfaces using a virtual comparator (see Procedure for details).

304

Please cite this article in press as: Wardle, S. G., et al. Monocular and binocular edges enhance the perception of stereoscopic slant. Vision Research (2014), http://dx.doi.org/10.1016/j.visres.2014.04.012

291 292 293 294 295 296 297 298 299 300 301 302

305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337

VR 6817

No. of Pages 11, Model 5G

8 May 2014 S.G. Wardle et al. / Vision Research xxx (2014) xxx–xxx 338

3.1. Method

339

3.1.1. Participants Eight observers with normal or corrected-to-normal vision and normal stereovision participated. Stereovision was assessed using the Stereo Titmus test (Stereo Optical, Chicago, IL, USA), and a slant-matching training task (see Procedure). One additional observer was excluded because of high standard deviations (range: 15– 64 deg) for all conditions in the practice task. Observers were recruited from the first year Psychology participant pool at the University of New South Wales and received course credit.

340 341 342 343 344 345 346 347

348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364

3.1.2. Stimuli Stereoscopic stimuli were generated on a MacPro computer with MATLAB (The MathWorks) and functions from the Psychtoolbox (Brainard, 1997; Kleiner, Brainard, & Pelli, 2007; Pelli, 1997). A mirror stereoscope was used to present separate images to each eye, which were displayed on two identical LCD monitors (Dell U2412M) at a screen resolution of 1920  1200 pixels. The slant stimuli were rectangular pseudo-random line patterns (H: 1.95  W: 3.90 deg). The lines (4  1 arcmin) had random orientations drawn from a uniform distribution (0–360 deg). The pseudo-random patterns were generated by randomly allocating 3 lines to each 7  7 arcmin region of the pattern in order to produce a pattern with even density. The horizontal screen positions of the lines (not the actual lines) were magnified from the center of the stimulus boundaries in one eye to produce the perception of slant around a vertical axis when viewed binocularly. Two levels of stimulus magnification were used, 3% or 6%, which corre-

5

sponded to surface slants of 21 and 36 deg respectively (using Eq. (1)). A new line pattern was randomly generated on each trial. Three types of slant stimuli were used in Experiment 2: slant without sidebands, slant with monocular sidebands, and slant with binocular sidebands (see Fig. 5b–d). The monocular sidebands were created by adding extra strips of random texture to the non-magnified eye to equate the image width in each eye. The binocular sidebands were additional regions (H: 1.95  W: 1.3 deg) of texture placed to the left and right of the slant stimulus in each eye’s view directly adjacent to the slant stimulus (thus the boundary was not visible in the magnified eye’s image). The binocular sidebands were each at zero disparity, and thus were at the same depth as the central axis of slant, with relative disparity between the edges of the slanted surface and the edges of the binocular sidebands. The monocular sidebands created an equivalent depth discontinuity at the edges of the surface, but in this case by occlusion geometry instead of relative disparity (Fig. 2). (Refer to Fig. 10 in Section 5 for a more detailed explanation of the depth discontinuities in the stimuli.) The virtual comparator for matching slant was a thin horizontal line (170  2 arcmin) surrounded by a stationary rectangular dotted frame (H: 0.53  W: 3.19 deg) with zero disparity (see Fig. 5a). The frame provided a reference for the slant of the line. The line length was extended in one eye’s view to produce slant to the left or right. A small vertical line (32  4 arcmin) was positioned in the center of the comparator as an anchor. The slant of the comparator could be adjusted in steps of ±0.2% magnification (±1 degree of slant) using the keyboard. To avoid cue conflict, the width of the comparator line was adjusted as it was rotated in

Fig. 5. Examples of the experimental stimuli for Experiments 2 and 3, left and right eye views are shown for each. The stereograms may be viewed with crossed or divergent fusion. (a) The comparator used for matching slant in Experiment 2, (b) slant without sidebands, (c) slant with monocular sidebands, (d) slant with binocular sidebands, and (e) slant with vertical flankers (used as a practice stimulus in Experiment 2 and an additional experimental condition in Experiment 3). The probe dots used to measure the degree of slant bias in Experiment 2 are shown in red. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Please cite this article in press as: Wardle, S. G., et al. Monocular and binocular edges enhance the perception of stereoscopic slant. Vision Research (2014), http://dx.doi.org/10.1016/j.visres.2014.04.012

365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393

VR 6817

No. of Pages 11, Model 5G

8 May 2014 6

396 397 398 399 400 401 402

403 404 405 406 407 408 409 410 411 412 413 414 415 416 417

depth to be consistent with a real 3D object, which shrinks in horizontal retinal size as it is rotated away from the frontal plane due to parallel projection. This meant that the comparator was perceived as a line of constant size (with shrinking or expanding retinal images as expected from natural viewing) rotating in depth. The comparator was placed at a distance of 3.9 deg below the slant stimulus. A large separation between the slant stimulus and the comparator is necessary to prevent the comparator from influencing perceived slant. 3.1.3. Procedure Observers viewed the stimuli through a mirror stereoscope at a distance of 84 cm. Prior to the main experiment observers completed a practice task that involved matching the slant of surfaces using the comparator. The stimuli used for practice were identical to the stimuli used in the main experiment, except for the addition of frontal-plane flankers (H: 0.98  W: 3.90 deg) above and below the slanted surface. These formed twist configurations, which are known to increase perceived slant (Gillam & Blackburn, 1998; Gillam, Blackburn, & Brooks, 2007). Participants adjusted the slant of the comparator using the keyboard, and pressed the space bar to enter their response when they perceived the slant to be matched. Initially this task was completed with feedback to give observers practice in using the comparator. The vertical line through the central axis of the comparator turned orange when it was matched

