Vision Research 41 (2001) 187–199

Phantom surface captures stereopsis

Jukka Hakkinen *, Gote NymanDepartment of Psychology, General Psychology Di6ision, Uni6ersity of Helsinki, P.O. Box 13, 00014 Helsinki, Finland

Received 19 November 1999; received in revised form 30 May 2000

Abstract

A phantom surface is a stereoscopic illusory area that can be seen in depth although there is no conventional stereoscopic cues[Liu, L., Stevenson, S.B., & Schor, C.M. (1994). Quantitative stereoscopic depth without binocular correspondence. Nature, 367,66–69; Gillam, B. & Nakayama, K. (1999). Quantitative depth for a phantom surface can be based on cyclopean occlusion cuesalone. Vision Research, 39, 109–112]. The phenomenon has been explained as an example of half-occlusion processing in whichthe visual system uses information about cyclopean occlusion structure of the visual world. We created stereo capture stereogramsin which phantom surfaces changed the perceived depth of conventionally defined binocular textures. Because conventionalstereoscopic matching is strongly affected by half-occlusion processing, we suggest that half-occlusion processing is an integralpart of the early stereoscopic processing and solving of the correspondence problem. © 2001 Elsevier Science Ltd. All rightsreserved.

Keywords: Stereopsis; Stereo capture; Stereo matching; Phantom stereopsis; Half-occlusion

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1. Introduction

To construct a three-dimensional perception from thedifferences in the views of the left and right eye, theprocesses of stereo vision have to determine, whichimage in the left eye corresponds to a certain image inthe right eye. Usually it is assumed that there have tobe elements both in the left and right eye, becauseotherwise it seems meaningless to talk about correspon-dence. Contrary to this basic assumption of stereovision research, it has been found out that noncorre-sponding areas are more than meaningless noise.Monocular areas that can be interpreted as half-oc-cluded by an adjacent binocular structure affect thestereoscopic segmentation of a scene (da Vinci, 1989;Szily, 1921/1998). For example, the visual system canlocalize an ambiguous monocular object by using half-occlusion assumptions (Kaye, 1978; Nakayama & Shi-mojo, 1990; Hakkinen & Nyman, 1996). Also,half-occlusions affect binocular fusion (Gillam &Borsting, 1988), rivalry (Shimojo & Nakayama, 1990),matching (Anderson, 1994; Anderson & Nakayama,

1994), three-dimensional slant processing (Hakkinen &Nyman, 1997; Gillam, Blackburn, & Nakayama, 1999)and volumetric perception (Idesawa, Iwamoto, Hara, &Sakaguchi, 1997).

Liu, Stevenson, and Schor (1994) have presented avariation of this phenomenon called phantom stereopsis(Fig. 1a) in which the surface is seen in front ofbackground although the stereogram does not containmatching features for conventional stereopsis. How-ever, later it has been argued that conventional dispar-ity processing may account for the perceived depth inthe phantom stereopsis stereograms of Liu et al., be-cause the stereograms contain contours that may bematched (Gillam, 1995). To check the possibility ofconventional matching process, Liu, Stevenson, andSchor (1997) have modelled the matching process withGabor filters. According to their results, oblique Gaborfilters create matchable features to the corner areas ofthe central rectangle (Fig. 1a) and thus could explainthe three-dimensional perception. However, Gillam andNakayama (1999) have presented a new variation ofthis phenomenon in which the possible cues for conven-tional disparity processing have been removed. In theirstereogram (Fig. 1b) the phantom surface appears witha simpler stereogram that consist of lines and does not

* Corresponding author. Tel.: +358-9-19123409; fax: 358-91-9123493.

E-mail address: jukka.hakkinen@helsinki.fi (J. Hakkinen).

0042-6989/01/$ - see front matter © 2001 Elsevier Science Ltd. All rights reserved.PII: S 0 0 4 2 -6989 (00 )00231 -5

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contain corners that could be a cue for conventionalstereo matching. Gillam and Nakayama conclude in theirarticle that cyclopean occlusion cues alone can producea perception of illusory surface in front of background.

