{"title": "Structural inference affects depth perception in the context of potential occlusion", "book": "Advances in Neural Information Processing Systems", "page_first": 1777, "page_last": 1784, "abstract": "In many domains, humans appear to combine perceptual cues in a near-optimal, probabilistic fashion: two noisy pieces of information tend to be combined linearly with weights proportional to the precision of each cue. Here we present a case where structural information plays an important role. The presence of a background cue gives rise to the possibility of occlusion, and places a soft constraint on the location of a target \u2013 in effect propelling it forward. We present an ideal observer model of depth estimation for this situation where structural or ordinal information is important and then fit the model to human data from a stereo-matching task. To test whether subjects are truly using ordinal cues in a probabilistic manner we then vary the uncertainty of the task. We find that the model accurately predicts shifts in subject\u2019s behavior. Our results indicate that the nervous system estimates depth ordering in a probabilistic fashion and estimates the structure of the visual scene during depth perception.", "full_text": "Structural inference affects depth perception in the\n\ncontext of potential occlusion\n\nIan H. Stevenson and Konrad P. K\u00a8ording\n\nDepartment of Physical Medicine and Rehabilitation\n\nNorthwestern University\n\nChicago, IL 60611\n\ni-stevenson@northwestern.edu\n\nAbstract\n\nIn many domains, humans appear to combine perceptual cues in a near-optimal,\nprobabilistic fashion: two noisy pieces of information tend to be combined lin-\nearly with weights proportional to the precision of each cue. Here we present\na case where structural information plays an important role. The presence of a\nbackground cue gives rise to the possibility of occlusion, and places a soft con-\nstraint on the location of a target - in effect propelling it forward. We present\nan ideal observer model of depth estimation for this situation where structural\nor ordinal information is important and then \ufb01t the model to human data from a\nstereo-matching task. To test whether subjects are truly using ordinal cues in a\nprobabilistic manner we then vary the uncertainty of the task. We \ufb01nd that the\nmodel accurately predicts shifts in subject\u2019s behavior. Our results indicate that the\nnervous system estimates depth ordering in a probabilistic fashion and estimates\nthe structure of the visual scene during depth perception.\n\n1\n\nIntroduction\n\nUnderstanding how the nervous system makes sense of uncertain visual stimuli is one of the central\ngoals of perception research. One strategy to reduce uncertainty is to combine cues from several\nsources into a good joint estimate. If the cues are Gaussian, for instance, an ideal observer should\ncombine them linearly with weights proportional to the precision of each cue.\nIn the past few\ndecades, a number of studies have demonstrated that humans combine cues during visual perception\nto reduce uncertainty and often do so in near-optimal, probabilistic ways [1, 2, 3, 4].\nIn most situations, each cue gives noisy information about the variable of interest that can be mod-\neled as a Gaussian likelihood function about the variable. Recently [5] have suggested that subjects\nmay combine a metric cue (binocular disparity) with ordinal cues (convexity or familiarity of faces)\nduring depth perception. In these studies ordinal cues were modeled as simple biases. We argue that\nthe effect of such ordinal cues stems from a structural inference process where an observer estimates\nthe structure of the visual scene along with depth cues.\nThe importance of structural inference and occlusion constraints, particularly of hard constraints,\nhas been noted previously [6, 7, 8]. For instance, it was found that points presented to one eye but\nnot the other have a perceived depth that is constrained by the position of objects presented to both\neyes. Although these unpaired image points do not contain depth cues in the usual sense, subjects\nwere able to estimate their depth. This indicates that human subjects indeed use the inferred structure\nof a visual scene for the estimation of depth.