60

left slant

55

right slant predicted

50 45 40 35 30 25 20 15 10

N=8

5 0 3

5

7

magnication (%) Fig. 6. Practice data for Experiment 2. The average comparator settings for all observers (N = 8) are shown for left slant (circles) and right slant (triangles). The dashed line indicates the slant predicted from horizontal magnification using Eq. (1). Error bars are between-subjects SEM.

40

matched slant (degrees)

395

matched slant (degrees)

394

S.G. Wardle et al. / Vision Research xxx (2014) xxx–xxx

(a) left slant

40

35

35

30

30

25

25

20

20

15

15

10

10

5

5

0

0 3

6

magnication (%)

within ±14 deg of the stimulus’s slant, and green when it was within ±1 deg. The slanted surfaces used for practice were 3%, 5%, or 7% magnification in the left or right eye (corresponding to slant in the left and right directions of 21, 32, and 40 deg). Each of the six conditions was repeated twice for a total of 12 trials with feedback. Following the training, the observers completed the same task (4 repeats, 24 trials total) without feedback to serve as a screening test. Observers completed the main experiment directly after the training and practice trials. In the experiment they matched the slant of each surface using the comparator following the same procedure as that used for the practice task. There were 3 slant types (no sidebands, monocular sidebands, binocular sidebands), 2 magnitudes of slant (3% and 6%) and 2 directions of slant (left and right around a vertical axis). The 12 conditions were repeated 10 times in random order and produced a total of 120 trials. The minimum trial duration was 3 s, the maximum duration was unconstrained.

418

3.2. Results and discussion

435

The practice data for the eight included observers is shown in Fig. 6 (only trials without feedback are included). Although on average, observers slightly overestimated the slant for all magnifications, their estimation of slant increased as expected with increasing horizontal magnification. We expected that perceived slant would approximate the geometric predictions based on magnification because the practice stimuli had flankers above and below the slanted surface, which are known to increase perceived slant relative to an isolated surface (Gillam & Blackburn, 1998; Gillam, Blackburn, & Brooks, 2007). Thus the results of the practice task indicate that observers were sufficiently accurate at matching the slant of the surface using the virtual comparator. The mean settings of the comparator are shown in Fig. 7 for each slant condition in Experiment 2. For both directions (left and right) and magnifications (3% and 6%), slant was underestimated the most for the stimulus without sidebands. The addition of monocular and binocular sidebands increased the perceived slant for each magnification. The data were analyzed in a withinsubjects ANOVA, including a set of pre-planned orthogonal contrasts with the error rate controlled at a = 0.05 using the Bonferroni procedure. There were significant main effects for the type of slant (F(2, 14) = 20.392, p < .01) and for the amount of horizontal magnification (F(1, 7) = 26.472, p < .01). As expected from the relationship between magnification and slant angle shown in Eq. (1), greater slant was perceived for 6% magnification than for 3%. The main effect for the direction of slant (F(1, 7) = 5.126, p > .05), and all of the interactions were not significant. The presence of sidebands (monocular or binocular) significantly increased perceived slant

436

(b) right slant

no sidebands monocular sidebands binocular sidebands predicted slant

N=8 3

6

magnication (%)

Fig. 7. Results of Experiment 2, average data for all eight observers. The mean comparator settings for slant with no sidebands (circles), monocular sidebands (squares), and binocular sidebands (triangles). The dashed line shows the predicted slant for magnifications of 3% and 6% from Eq. (1). Error bars are between-subjects SEM.

Please cite this article in press as: Wardle, S. G., et al. Monocular and binocular edges enhance the perception of stereoscopic slant. Vision Research (2014), http://dx.doi.org/10.1016/j.visres.2014.04.012

419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434

437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463

VR 6817

No. of Pages 11, Model 5G

8 May 2014 7

S.G. Wardle et al. / Vision Research xxx (2014) xxx–xxx

465 466 467 468 469 470 471 472 473

474

compared to a horizontally magnified surface without any sidebands (F(1, 7) = 23.415, p < .01). In addition, binocular sidebands increased perceived slant significantly more than monocular sidebands (F(1, 7) = 10.308, p < .05). As shown in Fig. 7, the addition of binocular sidebands produced slant that was very close to the geometric prediction. An explanation for why binocular sidebands enhance slant to a greater extent than monocular sidebands is proposed in the General discussion (Section 5). In the following experiment we obtained a complementary measure of the extent of slant enhancement with sidebands using a measure of bias. 4. Experiment 3

494

The aim of Experiment 3 was to obtain a second, independent measure of the degree of perceived slant with and without monocular or binocular sidebands. Two dots positioned at the same depth in front of an isolated stereoscopically slanted surface appear offset in depth because the slant is underestimated, while the depths of the dots relative to the surface are perceived correctly (Mitchison & Westheimer, 1984). When flankers are added to the top and bottom of the slanted surface (as in Fig. 2e), the slant underestimation diminishes, and consequently the bias in the depth of the probes is reduced (Gillam, Sedgwick, & Marlow, 2011). Thus the degree of bias reflects the degree to which the surface slant is underestimated. The probe bias method may also provide a better estimate of the interpolation of depth across the surface than the slantmatching task. In the slant-matching task, it is possible that observers concentrated on the edges of the slanted surface while moving the comparator. In the probe task there would be no benefit from focusing on the edges because the probe dots are matched to each other. Here we compare the amount of bias for slant with and without sidebands to determine the degree to which the sidebands reduce slant underestimation.