Because the experiments suggest that half-occlusionprocessing is independent from conventional stereopsis,the interaction of binocular and monocular elements isan interesting research question. The studies on this topichave usually investigated how binocular objects affectmonocular objects (Kaye, 1978; Nakayama & Shimojo,1990; Hakkinen & Nyman, 1996), but there are no studieson the effect of monocular objects on binocular objects.The reason for this may be the assumption that unam-biguous binocular objects always determine the positionof highly ambiguous monocular objects (Gogel, 1956).However, this assumption may not always be valid. If thebinocular object has multiple depth interpretations, i.e.it contains a large amount of matching ambiguity, it maybe affected by a monocular object that can be interpretedas a depth discontinuity. One way to increase theambiguity is to create a binocular periodic texture thathas multiple matching solutions. Each of these matchescorresponds to a plane of depth, so the perceivedthree-dimensional position of the central dots is changedeasily. Because of its ambiguity, the periodically texturedwallpaper stereogram can be used as a sensitive indicatorof interactions in stereopsis and could be used to demon-strate a phenomenon in which a monocular area changesthe perceived depth of a binocular area (Julesz & Chang,1976; Mitchison & McKee, 1985; Ramachandran &Cavanagh, 1985; Papathomas & Julesz, 1989; Ishigushi& Wolfe, 1993).

Ramachandran and Cavanagh (1985) demonstratedthat a Kanizsa illusory surface that contains disparity

pulls wallpaper texture bounded by the illusory surfaceto the same depth level. They also showed that otherobjects, like thin line corners, do not capture backgroundtexture. Later it has been demonstrated that a monocularillusory surface is not a necessary condition for thecapture (Mather, 1989) and that slanted illusory surfacescan also capture textures (Hakkinen, Liinasuo, Kojo, &Nyman, 1998). In our experiment we measured whetherphantom surfaces can capture ambiguous wallpaperdots. To test the capture effect we created phantomversions of ordinary Kanizsa surfaces. In a phantomKanizsa surface the vertical parts of two inducing figureshave been removed in one half-image so that it is notpossible to match the vertical cut-out sectors that usuallycreate the perception of three-dimensional illusory sur-face. If a three-dimensional illusory surface is perceivedin a phantom Kanizsa figure it is either due to ahalf-occlusion interpretation made possible by themonocular areas or because the corner areas are match-able features. Because of the latter alternative, we alsotested phantom surfaces induced by lines (Fig. 4a; Gillam& Nakayama, 1999) and phantom Kanizsa stereogramswithout a corner matching possibility (Fig. 8a and b).

2. General methods

2.1. Stimuli

Capture stereograms in Fig. 2a–Fig. 9d were used asstimuli. Each configuration was shown as crossed anduncrossed versions, so the total number of differentcapture stereograms was twice the number of configura-tions. Each dot in the display was 1×0.9 arc min(horizontal×vertical). The dots were spaced 6 arc minhorizontally and 5.4 arc min vertically. The diameters ofthe circular inducing figures were 25×24.3 arc min. Thedisparity of the illusory surface was 6 arc min in Fig. 2aand Fig. 3a. A frame surrounded the stereogram. Thehorizontal edges of the frame were 161×6.3 arc min andvertical edges were 7×144.9 arc min.

A comparison probe (3×21.6 arc min) was located 11arc min vertically under the frame of the capturestereogram. The comparison probe was given one ofeleven equally spaced disparities between 2 arc minuncrossed to 8 arc min crossed disparity. Each stimuluscondition was repeated 25 times.

2.2. Apparatus

The stimuli were presented on a 21-in. Nokia 445×multigraph screen and were viewed through circularapertures (diameter 16°) with a mirror stereoscope. Theviewing distance was 1 m. The subjects placed their headsin a chinrest with a headstop.