\nHere we formalize the constraints presented by occlusion using a probabilistic framework. We \ufb01rst\npresent the model and illustrate its ability to describe data from [7]. Then we present results from\na new stereo-vision experiment in which subjects were asked to match the depth of an occluding\n\n1\n\n\for occluded circle. The model accurately predicts human behavior in this task and describes the\nchanges that occur when we increase depth uncertainty. These results cannot be explained by tradi-\ntional cue combination or even more recent relevance (causal inference) models [9, 10, 11, 12]. Our\nconstraint-based approach may thus be useful in understanding how subjects make sense of cluttered\nscenes and the impact of structural inference on perception.\n\n2 Theory\n\n2.1 An Ordinal Cue Combination Model\n\nWe assume that observers receive noisy information about the depth of objects in the world. For\nconcreteness, we assume that there is a central object c and a surrounding object s. The exact shapes\nand relative positions of these two objects are not important, but naming them will simplify the\nnotation that follows. We assume that each of these objects has a true, hidden depth (xc and xs) and\nobservers receive noisy observations of these depths (yc and ys).\nIn a scene with potential occlusion there may be two (or more) possible interpretations of an image\n(Fig 1A). When there is no occlusion (structure S1) the depth observations of the two objects are\nindependent. That is, we assume that the depth of the surrounding object in the scene s has no in\ufb02u-\nence on our estimate of the depth of c. The distribution of observations is assumed to be Gaussian\nand is physically determined by disparity, shading, texture, or other depth cues and their associated\nuncertainties. In this case the joint distribution of the observations given the hidden positions is\n\np(yc, ys|xc, xs, S1) = p(yc|xc, S1)p(ys|xs, S1) = Nyc(xc, \u03c3c)Nys(xs, \u03c3s).\n\n(1)\n\nWhen occlusion does occur, however, the position of the central object c is bounded by the depth of\nthe surrounding, occluded object (structure S2)\n\n(cid:26)Nyc(xc, \u03c3c)Nys(xs, \u03c3s)\n\np(yc, ys|xc, xs, S2) \u221d\n\n0\n\nif xc > xs,\nif xc \u2264 xs.\n\n(2)\n\nAn ideal observer can then make use of this ordinal information in estimating the depth of the\noccluding object. The (marginal) posterior distribution over the hidden depth of the central object\nxc can be found by marginalizing over the depth of the surrounding object xs and possible structures\n(S1 and S2).\n\np(xc | yc, ys) = p(xc | yc, ys, S1)p(S1) + p(xc | yc, ys, S2)p(S2)\n\n(3)\n\nFigure 1: An occlusion model with soft-constraints.\n(A) Two possible structures leading to the\nsame observation: one without occlusion S1 and one with occlusion S2. (B) Examples of biases in\nthe posterior estimate of xc for complete (left), moderate (center), and no relevance (right). In the\ncases shown, the observed depth of the central stimulus yc is the same as the observed depth of the\nsurrounding stimulus ys. Note that when yc (cid:29) ys the constraint will not bias estimates of xc.\n\n2\n\nConstraintp(S1) = 0p(xc| yc, ys)p(S1) = 0.25p(S1) = 1MarginalPosteriorS1S2ObservationABsccscsp(xc| yc, ys,S1)xcycycycysysys\fUsing the assumption of conditional independence and assuming \ufb02at priors over the hidden depths\nxc and xs, the \ufb01rst term in this expression is\n\n(cid:90)\n(cid:90)\n\np(xc | yc, ys, S1) =\n\n=\n\np(xc|yc, ys, xs, S1)p(xs | yc, ys, S1)dxs\np(xc|yc, S1)p(xs|ys, S1)dxs =\n\n(cid:90)\n\nNxc(yc, \u03c3c)Nxs(ys, \u03c3s)dxs\n\n(4)\n\n(5)\n\n= Nxc(yc, \u03c3c).\n\nThe second term is then\n\np(xc | yc, ys, S2) =\n\n=\n\n=\n\n(cid:90)\n(cid:90)\n(cid:90) xc\n\np(xc|yc, ys, xs, S2)p(xs | yc, ys, S2)dxs\np(yc, ys|xc, xs, S2)dxs\n\nNxc(yc, \u03c3c)Nxs(ys, \u03c3s)dxs\n\n\u2212\u221e\n1\n[erf(\u03c1s(xc \u2212 ys))/2 + 1/2]Nxc(yc, \u03c3c),\nZ\n\nwhere step 2 uses Bayes\u2019 rule and the assumption of \ufb02at priors, \u03c1s = 1/(cid:112)(2\u03c0)/\u03c3s and Z is a\n\n=\n\nnormalizing factor. Combining these two terms gives the marginal posterior\n\np(xc | yc, ys) =\n\n1\nZ\n\n[(1 \u2212 p(S1))(erf(\u03c1s(xc \u2212 ys))/2 + 1/2) + p(S1)] Nxc(yc, \u03c3c),\n\n(6)\n\nwhich describes the best estimate of the depth of the central object. Intuitively, the term in square\nbrackets constrains the possible depths of the central object c (Fig 1B). The p(S1) term allows for the\npossibility that the constraint should not apply. Similar to models of causal inference [11, 12, 9, 10],\nthe surrounding stimulus may be irrelevant, in which case we should simply rely on the observation\nof the target.