495

4.1. Method

496

4.1.1. Participants Eleven observers with normal or corrected-to-normal vision and normal stereovision participated. Stereovision was assessed using the Stereo Titmus test (Stereo Optical, Chicago, IL, USA), and a training task (see Procedure). Participants were recruited from within the Psychology department at the University of New South Wales and received financial reimbursement.

475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493

497 498 499 500 501 502

503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519

4.1.2. Stimuli The experimental setup and stimuli were identical to Experiment 2, with the following modifications. In Experiment 3 four types of slant stimulus were used (see Fig. 5b–e): slant without sidebands, slant with monocular sidebands, slant with binocular sidebands, and slant with binocular strips of texture above and below the slanted surface, located at zero disparity (i.e. the same depth as the central axis of slant). This stimulus was similar to the ‘‘twist’’ configuration, and produced a gradient of relative disparity along the top and bottom edges of the slanted surface. This condition was included as a control for the other slant conditions because it is known that the ‘‘twist’’ configuration reduces the probe bias (Gillam, Sedgwick, & Marlow, 2011). An additional frontal plane condition was included as a baseline, in which the same image was presented to each eye without horizontal magnification, and was perceived as a flat surface (and thus no probe bias was expected).

depth of two vertical black bars (H: 127  W: 4 arcmin, horizontal separation: 0.7 deg). On each trial, the bars started at a relative disparity between 2 and 23 arcmin. Observers adjusted the relative disparity of the bars in steps of 0.5 arcmin using the keyboard. When the up arrow key was pressed, the left bar moved nearer by 0.25 arcmin and the right bar moved further by 0.25 arcmin. The direction of adjustment was reversed when the down arrow key was pressed. When observers perceived the two bars to be matched in depth, they pressed the space bar to initiate the next trial. Observers initially completed 12 practice trials with feedback; the bars turned orange when within 2 arcmin of relative disparity, and green when within 0.5 arcmin of disparity. This was followed by 24 trials without feedback. In the main experiment observers matched the depth of two red circular probes (diameter: 6 arcmin) positioned 7 arcmin in front of the slanted surface (when at zero relative disparity) (see Fig. 5e). The probes were horizontally separated by a distance of 2.8 deg and their relative disparity was randomly selected between ±4 arcmin for the start of each trial. Observers adjusted the relative depth of the probes using the same method as in the practice task. On each trial the stimulus was displayed for a minimum of 3 s, however there was no upper time limit and observers pressed the space bar to enter their response when they perceived the probes to be matched in depth. There were four types of slanted surface behind the probes (no sidebands, monocular sidebands, binocular sidebands, vertical flankers), 2 magnitudes of slant (3% and 6%) and 2 directions of slant (left and right around a vertical axis). This produced 16 conditions in a factorial design, in addition to the flat surface condition, which served as a baseline measure. Each of the 17 conditions was repeated 7 times in a different random order for each observer, for a total of 119 trials.

523

4.2. Results and discussion

554

The practice data for Experiment 3 are shown in Fig. 8 (only trials without feedback are included). The means are clustered around zero disparity, confirming that observers were able to match the depth of the two bars in the practice task from a range of starting disparities. Note that the practice task is more difficult than the baseline condition in Experiment 3 because there is no reference surface behind the bars. This may explain the greater variability in the data for the practice task (Fig. 8) compared to the baseline condition (Fig. 9).

555

matched relative disparity (arcmin)

464

6 4 2 0 -2 -4 -6

N = 11 2

6

10

14

18

22

inital relative disparity (arcmin) 520 521 522

4.1.3. Procedure As in Experiment 2, observers completed a practice task before the main experiment. The practice task involved matching the

Fig. 8. Practice data for all observers (N = 11) in Experiment 3. The dashed line at zero disparity indicates a perfect depth match between the two bars. Error bars are between-subject SEMs.