Fig. 1. (a) A phantom surface. When the rightmost stereo-pair isviewed with diverging eyes, the phantom surface appears above theblack rectangle. In the leftmost stereo-pair, the phantom surface isseen further away than the black area. If the stereograms are viewedwith converging eyes, the stereoscopical appearances are the opposite,i.e. rightmost stereopair produces far phantom surface and leftmostproduces near phantom surface. (b) A line induced phantom rectan-gle is perceived in this stereogram although possible cues for conven-tional stereopsis have been reduced (Gillam & Nakayama, 1999).

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Fig. 2. (a) Stereoscopic capture. The illusory surface in front captures the background dots bounded by the illusory rectangle to the same depthlevel. In uncrossed disparity, the dots are not captured to the far depth. (b) Stereoscopic capture without horizontal and vertical supporting bars.(c) Results for experiment 1, stereogram in Fig. 2a. The figure plotted the percentage of central dots that was perceived nearer than the comparisonbar as a function of the disparity of the comparison bar. The filled dots indicate results from crossed configuration and the unfilled dots fromuncrossed configuration. Each dot represents a mean of 25 repetitions. (d) Result for experiment 2, stereogram in Fig. 2b. The figure contains thepercentage of central dots that were perceived nearer than the comparison bar plotted as a function of the disparity of the comparison bar. Thefilled dots indicate results from crossed configuration and the unfilled dots from uncrossed configuration. Each dot represents a mean of 25repetitions.

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Fig. 3. (a) A stereo capture stereogram with a phantom Kanizsa surface and supporting bars. (b) A stereo capture stereogram with a phantomKanizsa surface and no supporting bars. (c) Results for experiment 1, stereogram in Fig. 3a. (d) Results for experiment 1, stereogram in Fig. 3b.

2.3. Procedure

The task of the subject was to report whether thedots in the central part of the capture stereogram or thecomparison bar appeared to be nearer. Subjects indi-cated their decision by pressing one of two buttons in a

computer keyboard. Viewing time was not limited. Afixation stimulus was presented before each target stim-ulus. The fixation stimulus consisted of a frame and afixation cross with nonius lines. The subject was askedto align the lines if they appeared to be nonaligned.Subjects fixated the cross for 2 s. A flash occurred at

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Fig. 4. (a) A line phantom surface with horizontal and verticalsupporting bars. (b) A line phantom surface with vertical supportingbars (c) A line phantom surface with horizontal supporting bars. (d)A line phantom surface without supporting bars.

3.1.2. StimuliEight capture configurations shown in Fig. 2a–Fig.

4d were used as stimuli. Each configuration was shownas crossed and uncrossed versions, so the total numberof different capture stereograms was sixteen With 25repetitions the complete experiment consisted of 4400stimuli (16 capture configurations×11 probe posi-tions×25 repetitions). Because each capturestereogram was shown with 11 different probe posi-tions, each capture configuration was shown 275 times.

3.2. Results

In a conventional capture stereogram (Ramachan-dran & Cavanagh, 1985) disparity is introduced to thecut-out sectors of the inducing figures and the dots thatare pulled to the same depth level with the illusorysurface (Fig. 2a). According to Ramachandran andCavanagh capture occurs only if the disparity in thecorner elements equals the interdot spacing. Further-more, the effect is also depth asymmetric, i.e. stereocapture is different in near and far depth. In near depthall the central dots are pulled in front of the back-ground but in far depth only the dots inside the cornerslocalize further away. Our results (Fig. 2c) confirmRamachandran’s results. The filled symbols representthe configuration in which the illusory surface was innear depth and the unfilled symbols correspond to thefar configuration. The x-axis indicates the depth of thecomparison probe and the y-axis shows the percentageof cases in which the central dots were perceived nearerthan the comparison probe. In the near configurationthe central dots were usually seen nearer than thecomparison probe until a depth of 5–7 arc min wherethe results drop below 75% level. This corresponds tothe stimulus in which the disparity of the illusorysurface and captured dots was 6 arc min. On the otherhand, the results from the far configuration show thatthe central dots were not usually seen nearer than theprobe until the disparity of the probe was 2 arc minuncrossed to 0 arc min. In other words, the central dotswere usually seen in the fixation plane. However, theresults in the far configuration are completely differentin one subject. In his case the curve does not rise near0 arc min disparity but stays near 0% level. One possi-ble interpretation of the result is that the subject per-ceived stereo captures to a far direction in thestereogram. This hypothesis cannot be confirmed withthe current experiment because the depth probe was notlocalized further in uncrossed disparity.

