Does vertical disparity scale the perception of stereoscopic depth?

It has been suggested that a measure of the gradients of vertical disparity over a surface may scale the mapping between horizontal disparity and perceived depth. We have investigated this possibility by obtaining estimates of the depth within stereograms that simulated two apposed fronto-parallel planes placed at different distances from an observer. The gradients of vertical disparity in a stereogram were set to simulate those appropriate to a viewing distance of 12.5 cm, 25 cm, 50 cm or 100 cm, whereas the distance specified by vergence and accommodative cues was always fixed at 50 cm. Judgements of the perceived depth between the two planes were uninfluenced by changes in the gradients of vertical disparity. It thus seems that the human visual system does not employ vertical disparity as a scaling parameter in stereoscopic depth judgements.     

Stereoscopic Vision in the Absence of the Lateral Occipital Cortex

Both dorsal and ventral cortical visual streams contain neurons sensitive to binocular disparities, but the two streams may underlie different aspects of stereoscopic vision. Here we investigate stereopsis in the neurological patient D.F., whose ventral stream, specifically lateral occipital cortex, has been damaged bilaterally, causing profound visual form agnosia. Despite her severe damage to cortical visual areas, we report that DF''s stereo vision is strikingly unimpaired. She is better than many control observers at using binocular disparity to judge whether an isolated object appears near or far, and to resolve ambiguous structure-from-motion. DF is, however, poor at using relative disparity between features at different locations across the visual field. This may stem from a difficulty in identifying the surface boundaries where relative disparity is available. We suggest that the ventral processing stream may play a critical role in enabling healthy observers to extract fine depth information from relative disparities within one surface or between surfaces located in different parts of the visual field.     

Spatial stereoresolution for depth corrugations may be set in primary visual cortex

Stereo "3D" depth perception requires the visual system to extract binocular disparities between the two eyes' images. Several current models of this process, based on the known physiology of primary visual cortex (V1), do this by computing a piecewise-frontoparallel local cross-correlation between the left and right eye's images. The size of the "window" within which detectors examine the local cross-correlation corresponds to the receptive field size of V1 neurons. This basic model has successfully captured many aspects of human depth perception. In particular, it accounts for the low human stereoresolution for sinusoidal depth corrugations, suggesting that the limit on stereoresolution may be set in primary visual cortex. An important feature of the model, reflecting a key property of V1 neurons, is that the initial disparity encoding is performed by detectors tuned to locally uniform patches of disparity. Such detectors respond better to square-wave depth corrugations, since these are locally flat, than to sinusoidal corrugations which are slanted almost everywhere. Consequently, for any given window size, current models predict better performance for square-wave disparity corrugations than for sine-wave corrugations at high amplitudes. We have recently shown that this prediction is not borne out: humans perform no better with square-wave than with sine-wave corrugations, even at high amplitudes. The failure of this prediction raised the question of whether stereoresolution may actually be set at later stages of cortical processing, perhaps involving neurons tuned to disparity slant or curvature. Here we extend the local cross-correlation model to include existing physiological and psychophysical evidence indicating that larger disparities are detected by neurons with larger receptive fields (a size/disparity correlation). We show that this simple modification succeeds in reconciling the model with human results, confirming that stereoresolution for disparity gratings may indeed be limited by the size of receptive fields in primary visual cortex.     

Consequences for retinal growth when vision occurs in S2 space

We postulate that the process of vision occurs in the S2 space. The retina is endowed with the topology of a part of a two-sphere S2, roughly, the topology of a hemisphere. There is a corresponding topology on the tectal surface, induced by the anatomy of the retino-tectal connections. Our analysis predicts the experimentally observed "near-neighbour" relationships between points in the visual field and their representation in the tectum. Further, in this context, topological arguments are presented to indicate that if the normal developing retinal disc in goldfish undergoes a process of deformation, a discontinuity is generated at the retinal surface. This discontinuity makes the differential patterns of the retinal and tectal tissues more compatible, and also enables the retina (which grows throughout the life of the animal) to conveniently connect to the tectum.     