Please cite this article in press as: Wardle, S. G., et al. Monocular and binocular edges enhance the perception of stereoscopic slant. Vision Research (2014), http://dx.doi.org/10.1016/j.visres.2014.04.012

524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553

556 557 558 559 560 561 562 563

VR 6817

No. of Pages 11, Model 5G

8 May 2014 S.G. Wardle et al. / Vision Research xxx (2014) xxx–xxx

probe bias (relative disparity in arcmin)

8

7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7

baseline (at surface) vertical ankers no sidebands monocular sidebands binocular sidebands

N = 11 3% left

3% right

6% left

6% right

slant Fig. 9. Average relative disparity between the two dot probes for each condition in Experiment 3 (N = 11). The dashed line at zero disparity indicates no bias. The predicted direction of the bias is positive for leftward slant (right probe nearer than the left probe) and negative for rightward slant (left probe nearer than the right probe). The baseline condition (flat surface) is replotted in each subsection of the graph for clarity. Error bars show between-subjects SEM. 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609

The mean probe bias for each slant condition in Experiment 3 is shown in Fig. 9. The predicted direction of the bias is coded as positive for leftward slant (right probe perceived as nearer than left probe), and negative for rightward slant (left probe perceived as nearer than right probe). The bias was calculated by subtracting the matched disparity of the right probe from the matched disparity of the left probe. The predicted direction of the bias is to perceive the probe that is further from the surface (i.e. in front of the side of the surface which is slanted away) as nearer than the probe that is closer to the surface. As expected, no bias was perceived when the probes were in front of a flat surface; the mean disparity is approximately zero (Fig. 9). There was also little or no bias for a slanted surface with flankers above and below the surface in a twist configuration. This is predicted because slant is known not to be underestimated in this stimulus (e.g. the practice task for Experiment 2 used this stimulus, see data in Fig. 2; also see Gillam & Blackburn, 1998; Gillam, Blackburn, & Brooks, 2007; Gillam, Sedgwick, & Marlow, 2011). However, a large bias was observed for slant without sidebands, in agreement with the slant-matching data from Experiment 2, which showed that the slant of this surface is significantly under-estimated. When monocular sidebands are added, a bias is still present but it is reduced in comparison to slant without sidebands. The magnitude of bias is reduced even further when binocular sidebands are added. Thus this pattern of results is in direct agreement with the slant-matching data from Experiment 2. Overall, in the conditions that had a bias, the bias was larger for the surfaces with greater slant (6% magnification). The results were analyzed in a repeated measures ANOVA. Prior to statistical analysis, the data was recoded so that the predicted direction of bias for left and right slant were both positive values (the data for rightward slant was multiplied by 1 to invert the sign). The main effects of slant type (F(3, 30) = 15.937, p < .01) and magnification (F(1, 10) = 26.425, p < .01) were significant, but there was no main effect for the direction of slant (F(1, 10) = 2.877, p > .05). None of the interactions were significant. The left and right directions of slant were thus combined for contrast analysis, with the error rate controlled at 0.05 for multiple comparisons using the Bonferroni procedure. The flankers above and below the surface significantly reduced the bias compared to all of the other conditions combined – monocular, binocular, and no sidebands (F(1, 10) = 15.219, p < .01). It is clear from the graph that adding the flankers eliminated the bias altogether for both directions and magnifications – the means are approximately zero in each case (Fig. 9). The addition of either monocular or binocular sidebands also significantly reduced the amount of bias compared

to the condition without sidebands (F(1, 10) = 27.301, p < .01). Although the means indicate that binocular sidebands tended to produce less bias than monocular sidebands (with the exception of the 6% right slant condition, which had higher variance in both the monocular and binocular conditions), this difference was not statistically significant (F(1, 10) = 6.430, p > .05). Overall, the data showed the same pattern as that found using the slant-matching task in Experiment 2. Reasons for the differences in perceived slant across conditions are discussed in detail in the General discussion (Section 5).

610

5. General discussion

620

Our experiments show in several different ways that stereoscopic slant around a vertical axis is enhanced by depth information at surface edges. In Experiment 1 we found that the proximity of a surface’s edges had an effect on perceived slant. Greater slant was perceived for narrower surfaces in which the edges of the surface were closer together, even though the relative disparity of the two surface edges was actually less than that for wider surfaces at the same magnification. Additional monocular sidebands at the edges produced a consistent enhancement of slant that did not differ across stimulus width, although it did increase significantly with magnification. We have interpreted the latter finding as indicating that, just as the relative depth signal relating the left edge and the right edge is more effective for narrower surfaces, relating the relative depth signal at the left edge (i.e. between edge and background) with the equivalent relative depth signal at the right edge is also more effective when the edges are closer together. In Experiments 2 and 3 we compared the enhancement of perceived slant for regions of monocular versus binocular texture at the outer edges of the slanted surface. Experiment 2 demonstrated with a slant-matching task that the magnitude of perceived slant is greater, and Experiment 3 demonstrated that the bias in the perceived depth of two probes in front of a slanted surface was significantly reduced when either binocular or monocular sidebands were present. In both cases, binocular sidebands produced a greater effect than monocular sidebands — a greater enhancement of slant (Experiment 2), and a greater reduction in the depth bias of the probes (Experiment 3).