Although stereo capture has been studied in numer-ous experiments, the significance of horizontal andvertical supporting bars in capture stereograms is notknown. The bars probably have an enhancing effect oncapture for at least three reasons. Firstly, the bars areadditional inducing elements, so they probably clarify

the end of the 2-s period. After the flash, subjectsproceeded to the target stimulus by pressing a button inthe keyboard. Before the actual experiment, the sub-jects performed one practice session (308 stimuli).

3. Experiment 1

3.1. Methods

3.1.1. SubjectsThree students and the first author served as subjects.

The subjects had normal or corrected-to-normal vision.The students were paid for their participation and werenot aware of the purpose of the experiment. Before theexperimental session, each subject was shown a teststereogram, which consisted of rectangles. Subjects notable to perceive the testwere excluded from the experi-ment. All subjects were able to perceive the test.

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the illusory edge (Shipley & Kellman, 1992). Secondly,the bars may reduce matching ambiguity of the periodicdot texture, thus diminishing the possibility of horizon-tal spreading over the illusory contour. Thirdly, thehorizontal bars may interact with the disparate illusoryedge to produce an additional cue for three-dimen-sional discontinuity. The discontinuity cue is producedbecause the horizontal lengths of the horizontal sup-porting bars are different in the left and right eye.According to (Ogle, 1950) a horizontal size difference,i.e. geometric effect results in a perception of three-di-mensional slant around a vertical axis. Later it has beendemonstrated that the geometric effect is actually am-biguous, because three-dimensional discontinuity canproduce similar retinal images (Hakkinen & Nyman,1997). Furthermore, if a slanted surface and anothersurface are horizontally adjacent so that the slant ex-tends from the edge of the surface to far depth, theperceived slant is reduced (Hakkinen & Nyman; Grove,Ono, & Kaneko, 1999). In the capture stereograms thevertical illusory edge in near depth and the horizontalbar which is of different size in left and right eyesconstitute identical configurations. The resulting dis-continuity percept may increase the clarity of illusorycontours similar to the way a monocular object cueingdepth discontinuity enhances an illusory edge in daVinci stereopsis (Nakayama & Shimojo, 1990). Becausethe bars’ possible enhancing effects may have a signifi-cant role in producing stereo capture when the captureis otherwise weak or ambiguous, we wanted to test theirrole in our experimental stereograms.

Fig. 2b is the conventional capture stereogram with-out horizontal and vertical supporting bars. The resultsin Fig. 2d demonstrate that stereo capture was stillperceived when the supporting bars were removed.However, the depth asymmetry was clearly reduced andit seems that all naıve subjects perceived the centraldots in far disparity, i.e. far capture occurred. Thiseffect seems paradoxical, because removing bars re-duces cues that signal the depth location of the illusoryedge. However, removal also increases the matchingambiguity near the vertical illusory edge and thus thismight increase the possibility to see the dots in fardepth. There are also other reports of capture to fardirection in certain conditions (Wu, Zhou, Qi, & Wang,1998), but the exact reason for this effect has not beenthoroughly investigated.

After replicating the stereo capture effect we createda phantom Kanizsa stereogram in which segments ofthe inducing figures were removed so that only amonocular half-occlusion cue for depth remained. Theprinciple behind the phantom Kanizsa surfaces is simi-lar to that of the original phantom surfaces by (Liu etal., 1994), i.e. the corresponding vertical edges that canbe binocularly matched were removed. One version ofthe stereogram contained supporting horizontal and

vertical bars (Fig. 3a) and in the other version theywere removed (Fig. 3b).