\nHere we have described two speci\ufb01c structures in the world that result in the same observation. Real\nworld stimuli may result from a much larger set of possible structures. Generally, we can simply\nsplit structures into those with occlusion O and those without occlusion \u00acO. Above, S1 corresponds\nto the set of possible structures without occlusion \u00acO, and S2 corresponds to the set of possible\nstructures with occlusion O. It is not necessary to actually enumerate the possible structures.\nSimilar to traditional cue combination models, where there is an analytic form for the expected value\nof the target (linear combination weighted by the precision of each cue), we can write down analytic\nexpressions for E[xc] for at least one case. For p(S1) = 0, \u03c3s \u2192 0 the mean of the marginal\nposterior is the expected value of a truncated Gaussian\n\nE(xc|ys < xc) = yc + \u03c3c\u03bb( ys \u2212 yc\n\n\u03c3c\n\n)\n\n(7)\n\nWhere \u03bb(\u00b7) = \u03c6(\u00b7)\nFor yc = ys, for instance,\n\n[1\u2212\u03a6(\u00b7)], \u03c6(\u00b7) is the PDF for the standard normal distribution and \u03a6(\u00b7) is the CDF.\n\nE(xc|ys < xc) = yc + 0.8\u03c3c\n\n(8)\n\nIt is important to note that, similar to classical cue combination models, estimation of the target is im-\nproved by combining depth information with the occlusion constraint. The variance of p(xc|yc, ys)\nis smaller than that of p(xc | yc, ys, S1).\n\n3\n\n\f2.2 Modeling Data from Nakayama and Shimojo (1990)\n\nTo illustrate the utility of this model, we \ufb01t data from [7]. In this experiment subjects were presented\nwith a rectangle in each eye. Horizontal disparity between the two rectangles gave the impression of\ndepth. To test how subjects perceive occluded objects, a small vertical bar was presented to one eye,\ngiving the impression that the large rectangle was occluding the bar and leading to unpaired image\npoints (Fig 2A). Subjects were then asked to match the depth of this vertical bar by changing the dis-\nparity of another image in which the bar was presented in stereo. Despite the absence of direct depth\ncues, subjects assigned a depth to the vertical bar. Moreover, for a range of horizontal distances, the\nassigned depth was consistent with the constraint provided by the stereo-rectangle (Fig 2B). These\nresults systematically characterize the effect of structural estimation on depth estimates. Without\nordinal information, the horizontal distance between the rectangle and the vertical bar should have\nno effect on the perceived depth of the bar.\nIn our model yc and ys are simply observations on the depth of two objects: in this case, the unpaired\nvertical bar and the large rectangle. Since there isn\u2019t direct disparity for the vertical bar, we assume\nthat horizontal distance from the large rectangle serves as the depth cue. In reality an in\ufb01nity of\ndepths are compatible with a given horizontal distance (Fig 2A, dotted lines). However, the size and\nshape of the vertical bar serve as indirect cues, which we assume generate a Gaussian likelihood\n(as in Eq. 1). We \ufb01t our model to this data with three free parameters: \u03c3s, \u03c3c, and a relevance\nterm p(O). The event O corresponds to occlusion (case S2), while \u00acO corresponds to the set of\npossible structures leading to the same observation without occlusion. For the valid stimuli where\nocclusion can account for the vertical bar being seen in only one eye, \u03c3s = 4.45 arcmin, \u03c3c = 12.94\narcmin and p(\u00acO) = 0.013 minimized the squared error between the data and model \ufb01t (Fig 2C).\nFor invalid stimuli we assume that p(\u00acO) = 1, which matches subject\u2019s responses.\n\nFigure 2: Experiment and data from [7]. A) Occlusion puts hard constraints on the possible depth of\nunpaired image points (top). This leads to \u201dvalid\u201d and \u201dinvalid\u201d stimuli (bottom). B) When subjects\nwere asked to judge the depth of unpaired image points they followed these hard constraints (dotted\nlines) for a range of distances between the large rectangle and vertical bar (top). The two \ufb01gures\nshow a single subject\u2019s response when the vertical bar was positioned to the left or right of a large\nrectangle. The ordinal cue combination model can describe this behavior as well as deviations from\nthe constraints for large distances (bottom).