621

5.1. Monocular and binocular edges constrain stereoscopic slant

648

We suggest that the advantage afforded by binocular and monocular sidebands in the perception of stereoscopic slant is a result of adding relative depth signals at the near and far edges of the

649

Please cite this article in press as: Wardle, S. G., et al. Monocular and binocular edges enhance the perception of stereoscopic slant. Vision Research (2014), http://dx.doi.org/10.1016/j.visres.2014.04.012

611 612 613 614 615 616 617 618 619

622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647

650 651

VR 6817

No. of Pages 11, Model 5G

8 May 2014 S.G. Wardle et al. / Vision Research xxx (2014) xxx–xxx

9

Fig. 10. A schematic diagram (aerial view) of relative depth at the edges of a slanted surface produced by (a) vertical flankers, (b) binocular sidebands, and (c) monocular sidebands. The horizontal dashed line marks the axis of slant; red arrows indicate the relative disparity between the edges of the slanted surface and the sidebands. (a) The presence of vertical flankers (v1) produce relative disparities along the entire slanted surface, not only at the edges x and y. (b) The inner edges of the binocular sidebands (b1, b2) produce relative disparity with the edges of the slanted surface at points d and e. However, for monocular sidebands (c), there is no relative disparity at the edges. Instead, there is relative depth from occlusion geometry, which is specified differently at each side of the slanted surface. On the right side, relative depth is between the monocular region attached to the near side of the slanted surface (m2) and one side of the slanted surface (q). On the left, the monocular region adjacent to the far side of the surface (m1) is perceived as a continuation of the slant. A phantom occluder accounts for this region seen by only one eye, thus here the relative depth is between the edge of the slanted surface (p) and the phantom. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693

slanted surface (see Fig. 10). The pattern of data in Experiment 2 and Experiment 3 can be related to how constrained the relative depth signals at the edges of the slanted surface are in each case. The greatest magnitude of slant, and the greatest reduction in the probe bias, was observed for a slanted surface with flankers above and below the surface (a version of the ‘‘twist’’ stimulus). As illustrated in Fig. 10a, the change in depth of this surface is constrained across the entire surface by the relative disparity gradient between the slanted surface and the flankers. Binocular sidebands were the second most effective at enhancing slant, and here the depth of the slanted surface is constrained by relative disparities at the edges of the slanted surface and the binocular sidebands (Fig. 10b). Monocular sidebands present an entirely different situation, as the relative depth at the edges of the slanted surface is specified by occlusion geometry instead of relative disparity. In contrast to the precise depth specified by relative disparity, in most cases, depth from occlusion geometry is only partially constrained.1 There is also a qualitative difference in the edges produced by binocular and monocular sidebands, as the edge on one side of the surface with monocular sidebands is not supported by a physically present occluding surface. However, the occlusion information is powerful enough to create a strong phantom occluder on this side (Fig. 10b). Phantom occluding surfaces arising from monocular regions have geometrically predictable quantitative depth (Wardle & Gillam, 2013b). However, as evident in the example stereograms of our stimuli, the thin edges produced by monocular sidebands are not as obvious as the edges produced by the large binocular sidebands (compare Fig. 5c and d). In sum, a comparison across the experimental stimuli suggests that greater slant is perceived as the relative depth of the surface is more constrained – either specifying the entire slant by a relative disparity gradient at the upper and lower edges in the case of the twist stimulus (vertical flankers), or by the relative depth steps at the sides of the surface in the stimuli with monocular or binocular sidebands. The enhancement of slant produced by monocular and binocular edge information can be considered as an extension of the ‘‘boundary process’’ of stereoscopic slant resolution. When upper or lower frontal plane surfaces are placed above or below a slanted surface, a gradient of relative disparities is produced along the horizontal boundary between the two surfaces, orthogonal to the axis of slant (Fig. 1a). On this basis, Gillam, Flagg, and Finlay (1984) proposed two processes for slant resolution: a ‘‘boundary’’ process and

1

Assee and Qian (2007) propose that monocular regions operate as a form of double fusion or Panum’s Limiting Case (which is a form of occlusion geometry). However, this would be an unorthodox form of Panum’s Limiting Case, in which one fusion is of the outer edges of the left and right eye images and the other is of the outer edge of the narrower image in one eye and the monocularly invisible intersection of the binocular and monocular regions in the other.

a ‘‘surface’’ process. Gillam, Flagg, and Finlay (1984) argued that the boundary process may be more important (at least for slant around a vertical axis), producing a faster and more veridical perception of slant based on the relative disparity at depth discontinuities. Monocular and binocular edge information could facilitate a variant of the boundary process, as relative depth signals are produced at both the near and far edges of the slanted surface. In order to understand why processes based on relative disparities at surface boundaries improve slant, it is necessary to consider why the surface process alone produces such poor slant, as we have confirmed in the underestimation of slant for the isolated surface in Experiment 2, and the large probe bias for an isolated slanted surface in Experiment 3.