According to the results, capture was perceived inboth versions of the phantom Kanizsa stereogram (Fig.3c and d). The near capture seems particularly strongwith phantom Kanizsa surfaces, since two curves donot bend below 75% border and two curves barely gobelow the 75% level. The results could be interpreted asa demonstration that phantom Kanizsa surface is per-ceived nearer than a conventional Kanizsa surface. Thisis consistent with the idea that matching occurs be-tween the vertical cut-out sector and the matchingfeature created by the corner of the other inducingfigure. On the other hand, when the supporting barswere removed (Fig. 3b) the strength of near capture wasslightly diminished (Fig. 3d). Removing the bars in-creases matching ambiguity and depth spreading overthe vertical illusory edge and the results may reflect theincreased unstability in matching. This hypothesis issupported if the near configurations of the traditionalcapture stereogram and phantom Kanizsa figure arecompared. The removal of supporting bars has astronger effect in the phantom Kanizsa configuration,because the phantom illusory surface has larger depthboth in terms of binocular disparity and dot period andthus the tendency to consider other matching solutionsincreases.

Because a phantom Kanizsa surface may containcues for conventional stereoscopic matching, we createdline phantom surfaces similar to those used by Gillamand Nakayama (1999). In these stereograms the illusorysurface is perceived, because parts of the inducing barsin each half-image are seen monocularly and conse-quently they act as a half-occlusion cue (Fig. 4a). Wemeasured the effect of supporting bars, so one configu-ration contained both horizontal and vertical bars (Fig.4a), the second version contained only vertical bars(Fig. 4b), the third only horizontal bars (Fig. 4d) andthe last one no additional supporting bars (Fig. 4d).

The results (Fig. 5a–d) show that phantom surfacesinduced by lines produced clear stereo capture. Whenboth supporting bars were present (Fig. 4a), the captureeffect was strongest (Fig. 5a) but removing bars did notchange the result significantly (Fig. 5b–d). The linephantom stereograms also produced clear depth asym-metric results in which the far phantom surface did notcapture the central dots in a far direction.

4. Experiment 2

4.1. Introduction

In experiment 1 we demonstrated that phantom sur-faces induced by phantom Kanizsa figures and linephantom surfaces can capture binocular dots to near

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Fig. 5. (a) Results for experiment 1, stereogram in Fig. 4a. (b) Results for experiment 1, stereogram in Fig. 4b. (c) Result for experiment 1,stereogram in Fig. 4c. (d) Result for experiment 1, stereogram in Fig. 4d.

depth. The result with phantom Kanizsa surfaces couldbe explained by the theory of Liu et al. (1997)according to which the corner areas are matchablefeatures. This explanation does not apply to linephantom stereograms, where the possibility of cornermatching is reduced, so phantom capture requiresadditional explanatory principles. One important factormight be the linking of monocular and binocular areas,which occurs when there are sufficient continuity cuesfrom monocular to binocular area. Monocularity doesnot contain cues for depth localization, but whenpresented with an accompanying binocular area, thedepth ambiguity is greatly reduced and the localizationbecomes easier. For example, in da Vinci stereopsis thehalf-occlusion interpretation of a monocular objectreduces the localization ambiguity of the object(Nakayama & Shimojo, 1990), but the perceived depthposition of the monocular object is still unstable.However, in phantom Kanizsa and line phantomsurfaces the monocular area can be unambiguouslylocalized because the adjacent binocular elements canbe seen as continuations of the monocular part. Theincreased stability of the monocular areas may be the

reason for the possibility of rematching initiated bymonocular areas. If this is the case, phantom stereopsiscould be defined as a half-occlusion cue in which themonocular area can be linked to a binocular area.Thus, reducing the possibility of binocular–monocularlinking should disrupt stereo capture.