\n\n4\n\nRABLUnpairedImage PointsDISTANCE (min arc)0204060010200204060LRValid StimuliInvalid StimuliLRValidInvalidDataModel\f3 Experimental Methods\n\nTo test this model in a more general setting where depth is driven by both paired and unpaired\nimage points we constructed a simple depth matching experiment. Subjects (N=7) were seated\n60cm in front of a CRT wearing shutter glasses (StereoGraphics CrystalEyes, 100Hz refresh rate)\nand asked to maintain their head position on a chin-rest. The experiment consisted of two tasks: a\ntwo-alternative forced choice task (2AFC) to measure subjects\u2019 depth acuity and a stereo-matching\ntask to measure their perception of depth when a surrounding object was present. The target (central)\nobjects were drawn on-screen as circles (13.0 degrees diameter) composed of random dots on a\nbackground pedestal of random dots (Fig 3).\nIn the 2AFC task, subjects were presented with two target objects with slightly different horizontal\ndisparities and asked to indicate using the keyboard which object was closer. The reference object\nhad a horizontal disparity of 0.57 degrees and was positioned randomly each trial on either the left\nor right side. The pedestal had a horizontal disparity of -0.28 degrees. Subjects performed 100 trials\nin which the disparity of the test object was chosen using optimal experimental design methods [13].\nAfter the \ufb01rst 10 trials the next sample was chosen to maximize the conditional mutual information\nbetween the responses and the parameter for the just-noticeable depth difference (JND) given the\nsample position. This allowed us to ef\ufb01ciently estimate the JND for each subject.\nIn the stereo-matching task subjects were presented with two target objects and a larger surrounding\ncircle (25.2 degrees diameter) paired with one of the targets. Subjects were asked to match the depth\nof the unpaired target with that of the paired target using the keyboard (100 trials). The depth of\nthe paired target was held \ufb01xed across trials at 0.57 degrees horizontal disparity while the position\nof the surrounding circle was varied between 0.14-1.00 degrees horizontal disparity. The depth of\nthe unpaired target was selected randomly at the beginning of each trial to minimize any effects\nof the starting position. All objects were presented in gray-scale and the target was presented off-\ncenter from the surrounding object to avoid confounding shape cues. The side on which the paired\ntarget and surrounding object appeared (left or right side of the screen) was also randomly chosen\nfrom trial to trial, and all objects were within the fusional limits for this task. When asked, subjects\nreported that diplopia occurred only when they drove the unpaired target too far in one direction or\nthe other.\nEach of these tasks (the 2AFC task and the stereo-matching task) was performed for two uncer-\ntainty conditions: a low and high uncertainty condition. We varied the uncertainty by changing the\ndistribution of disparities for the individual dots which composed the target objects and the larger\noccluding/occluded circle. In the low uncertainty condition the disparity for each dot was drawn\nfrom a Gaussian distribution with a variance of 2.2 arc minutes. In the high uncertainty condition\n\nFigure 3: Experimental design. Each trial consists of a matching task in which subjects control the\ndepth of an unpaired circle (A, left). Subjects attempt to match the depth of this unpaired circle to\nthe depth of a target circle which is surrounded by a larger object (A, right). Divergent fusers can\nfuse (B) to see the full stimulus. The contrast has been reversed for visibility. To measure depth\nacuity, subjects also complete a two-alternative forced choice task (2AFC) using the same stimulus\nwithout the surrounding object.\n\n5\n\nAB\fthe disparities were drawn with a variance of 6.5 arc minutes. All subjects had normal or corrected\nto normal vision and normal stereo vision (as assessed by a depth acuity < 5 arcmin in the low\nuncertainty 2AFC task). All experimental protocols were approved by IRB and in accordance with\nNorthwestern University\u2019s policy statement on the use of humans in experiments. Informed consent\nwas obtained from all participants.