694

5.2. Why slant around a vertical axis is poorly perceived for isolated surfaces

707

There are at least two possible reasons why the stereoscopic slant of an isolated surface is underestimated. The first possibility, as mentioned in the introduction (Section 1), relates to the difference between absolute and relative disparity. Magnification of the entire visual field produces a gradient of absolute disparities. However, the relative disparity between any two points at a fixed distance along the slanted surface is a constant. Gillam, Flagg, and Finlay (1984) proposed that the ‘‘surface process’’ could be based on the gradient of absolute disparity or the integration of small identical disparity differences across the surface. The poor slant given by the surface process could be due to the insensitivity of the visual system to absolute disparity, and the inefficiency of integrating successive relative disparities within the surface. The finding of Fahle and Westheimer (1988) that depth detection thresholds between two points are elevated by adding intervening points supports the idea that the poor slant in an isolated textured surface is the result of an integration process. The long latency for perceiving slant around a vertical axis for isolated surfaces (Gillam, Flagg, & Finlay, 1984) is also consistent with a time-consuming integration process for resolving its slant. The second possible reason why slant about a vertical axis may be underestimated is that absolute disparity gradients are ambiguous with respect to slant about that axis. Stereo slant of a given degree results in different disparity gradients at different azimuths of the surface. Thus a surface slanted at 20 deg (for example) will have a different absolute disparity gradient when the surface is in front of the observer compared to when it is eccentric. Conversely, the same absolute disparity gradient specifies slants of different degrees depending on its azimuth. Mitchison and Westheimer (1990) suggested that because of this ambiguity, horizontal disparity gradients tend to be disregarded in favor of ‘‘salience’’, a concept that can be roughly equated with what we

709

Please cite this article in press as: Wardle, S. G., et al. Monocular and binocular edges enhance the perception of stereoscopic slant. Vision Research (2014), http://dx.doi.org/10.1016/j.visres.2014.04.012

695 696 697 698 699 700 701 702 703 704 705 706

708

710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740

VR 6817

No. of Pages 11, Model 5G

8 May 2014 10 741 742 743 744 745 746

S.G. Wardle et al. / Vision Research xxx (2014) xxx–xxx

have called relative disparity signals.2 Thus it is possible that slant around a vertical axis is underestimated because the absolute disparity gradient is ambiguous with respect to the slant specified and is disregarded. In the following section we consider how a boundary process might facilitate slant in our stimuli when there is additional monocular or binocular edge information.

747

5.3. Depth spreading of edge signals

748

The slant of the entire surface appears to be enhanced by any of the three kinds of edge depth steps that we have investigated (Fig. 10). We assume that this enhancement requires depth spreading from the edges to the details on the surface. In the case of the vertical flankers (twist stimulus), the relative slant given by the gradient of relative disparity is largely attributed to the slanted surface. This suggests that even though the absolute disparity gradient is weak when in isolation, it influences the allocation of the relative slant to the surface that contains the absolute disparity gradient. Once the depth variations are assigned to the upper and lower edges of the slanted surface, they could be transmitted vertically (parallel to the slant axis) to all points with the same disparity. The surface appears opaque even though it is randomly textured (with a medium density), and the depth spreading may be subsequent to some process by which surface planarity is determined. In the case of interpolation of the relative depth signals at the left and right edges (from the monocular or binocular sidebands), the relative depth is also largely attributed to the slanted surface. It appears that the relative depth signals at each end of the surface act as ‘‘anchors’’ for the absolute disparity gradient. In the case of the binocular sidebands, they provide equidistant frames against which the inner slanted surface is seen. Although the depth of the monocular sidebands is ambiguous (Fig. 2), it seems that they are also treated as equidistant frames. It is clear that anchors at each end of a surface could resolve an ambiguous absolute disparity gradient by pushing one side of the central surface forward, and the other side backward, relative to the sideband surrounds. It is less obvious how end anchors would enhance the response of a poorly registered absolute disparity gradient or enhance the integration of identical local relative disparities across the surface. The mechanisms by which the relative disparity at the edges combines with an absolute disparity gradient orthogonal to the edges require further investigation. There is a considerable literature on depth interpolation in stereopsis which demonstrates depth spreading across regions without disparity, either in areas that are blank in one eye and textured in the other eye (Buckley, Frisby, & Mayhew, 1989; Collett, 1985), or across horizontal lines that are binocular but lack disparity information (Georgeson, Yates, & Schofield, 2009). Depth interpolation also occurs across regions of rivalrous texture between edges with disparity (Würger & Landy, 1989). Edge disparities can disambiguate how intervening ambiguous disparities are fused (the wallpaper effect) (Mitchison & McKee, 1987). Smooth surface reconstruction by depth interpolation occurs for sinusoidally-shaped surfaces in random-dot stereograms which contain disparity discontinuities up to 0.3 deg (Yang & Blake, 1995). However, none of these situations is like the one we investigate in Experiments 2 and 3 where the surface disparities are

749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796

2

Since the eyes are separated horizontally, this ambiguity with respect to azimuth does not apply to slants around the horizontal axis, which may explain the wellknown anisotropy in slant perception for isolated surfaces – slant around a horizontal axis is generally perceived more veridically than slant around a vertical axis. This could also be because the former contains global shear disparity whereas the latter has the less effective global compression disparity (see Gillam, Chambers, & Russo, 1988).