To test this, we created phantom surfaces in whichcontinuation cues were reduced. Pilot experimentsdemonstrated that line phantom stereograms withoutbinocular parts are difficult to use because the stereosystem tries to fuse the monocular components andthus makes it difficult to study effects initiated by themonocular elements. On the other hand, phantomKanizsa stereograms contain more inducing compo-nents, so stereograms with reduced binocular–monocu-lar continuity are easier to design. The basic idea ofreduced monocular–binocular discontinuity is demon-strated in Fig. 6. In normal capture stereoscopicmatching occurs between the vertical cut-out sectors(Fig. 6a) and in phantom capture matching occursbetween the vertical cut-out sector and the corner ofother inducing figure (Fig. 6b). If an additional sector isremoved from the figure (Fig. 6c), the matching should

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Fig. 6. (a) Matching configuration in conventional stereo capture. (b)Matching configuration in phantom capture. (c) Matching configura-tion in phantom capture with reduced binocular–monocular continu-ity.

4.3. Results

We used a normal stereo capture figure as a baselinefor all subjects and the results showed that all subjectsperceived stereo capture and depth asymmetry (Fig. 7).We then tested stereo capture with phantom Kanizsasurfaces in which the binocular–monocular linkage wasweakened by removing sectors from inducing figures.Surprisingly, the results show that near capture was stillperceived when the linkage was removed (Fig. 8c).However, when the supporting bars were also removed,capture was disrupted, suggesting a strong capture ef-fect by supporting bars alone (Fig. 8d). The resultindicates that a monocular area that cannot be seg-mented with a binocular area is only a weak capturingelement, that does not produce a stable and clearpercept of stereo capture.

To further reduce the continuity cues, we removedthe binocular parts of the circular inducing figurescompletely and varied the presence of the supportingbars (Fig. 9a–d). According to the results, capture wasnot perceived in any of these figures (Fig. 10a–d). Thissuggests that monocular elements without binocularlinkage cannot capture binocular objects.

5. General discussion

Our experiments demonstrate that a phantom surfaceinduced by monocular areas can affect the perceiveddepth of textures defined by conventional disparity.However, in order that monocularly defined areas cancapture binocular areas, the monocular areas have tobe linked to binocular figures so that the localizationambiguity of the monocular areas is reduced. By link-ing we mean that two surface patches, one monocularlyoccluded and other not, appears as one continuoussurface. Furthermore, the monocular area inherits thebinocular properties of the binocular area and begins tofunction as part of the binocular area. The effect ofbinocular–monocular linkage widens the possible roleof monocular areas in depth segmentation. Previously ithas been demonstrated that horizontally adjacentbinocular areas that can be interpreted as a half-oc-cluder affect the depth interpretation of monocularareas (Nakayama & Shimojo, 1990). This has lead tothe idea that monocular objects are always ambiguouswith respect to depth magnitude and in a typical exper-iment the effect of a binocular object on a monocularobject has been measured (Kaye, 1978; Nakayama &Shimojo; Hakkinen & Nyman, 1996). However, theassumption of ambiguity is not applicable to allconfigurations as our experiment shows and conse-quently the significance of binocular–monocular inter-actions is wider. If a monocular area can be linked to abinocular area during fusion, as in phantom surfaces,

Fig. 7. Stereo capture results for experiment 2, conventional capturestereogram.

occur between the identical binocular parts of the in-ducer and no capture should occur. On the otherhand,if the monocular area that can be interpreted as ahalf-occlusion affects the capture, capture should beperceived.

4.2. Methods

4.2.1. SubjectsFour students served as subjects. The subjects had

normal or corrected-to-normal vision. They were paidfor their participation and were not aware of the pur-pose of the experiment. Before the experimental session,each subject was shown a test stereogram that consistedof rectangles. Subjects, not able to perceive depth in thetest, were excluded from the experiment.

4.2.2. StimuliSeven capture configurations shown in Fig. 2a and

Fig. 8a–Fig. 9d were used as stimuli. Each configura-tion was shown as crossed and uncrossed versions, sothere were 14 different capture stereograms. With 25repetitions the complete experiment consisted of 3850stimuli (14 capture configurations×11 probe posi-tions×25 repetitions). Because each capturestereogram was shown with 10 different probe posi-tions, each capture stereogram was shown 275 times.