\n\n4 Results\n\nAll subjects showed increased just-noticeable depth differences between the low and high uncer-\ntainty conditions. The JNDs were signi\ufb01cantly different across conditions (one-sided paired t-test,\np= 0.0072), suggesting that our manipulation of uncertainty was effective (Fig 4A). In the matching\ntask, subjects were, on average, biased by the presence of the surrounding object. As the disparity\nof the surrounding object was increased and disparity cues suggested that s was closer than c, this\nbias increased. Consistent with our model, this bias was higher in the high uncertainty condition\n(Fig 4B and C). However, the difference between uncertainty conditions was only signi\ufb01cant for\ntwo surround depths (0.6 and 1.0 degrees, one-sided paired t-test p=0.004, p=0.0281) and not sig-\nni\ufb01cant as a main effect (2-way ANOVA p=0.3419). To model the bias, we used the JNDs estimated\nfrom the 2AFC task, and \ufb01t two free parameters: \u03c3s and p(\u00acO), by minimizing the squared error\nbetween model predictions and subject\u2019s responses. The model provided an accurate \ufb01t for both\nindividual subjects and the across subject data (Fig 4B and C). For the across subject data, we found\n\u03c3s = 0.085 arcmin for the low uncertainty condition and \u03c3s = 0.050 arcmin for the high uncertainty\n\nFigure 4: Experimental results. (A) Just noticeable depth differences for the two uncertainty condi-\ntions averaged across subjects. (B) and (C) show the difference between the perceived depth of the\nunpaired target and the paired target (the bias) as a function of the depth of the surrounding circle.\nResults for a typical subject (B) and the across subject average (C). Dots and error-bars denote sub-\nject responses, solid lines denote model \ufb01ts, and dotted lines denote the depth of the paired target,\nwhich was \ufb01xed. Error bars denote SEM (N=7).\n\n6\n\n00.511.522.533.5Just noticeable depth di(cid:31)erence(arcmin)LowUncertaintyHighUncertainty*ABC0.20.40.60.81\u22124\u2212202468Depth of surrounding object (degrees)Di(cid:31)erence in perceived depth(arcmin)Subject IV\u2212202468101214\u221240.20.40.60.81Across Subject AverageN = 7Depth of surrounding object (degrees)ycyc\fcondition. In these cases, p(\u00acO) was not signi\ufb01cantly different from zero and the simpli\ufb01ed model\nin which p(\u00acO) = 0 was preferred (cross-validated likelihood ratio test). Over the range of depths\nwe tested, this relevance term does not seem to play a role. However, we predict that for larger\ndiscrepancies this relevance term would come into play as subjects begin to ignore the surrounding\nobject (as in Fig 2).\nNote that if the presence of a surrounding object had no effect subjects would be unbiased across\ndepths of the occluded object. Two subjects (out of 7) did not show bias; however, both subjects\nhad normal stereo vision and this behavior did not appear to be correlated with low or high depth\nacuity. Since subjects were allowed to free-view the stimulus, it is possible that some subjects were\nable to ignore the surrounding object completely. As with the invalid stimuli in [7], a model where\np(\u00acO) = 1 accurately \ufb01t data from these subjects. The rest of the subjects demonstrated bias (see\nFig 4B for an example), but more data may be need to conclusively show differences between the\ntwo uncertainty conditions and causal inference effects.\n\n5 Discussion\n\nThe results presented above illustrate the importance of structural inference in depth perception.\nWe have shown that potential occlusion can bias perceived depth, and a probabilistic model of the\nconstraints accurately accounts for subjects\u2019 perception during occlusion tasks with unpaired image\npoints [7] as well as a novel task designed to probe the effects of structural inference.\n\nFigure 5: Models of cue combination. (A) Given the observations (y1 and y2) from two sources, how\nshould we estimate the hidden sources x1 and x2? (B) Classical cue combination models assume\nx1 = x2. This results in a linear weighting of the cues. Non-linear cue combination can be explained\nby causal inference models where x1 and x2 are probabilistically equal. (C) In the model presented\nhere, ordinal information introduces an asymmetry into cue combination. x1 and x2 are related here\nby a probabilistic inequality. (D) A summary of the relation between x1 and x2 for each model class.