dense, fully specified and unambiguous, but the edge signals have a large effect on the slant resolution of the surface. There is already evidence that monocular sidebands can disambiguate slant in a different context. Gillam and Blackburn (1998) measured perceived slant in ‘‘twist’’ stimuli for a range of vertical separations between the two surfaces. A small amount of slant was perceived in the frontal-parallel surface in the ‘‘twist’’ because the relative-disparity gradient in the twist stimulus does not specify which of the two surfaces is slanted. They found that adding monocular sidebands increased perceived slant of the slanted surface and also decreased perceived slant due to contrast effects in the frontal-parallel surface, suggesting that monocular regions resolved the ambiguity as to which surface was slanted. Monocular regions increased slant by a constant amount for a range of vertical separations between the slanted and frontal-parallel surface in the twist stimulus. This is consistent with the results of Experiment 1, in which monocular regions increased perceived slant by a constant amount in surfaces of different widths. Berends, Zhang, and Schor (2003) found evidence from eye movements for the involvement of edges in slant perception. Eye movements facilitated discrimination of the direction of slant in a large stereoscopic surface when horizontal disparity noise was present, but not in conditions without disparity noise. The authors concluded that when estimates of disparity across the surface were noisy, slant discrimination could be improved by making eye movements to the edges of the slanted stimulus. Although the edges also contained disparity noise, their signal-to-noise ratios were higher, as disparities were largest at the edges of the slanted surface. Here we have shown that edges are used in resolving stereoscopic slant even in the absence of disparity noise, and that perceived slant for isolated surfaces with only an absolute disparity gradient is significantly underestimated. Berends, Zhang, and Schor (2003) used much larger stimuli than our experiments (60  32 compared to 1.95  3.90 deg) and at a closer viewing distance (30 versus 70 cm), which is likely to account for the differences. A role for depth discontinuities in stereo surface processing is further supported by the finding of cells in area V2 of the visual cortex that respond to a depth step in random dot stereograms (von der Heydt, Zhou, & Friedman, 2000). Some of these cells are also selective for the direction of the depth step. Although these recordings were made using frontal-parallel surfaces (a square standing out from a background when viewed stereoscopically), cells selective for stereoscopic depth edges may also be involved in the perception of slant. An interesting issue highlighted by these results, which is also acknowledged by the authors, is that the cells could be responding to the presence of a monocular region rather than the stereoscopic edge. A depth step in a random dot stereogram is typically accompanied by an adjacent monocular region of texture, because some of the dots must be shifted horizontally to simulate the conditions of a plane seen in depth against a background. Further research will determine whether there are cells tuned specifically to monocular regions.

797

5.4. Conclusion

850

Overall, the results show that relative depth information at the edges of a slanted surface enhance the perception of stereoscopic slant. This occurs with the addition of binocular regions consistent with a background and also for monocular regions that naturally occur with binocular viewing of 3D scenes. The edges produced by monocular regions have relative depth specified by occlusion geometry instead of binocular disparity, thus the depth of these edges is less precise than binocular edges. However, even though the depth of the edges is under-constrained, monocular regions significantly increase perceived slant. Together the results suggest

851

Please cite this article in press as: Wardle, S. G., et al. Monocular and binocular edges enhance the perception of stereoscopic slant. Vision Research (2014), http://dx.doi.org/10.1016/j.visres.2014.04.012

798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849

852 853 854 855 856 857 858 859 860

VR 6817

No. of Pages 11, Model 5G

8 May 2014 S.G. Wardle et al. / Vision Research xxx (2014) xxx–xxx

866

that depth information from monocular regions and binocular disparities can interact to produce coherent perception of slanted surfaces. Future physiological research will reveal whether cells in visual cortex exist that are selective for the location of monocular regions, and whether such cells underlie depth perceived from occlusion geometry.

867

6. Uncited references

861 862 863 864 865

868 869

Gillam (2011), Harris and Wilcox (2009) and Howard and Q3 Rogers (2012). Acknowledgments

870

874

This research was supported by Australian Research Council Discovery Grant DP110104810 awarded to B.G. and S.P. The authors thank Shane Blackburn for assistance in running Experiment 1.

875

References

876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907

Assee, A., & Qian, N. (2007). Solving da Vinci stereopsis with depth-edge-selective V2 cells. Vision Research, 47, 2585–2602. Backus, B. T., Banks, M. S., van Ee, R., & Crowell, J. A. (1999). Horizontal and vertical disparity, eye position, and stereoscopic slant perception. Vision Research, 39, 1143–1170. Berends, E. M., Zhang, Z. L., & Schor, C. M. (2003). Eye movements facilitate stereoslant discrimination when horizontal disparity is noisy. Journal of Vision, 3, 780–794. http://dx.doi.org/10.1167/3.11.12. Brainard, D. H. (1997). The psychophysics toolbox. Spatial Vision, 10, 433–436. Buckley, D., Frisby, J. P., & Mayhew, J. E. W. (1989). Integration of stereo and texture cues in the formation of discontinuities during three-dimensional surface interpolation. Perception, 18, 563–588. Collett, T. S. (1985). Extrapolating and interpolating surfaces in depth. Proceedings of the Royal Society of London Series B, 224, 43–56. Erkelens, C. J., & Collewijn, H. (1985). Motion perception during dichoptic viewing of moving random-dot stereograms. Vision Research, 25, 583–588. Fahle, M., & Westheimer, G. (1988). Local and global factors in disparity detection of rows of points. Vision Research, 28, 171–178. Georgeson, M. A., Yates, T. A., & Schofield, A. J. (2009). Depth propagation and surface construction in 3-D vision. Vision Research, 49, 84–95. Gillam, B. J., & Blackburn, S. G. (1998). Surface separation decreases stereoscopic slant but a monocular aperture increases it. Perception, 27, 1267–1286. Gillam, B., Blackburn, S., & Brooks, K. (2007). Hinge versus twist: The effects of ‘reference surfaces’ and discontinuities on stereoscopic slant perception. Perception, 36, 596–616. Gillam, B., & Borsting, E. (1988). The role of monocular regions in stereoscopic displays. Perception, 17, 603–608. Gillam, B., Chambers, D., & Russo, T. (1988). Postfusional latency in stereoscopic slant perception and the primitives of stereopsis. Journal of Experimental Psychology: Human Perception and Performance, 14, 163–175. Gillam, B., Flagg, T., & Finlay, D. (1984). Evidence for disparity change as the primary stimulus for stereoscopic processing. Perception and Psychophysics, 36, 559–564.