Probing depth in monocular images

It is generally expected that depth (distance) is the internal representational primitive that corresponds to much of the perception of 3D. We tested this assumption in monocular surface stimuli that are devoid of distance information (due to orthographic projection and the chosen surface shape, with perspective projection used as a control) and yet are vividly three-dimensional. Slant judgments were found to be in close correspondence with the actual geometric slant of the stimuli; the spatial orientation of the surfaces was perceived accurately. The apparent depth in these stimuli was then tested by superimposing a stereo depth probe over the monocular surface. In both the perspective and orthographic projection the gradient of perceived depth, measured by matching the apparent depth of the stereo probe with that of the monocular surface at a series of locations, was substantial. The experiments demonstrate that in orthographic projection the visual system can compute from local surface orientation a depth quantity that is commensurate with the relative depth derived from stereo disparity. The depth data suggests that, at least in the near field, the zero value for relative depth lies at the same absolute depth as the stereo horopter (locus of zero stereo disparity). Relative to this zero value, the depth-from-slant computation seems to provide an estimate of distance information that is independent of the absolute distance to the surface.Supproted by Office of Naval Research Contract N00014-K-84-0533. We gratefully acknowledge the suggestions of Jacob Beck regarding the experimental design, and the assistance provided by Cathryn Stanford     

Viewing geometry determines how vision and haptics combine in size perception

Vision and haptics have different limitations and advantages because they obtain information by different methods. If the brain combined information from the two senses optimally, it would rely more on the one providing more precise information for the current task. In this study, human observers judged the distance between two parallel surfaces in two within-modality experiments (vision-alone and haptics-alone) and in an intermodality experiment (vision and haptics together). In the within-modality experiments, the precision of visual estimates varied with surface orientation, as expected from geometric considerations; the precision of haptic estimates did not. An ideal observer that combines visual and haptic information weights them differently as a function of orientation. In the intermodality experiment, humans adjusted visual and haptic weights in a fashion quite similar to that of the ideal observer. As a result, combined size estimates are finer than is possible with either vision or haptics alone; indeed, they approach statistical optimality.     

Correction of Distortion in Flattened Representations of the Cortical Surface Allows Prediction of V1-V3 Functional Organization from Anatomy

Several domains of neuroscience offer map-like models that link location on the cortical surface to properties of sensory representation. Within cortical visual areas V1, V2, and V3, algebraic transformations can relate position in the visual field to the retinotopic representation on the flattened cortical sheet. A limit to the practical application of this structure-function model is that the cortex, while topologically a two-dimensional surface, is curved. Flattening of the curved surface to a plane unavoidably introduces local geometric distortions that are not accounted for in idealized models. Here, we show that this limitation is overcome by correcting the geometric distortion induced by cortical flattening. We use a mass-spring-damper simulation to create a registration between functional MRI retinotopic mapping data of visual areas V1, V2, and V3 and an algebraic model of retinotopy. This registration is then applied to the flattened cortical surface anatomy to create an anatomical template that is linked to the algebraic retinotopic model. This registered cortical template can be used to accurately predict the location and retinotopic organization of these early visual areas from cortical anatomy alone. Moreover, we show that prediction accuracy remains when extrapolating beyond the range of data used to inform the model, indicating that the registration reflects the retinotopic organization of visual cortex. We provide code for the mass-spring-damper technique, which has general utility for the registration of cortical structure and function beyond the visual cortex.     

Shading Beats Binocular Disparity in Depth from Luminance Gradients: Evidence against a Maximum Likelihood Principle for Cue Combination

Perceived depth is conveyed by multiple cues, including binocular disparity and luminance shading. Depth perception from luminance shading information depends on the perceptual assumption for the incident light, which has been shown to default to a diffuse illumination assumption. We focus on the case of sinusoidally corrugated surfaces to ask how shading and disparity cues combine defined by the joint luminance gradients and intrinsic disparity modulation that would occur in viewing the physical corrugation of a uniform surface under diffuse illumination. Such surfaces were simulated with a sinusoidal luminance modulation (0.26 or 1.8 cy/deg, contrast 20%-80%) modulated either in-phase or in opposite phase with a sinusoidal disparity of the same corrugation frequency, with disparity amplitudes ranging from 0’-20’. The observers’ task was to adjust the binocular disparity of a comparison random-dot stereogram surface to match the perceived depth of the joint luminance/disparity-modulated corrugation target. Regardless of target spatial frequency, the perceived target depth increased with the luminance contrast and depended on luminance phase but was largely unaffected by the luminance disparity modulation. These results validate the idea that human observers can use the diffuse illumination assumption to perceive depth from luminance gradients alone without making an assumption of light direction. For depth judgments with combined cues, the observers gave much greater weighting to the luminance shading than to the disparity modulation of the targets. The results were not well-fit by a Bayesian cue-combination model weighted in proportion to the variance of the measurements for each cue in isolation. Instead, they suggest that the visual system uses disjunctive mechanisms to process these two types of information rather than combining them according to their likelihood ratios.     