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the ambiguity of the monocular area is reduced and itcan have a strong effect on depth segmentation.

Reduced ambiguity due to binocular–monocularlinking might be the underlying reason for severalstereo segmentation phenomena. Firstly, the quantita-tive variation problem discussed by Gillam andNakayama (1999) is clearly related to binocular–monocular linking. If a strong binocular–monocular

linkage can be made, the monocular area inherits thebinocular properties of the binocular area and begins tofunction like a binocular area, thus leading to quantita-tive variation according to the size or position of themonocular area. Furthermore, the processes that medi-ate depth inheritance from binocular to monocularareas might provide clues for eye of origin differencesin perceived three-dimensionality of monocular dots.

Fig. 8. (a) A phantom surface in which sectors have been removed to decrease the possibility of binocular–monocular linking. Horizontal andvertical supporting bars are present. (b) A phantom surface with reduced binocular–monocular continuity and no horizontal or verticalsupporting bars. (c) Result for experiment 2, stereogram in Fig. 8a. (d) Result for experiment 2, stereogram in Fig. 8b.

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Fig. 9. (a) Capture stereogram with monocular inducing figures andhorizontal and vertical supporting bars. (b) Capture stereogram withmonocular inducing figures and vertical supporting bars. (c) Capturestereogram with monocular inducing figures and horizontal support-ing bars. (d) Capture stereogram with monocular inducing figures andno supporting bars.

dots are invalid, because the opaqueness of the binocu-lar surface prevents half-occlusion interpretation andfor this reason they are seen near the binocular surface.Invalid dots might be processed by another heuristiclocalization principle that resembles the equidistancetendency presented by Gogel (1956). It has been alsosuggested that the ‘so called’ invalid object might be anexample of situation with strong back and weak frontillumination. In such a configuration one-eye-camouflage may arise from silhuettes and thus an un-paired object would be perceived (Nakayama &Shimojo; Nakayama, 1996).

The differences between valid and invalid monoculardots can be re-evaluated if binocular-monocular linkingis considered as an explanation. There may be no needto interpret the other set of binocular-monocularconfigurations as invalid or silhuette only because theyare not seen further away. We suggest that the equidis-tant localization of ‘invalid’ configurations is also deter-mined by half-occlusion interpretation. If a monoculardot, only seen by the left eye is on the right side of abinocular surface or a monocular dot only seen by righteye is on the left side of a binocular surface, thisconfiguration could be produced by an assumed half-oc-cluding surface that is nearer than the binocular andmonocular parts of the figure. If the additional nearerhalf-occluding surface were present, the equidistancetendency would be explained by half-occlusion causedby it (Fig. 11c). It has been demonstrated that a validmonocular object can induce a stereoscopic surface(Nakayama & Shimojo, 1990), so an invalid objectmight also induce one.

Explaining the depth differences in valid and invaliddots as an example of binocular monocular linking issupported by earlier research. In the experiments con-ducted by Hakkinen and Nyman (1996), the perceivedthree-dimensional position of both valid and invaliddots was affected by the relation of half-occludingsurface and the perceived background. If the half-oc-cluding surface was in near depth, the resulting discon-tinuity interpretation was steep, i.e. the valid monoculardots that were interpreted as half-occluded recededquickly towards the background when they were hori-zontally increasingly far away from the half-occludingsurface. However, also invalid dots were similarly af-fected, i.e. they did not remain equidistant with theadjacent binocular surface but were also seen as furtheraway than the adjacent surface. The steepness of depthlocalization curves obtained both from valid and invaliddots were a function of the crossed disparity of thehalf-occluding surface. This result may reflect process-ing of binocular–monocular inheritance, when thecrossed disparity of the surface is large and the unam-biguously defined background is perceived behind thesurface, the invalid dot does not stay at the level of thesurface but rather recedes towards the background. Wesuggest that the equidistance perception vanishes be