871 872 873

Q4 Q5

11

Gillam, B. (2011). The influence of monocular regions on the binocular perception of spatial layout. In L. R. Harris & M. R. M. Jenkin (Eds.), Vision in 3D environments (pp. 46–69). New York: Cambridge University Press. Gillam, B. J., & Pianta, M. J. (2005). The effect of surface placement and surface overlap on stereo slant contrast and enhancement. Vision Research, 45, 3083–3095. Gillam, B. J., Sedgwick, H. A., & Marlow, P. (2011). Local and non-local effects on surface-mediated stereoscopic depth. Journal of Vision, 11(6), 1–14. http:// dx.doi.org/10.1167/11.6.5 (article no. 5). Gogel, W. C. (1956). Relative visual direction as a factor in relative distance perceptions. Psychological Monographs, 418, 1–19. Gogel, W. C., & Harker, G. S. (1955). The effectiveness of size cues to relative distance as a function of lateral visual separation. Journal of Experimental Psychology, 50, 309–315. Harris, J. M., & Wilcox, L. M. (2009). The role of monocularly visible regions in depth and surface perception. Vision Research, 49, 2666–2685. Hirsch, M. J., & Weymouth, F. W. (1948). Distance discrimination. II. Effect on threshold of lateral separation of the test objects’. Archives of Ophthalmology, 39, 224–231. Howard, I. P., & Rogers, B. J. (2012). Seeing in depth. Oxford: Oxford University Press. Kleiner, M., Brainard, D., & Pelli, D. (2007). What’s new in Psychtoolbox-3? Perception, 36 (ECVP Abstract Supplement). Marlow, P., & Gillam, B. J. (2011). Stereopsis loses dominance over relative size as target separation increases. Perception, 40, 1413–1427. Mitchison, G. J., & McKee, S. P. (1987). The resolution of ambiguous stereoscopic matches by interpolation. Vision Research, 27, 285–294. Mitchison, G. J., & Westheimer, G. (1984). The perception of depth in simple figures. Vision Research, 24, 1063–1073. Mitchison, G. J., & Westheimer, G. (1990). Viewing geometry and gradients of horizontal disparity. In C. Blakemore (Ed.), Vision: Coding and efficiency (pp. 302–309). Cambridge: Cambridge University Press. Nakayama, K., & Shimojo, S. (1990). da Vinci stereopsis: Depth and subjective occluding contours from unpaired image points. Vision Research, 30, 1811–1825. Ogle, K. N. (1950). Researches in binocular vision. Philadelphia: Saunders. Pelli, D. G. (1997). The VideoToolbox software for visual psychophysics: Transforming numbers into movies. Spatial Vision, 10, 437–442. Pierce, B. J., & Howard, I. P. (1997). Types of size disparity and the perception of surface slant. Perception, 26, 1503–1517. Rady, A. A., & Ishak, I. G. H. (1955). Relative contributions of disparity and convergence to stereoscopic acuity. Journal of the Optical Society of America, 45, 530–534. van Ee, R., & Erkelens, C. (1996). Temporal aspects of binocular slant perception. Vision Research, 36, 43–51. von der Heydt, R., Zhou, H., & Friedman, H. S. (2000). Representation of stereoscopic edges in monkey visual cortex. Vision Research, 40, 1955–1967. Wardle, S. G., & Gillam, B. J. (2013a). Color constrains depth in da Vinci stereopsis for camouflage but not occlusion. Journal of Experimental Psychology: Human Perception and Performance, 39, 1525–1540. http://dx.doi.org/10.1037/ a0032315. Wardle, S. G., & Gillam, B. J. (2013b). Phantom surfaces in da Vinci stereopsis. Journal of Vision, 13(2), 1–14. http://dx.doi.org/10.1167/13.2.16 (article no. 16). Westheimer, G. (1979). Cooperative neural processes involved in stereoscopic acuity. Experimental Brain Research, 36, 585–597. Wright, W. D. (1951). The role of convergence in stereoscopic vision. Proceedings of the Physical Society B, 64, 289–297. Würger, S. M., & Landy, M. S. (1989). Depth interpolation with sparse disparity cues. Perception, 18, 39–54. Yang, Y., & Blake, R. (1995). On the accuracy of surface reconstruction from disparity interpolation. Vision Research, 949–960.

908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967

Please cite this article in press as: Wardle, S. G., et al. Monocular and binocular edges enhance the perception of stereoscopic slant. Vision Research (2014), http://dx.doi.org/10.1016/j.visres.2014.04.012