Stereoscopic depth constancy

Depth constancy is the ability to perceive a fixed depth interval in the world as constant despite changes in viewing distance and the spatial scale of depth variation. It is well known that the spatial frequency of depth variation has a large effect on threshold. In the first experiment, we determined that the visual system compensates for this differential sensitivity when the change in disparity is suprathreshold, thereby attaining constancy similar to contrast constancy in the luminance domain. In a second experiment, we examined the ability to perceive constant depth when the spatial frequency and viewing distance both changed. To attain constancy in this situation, the visual system has to estimate distance. We investigated this ability when vergence, accommodation and vertical disparity are all presented accurately and therefore provided veridical information about viewing distance. We found that constancy is nearly complete across changes in viewing distance. Depth constancy is most complete when the scale of the depth relief is constant in the world rather than when it is constant in angular units at the retina. These results bear on the efficacy of algorithms for creating stereo content.This article is part of the themed issue ‘Vision in our three-dimensional world’.     

Invariance of visual operations at the level of receptive fields

The brain is able to maintain a stable perception although the visual stimuli vary substantially on the retina due to geometric transformations and lighting variations in the environment. This paper presents a theory for achieving basic invariance properties already at the level of receptive fields. Specifically, the presented framework comprises (i) local scaling transformations caused by objects of different size and at different distances to the observer, (ii) locally linearized image deformations caused by variations in the viewing direction in relation to the object, (iii) locally linearized relative motions between the object and the observer and (iv) local multiplicative intensity transformations caused by illumination variations. The receptive field model can be derived by necessity from symmetry properties of the environment and leads to predictions about receptive field profiles in good agreement with receptive field profiles measured by cell recordings in mammalian vision. Indeed, the receptive field profiles in the retina, LGN and V1 are close to ideal to what is motivated by the idealized requirements. By complementing receptive field measurements with selection mechanisms over the parameters in the receptive field families, it is shown how true invariance of receptive field responses can be obtained under scaling transformations, affine transformations and Galilean transformations. Thereby, the framework provides a mathematically well-founded and biologically plausible model for how basic invariance properties can be achieved already at the level of receptive fields and support invariant recognition of objects and events under variations in viewpoint, retinal size, object motion and illumination. The theory can explain the different shapes of receptive field profiles found in biological vision, which are tuned to different sizes and orientations in the image domain as well as to different image velocities in space-time, from a requirement that the visual system should be invariant to the natural types of image transformations that occur in its environment.     

Blur and disparity are complementary cues to depth

Estimating depth from binocular disparity is extremely precise, and the cue does not depend on statistical regularities in the environment. Thus, disparity is commonly regarded as the best visual cue for determining 3D layout. But depth from disparity is only precise near where one is looking; it is quite imprecise elsewhere. Away from fixation, vision resorts to using other depth cues-e.g., linear perspective, familiar size, aerial perspective. But those cues depend on statistical regularities in the environment and are therefore not always reliable. Depth from defocus blur relies on fewer assumptions and has the same geometric constraints as disparity but different physiological constraints. Blur could in principle fill in the parts of visual space where disparity is imprecise. We tested this possibility with a depth-discrimination experiment. Disparity was more precise near fixation and blur was indeed more precise away from fixation. When both cues were available, observers relied on the more informative one. Blur appears to play an important, previously unrecognized role in depth perception. Our findings lead to a new hypothesis about the evolution of slit-shaped pupils and have implications for the design and implementation of stereo 3D displays.     

The shadow of forgotten ancestors differently constrains the fate of Alligatoroidea and Crocodyloidea

Aim We tested the hypothesis that the evolutionary fates of two sister groups (Alligatoroidea and Crocodyloidea) are differently constrained by phylogenetic and ecological (functional) factors in the face of climatic change. Location Global. Methods We quantified disparity in skull rostrum shape by means of geometric morphometrics. Mechanical performance of the rostrum was analyzed by applying beam theory calculations to morphological data and experimentally measured bite force. The phylogeny was expressed in the form of principal coordinates, the first ones of which were used as a set of explanatory variables. Extents of species occurrence were computed using species distribution maps. Finally, species maximum skull size were measured and considered as a proxy of maximum body size. We performed variation partitioning analyses in order to compare differential contributions of phylogenetic and ecological factors in Alligatoroidea and Crocodyloidea. Results Alligatoroidea show higher ‘pure’ historical components than Crocodyloidea in explaining both rostrum shape and extent of occurrence (after controlling for body size). On the contrary, geometric variation of skull rostra of Crocodyloidea unequivocally shows a higher ‘pure’ functional component (linked to performance on prey capture) and a higher phylogenetically structured environmental variation than those found in Alligatoroidea. Results obtained for body size variation are consistent with these patterns. In Alligatoroidea, body size variation contains a higher phylogenetic signal than in Crocodyloidea. Main Conclusions Our results suggest that Crocodyloidea and Alligatoroidea may react differently when faced with significant environmental changes. We predict that global climatic changes will have a more important effect on Crocodyloidea than in Alligatoroidea by (1) promoting trait shift, adaptation to the new diet and speciation and (2) modifying the geographical range distribution of species (which may track favourable ecological conditions).     