According to Nakayama and Shimojo (1990) monocu-lar dots are perceived differently when they are shownto left or right eye. If the monocular object is on theright side of the half-occluding surface and is shown tothe right eye only or if it is on the left side of thehalf-occluding surface and is shown to left eye only, themonocular dot is seen further away than the half-oc-cluding surface (Fig. 11a). Nakayama and Shimojointerpret this as an example of the visual system usinginformation about typical half-occlusion configurationsderived from the natural world to solve ambiguousstimuli. On the other hand, if the monocular object is onthe right side of the half-occluding surface and is shownto the left eye only or if it is on the left side of thehalf-occluding surface and is shown to right eye only,the monocular dot is seen at the same depth level ornearer than the half-occluding surface (Fig. 11b).Nakayama and Shimojo explain this difference as anexample of ecological occlusion constraints that areused by stereo processing. The monocular objects thatcan be interpreted as being half-occluded by the adja-cent surface are ecologically valid and are seen furtheraway than the binocular surface. The other monocular

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cause the configurational information in this case re-duces the possibility of an assumed nearer surface. Ourinterpretation is supported by the results from configu-rations in which the binocular surface was at the fixa-tion plane or in uncrossed disparity, and the invaliddots were seen equidistant or nearer than the binocularsurface (Hakkinen & Nyman). In those configurations,it is easier to assume an adjacent occluding surface thatprovides cues for binocular–monocular continuity.

5.1. Capture as rematching

The stereo capture effect can be conceptualized as aspreading of rematchings that is initiated by significantsegmentation features (Hakkinen et al., 1998). Duringrematching the stereo matchings that localize the tex-ture to the fixation plane are broken and new match-ings are formed. The segmentation features can alsoreduce the possibility of rematching, as in Fig. 3a inwhich supporting bars anchor some areas of the back-ground texture to fixation plane. They can even preventsome dots from being matched, as in all the capturestereograms in which the dot column immediately out-side the near illusory surface has to remain monocular

so that depth discontinuity can be seen. Our experimentdemonstrates that a phantom surface was strongenough to initiate this rematching process that spreadsinside the central area. Because half-occlusion canchange stereo matchings, it is probable that half-occlu-sion processing is an integral part of the early stereoprocessing. The early involvement of half-occlusionprocessing is supported by the fact that eye of origininformation which is crucial for half-occlusion percep-tion, is not preserved after V1 (Burkhalter & VanEssen, 1986; Lennie, 1998), so important parts of half-occlusion based segmentation should be done when theeye of origin information is still available. Also, stereomatching is processed in complex cells of V1 (Ohzawa,DeAngelis, & Freeman, 1997), so rematching should berelated to these processes. However, the matter is com-plicated by the surface formation processes which arelocated in V2, as experiments with illusory surfacesindicate (Peterhans & von der Heydt, 1989; Von derHeydt & Peterhans, 1989). The final perception reflectsthe interaction of these processes, but their exact formremains unknown. Recent results have demonstratedthat surprisingly complex features, like movement(Berry, Brivanlou, Jordan, & Meister, 1999) or amo-

Fig. 10. (a) Result for experiment 2, stereogram in Fig. 9a. (b) Result for experiment 2, stereogram in Fig. 9b. (c) Result for experiment 2,stereogram in Fig. 9c. (d) Result for experiment 2, stereogram in Fig. 9d.

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Fig. 11. (a) Monocular dots that are adjacent to a binocular surfaceare perceived further away than the surface if a valid half-occlusioninterpretation can be found. (b) Monocular dots that can not beinterpreted as being half-occluded by the surface are perceivedequidistant or nearer than the surface. (c) The equidistance tendencyof dots in Fig. 11b could be explained by assuming nearer half-oc-cluding surfaces.

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dally completed bars (Sugita, 1999) are processed in theearliest levels of visual processing, so it is viable thatalso monocular–binocular segmentation could be ex-plained by early processes. Further research on thisphenomenon is clearly needed.

Acknowledgements

This work has been supported by grants from Uni-versity of Helsinki, Alfred Kordelin Foundation,Finnish Cultural Foundation and Emil AaltonenFoundation.

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