\n\n7\n\nx1x2y1y2AB?ModelRelationReferencesCue CombinationCausal InferenceOrdinal Cue Combinationx1 = x2probabilistic x1=x2probabilistic x1>x2e.g. Alais and Burr (2004), Ernst and Banks (2002)e.g. Knill (2007), Kording et al. (2007)model presented hereCueCombinationCausalInferenceOrdinalCue CombinationDy1E[x2]E[x2]E[x2]y1C\fA number of studies have proposed probabilistic accounts of depth perception [1, 4, 12, 14], and\na variety of cues, such as disparity, shading, and texture, can all be combined to estimate depth\n[4, 12]. However, accounting for structure in the visual scene and use of occlusion constraints is\ntypically qualitative or limited to hard constraints where certain depth arrangements are strictly ruled\nout [6, 14]. The model presented here accounts for a range of depth perception effects including\nperception of both paired and unpaired image points. Importantly, this model of perception explains\nthe effects of ordinal cues in a cohesive structural inference framework.\nMore generally, ordinal information introduces asymmetry into cue combination. Classically, cue\ncombination models assume a generative model in which two observations arise from the same hid-\nden source. That is, the hidden source for observation 1 is equal to the hidden source for observation\n2 (Fig 5A). More recently, causal inference or cue con\ufb02ict models have been developed that allow\nfor the possibility of probabilistic equality [9, 11, 12]. That is, there is some probability that the\ntwo sources are equal and some probability that they are unequal. This addition explains a number\nof nonlinear perceptual effects [9, 10] (Fig 5B). The model presented here extends these previous\nmodels by introducing ordinal information and allowing the relationship between the two sources\nto be an inequality - where the value from one source is greater than or less than the other. As with\ncausal inference models, relevance terms allow the model to capture probabilistic inequality, and\nthis type of mixture model allows descriptions of asymmetric and nonlinear behavior (Fig 5C). The\nordinal cue combination model thus increases the class of behaviors that can be modeled by cue\ncombination and causal inference and should have applications for other modalities where ordinal\nand structural information is important.\n\nReferences\n[1] M. O. Ernst and M. S. Banks. Humans integrate visual and haptic information in a statistically optimal\n\nfashion. Nature, 415(6870):429\u201333, 2002.\n\n[2] D. Kersten and A. Yuille. Bayesian models of object perception. Current Opinion in Neurobiology,\n\n13(2):150\u2013158, 2003.\n\n[3] D. C. Knill and W. Richards. Perception as Bayesian inference. Cambridge University Press, 1996.\n[4] M. S. Landy, L. T. Maloney, E. B. Johnston, and M. Young. Measurement and modeling of depth cue\n\ncombination: In defense of weak fusion. Vision Research, 35(3):389\u2013412, 1995.\n\n[5] J. Burge, M. A. Peterson, and S. E. Palmer. Ordinal con\ufb01gural cues combine with metric disparity in\n\ndepth perception. Journal of Vision, 5(6):5, 2005.\n\n[6] D. Geiger, B. Ladendorf, and A. Yuille. Occlusions and binocular stereo. International Journal of Com-\n\nputer Vision, 14(3):211\u2013226, 1995.\n\n[7] K. Nakayama and S. Shimojo. da vinci stereopsis: Depth and subjective occluding contours from unpaired\n\nimage points. Vision Research, 30(11):1811, 1990.\n\n[8] J. J. Tsai and J. D. Victor. Neither occlusion constraint nor binocular disparity accounts for the perceived\n\ndepth in the sieve effect. Vision Research, 40(17):2265\u20132275, 2000.\n\n[9] K. P. K\u00a8ording, U. Beierholm, W. J. Ma, S. Quartz, J. B. Tenenbaum, and L. Shams. Causal inference in\n\nmultisensory perception. PLoS ONE, 2(9), 2007.\n\n[10] K. Wei and K. K\u00a8ording. Relevance of error: what drives motor adaptation? Journal of Neurophysiology,\n\n101(2):655, 2009.\n\n[11] M. O. Ernst and H. H. B\u00a8ulthoff. Merging the senses into a robust percept. Trends in Cognitive Sciences,\n\n8(4):162\u2013169, 2004.\n\n[12] D. C. Knill. Robust cue integration: A bayesian model and evidence from cue-con\ufb02ict studies with\n\nstereoscopic and \ufb01gure cues to slant. Journal of Vision, 7(7):5, 2007.\n\n[13] L. Paninski. Asymptotic theory of information-theoretic experimental design. Neural Computation,\n\n17(7):1480\u20131507, 2005.\n\n[14] K. Nakayama and S. Shimojo. Experiencing and perceiving visual surfaces. Science, 257(5075):1357\u2013\n\n1363, Sep 1992.\n\n8\n\n\f", "award": [], "sourceid": 1151, "authors": [{"given_name": "Ian", "family_name": "Stevenson", "institution": null}, {"given_name": "Konrad", "family_name": "Koerding", "institution": null}]}