Inhomogeneous retino-cortical mapping is supported and stabilized with correlation-learning during self-motion

In primates, the area of primary visual cortex representing a fixed area of visual space decreases with increasing eccentricity. We identify visual situations to which this inhomogeneous retino-cortical mapping is well adapted and study their relevance during natural vision and development. We assume that cortical activations caused by stationary objects during self-motion along the direction of gaze travel on average with constant speed across the cortical surface, independent of retinal eccentricity. This is the case if the distribution of objects corresponds to an ellipsoid with the observer in its center. We apply the resulting flow field to train a simple network of pulse coding neurons with Hebbian learning and demonstrate that the density of learned receptive field centers is in close agreement with primate retino-cortical magnification. In addition, the model reproduces the increase of receptive field size and the decrease of its peak sensitivity with increasing eccentricity. Our results suggest that self-motion may have played an important role in the evolution of the visual system and that cortical magnification can be refined and stabilized by Hebbian learning mechanisms in ontogenesis under natural viewing conditions.     

A reaction-diffusion model to capture disparity selectivity in primary visual cortex

Decades of experimental studies are available on disparity selective cells in visual cortex of macaque and cat. Recently, local disparity map for iso-orientation sites for near-vertical edge preference is reported in area 18 of cat visual cortex. No experiment is yet reported on complete disparity map in V1. Disparity map for layer IV in V1 can provide insight into how disparity selective complex cell receptive field is organized from simple cell subunits. Though substantial amounts of experimental data on disparity selective cells is available, no model on receptive field development of such cells or disparity map development exists in literature. We model disparity selectivity in layer IV of cat V1 using a reaction-diffusion two-eye paradigm. In this model, the wiring between LGN and cortical layer IV is determined by resource an LGN cell has for supporting connections to cortical cells and competition for target space in layer IV. While competing for target space, the same type of LGN cells, irrespective of whether it belongs to left-eye-specific or right-eye-specific LGN layer, cooperate with each other while trying to push off the other type. Our model captures realistic 2D disparity selective simple cell receptive fields, their response properties and disparity map along with orientation and ocular dominance maps. There is lack of correlation between ocular dominance and disparity selectivity at the cell population level. At the map level, disparity selectivity topography is not random but weakly clustered for similar preferred disparities. This is similar to the experimental result reported for macaque. The details of weakly clustered disparity selectivity map in V1 indicate two types of complex cell receptive field organization.     

The singularities of the visual mapping

In this article we treat purely metrical properties of the visual image, e.g. the time changes of the relative positions and orientations of image details. Self-induced movements of an observer relative to rigid bodies in his environment generate charactertistic motion parallax fields. The observer may regard those fields as proprioceptive and interprete the geometrical invariants of the fields as indicators of solid shape. In this way his perceptions become object-oriented, which is the normal case as the many constancy-phenomena show. Similar arguments apply to the disparity field of binocular vision. In this paper we treat the qualitative nature of such fields. [In this case the qualitative nature is basic. Compare the case of an equation with a single unknown. Often one is interested primarily in the qualitative solution (are there roots? How many?), and only slightly in the quantitative information (the numerical value of a root).] The qualitative nature of the fields is fixed if their singularities are known. It is shown that the singularities are of two types: isolated points (so-called specular points) and line-singularities (so-called folds, cusps and T-junctions). It is shown that for most vantage points that an observer can occupy, the topological structure of the set of singularities does not change if the observer performs small exploratory movements. That is most vantage points are stable. At an unstable vantage point the set of singularities changes and the observer experiences an event. Because certain properties of the set of singularities are shown to be preserved, only a few simple types of event are possible. A complete list is presented. The occurrence of an event is shown to be simply related to the solid shape of the objects of vision. Our geometrical theory enables us to understand the structure of the observer's internal models of external bodies.     

Motion parallax contribution to perception of self-motion and depth

The object of this study is to mathematically specify important characteristics of visual flow during translation of the eye for the perception of depth and self-motion. We address various strategies by which the central nervous system may estimate self-motion and depth from motion parallax, using equations for the visual velocity field generated by translation of the eye through space. Our results focus on information provided by the movement and deformation of three-dimensional objects and on local flow behavior around a fixated point. All of these issues are addressed mathematically in terms of definite equations for the optic flow. This formal characterization of the visual information presented to the observer is then considered in parallel with other sensory cues to self-motion in order to see how these contribute to the effective use of visual motion parallax, and how parallactic flow can, conversely, contribute to the sense of self-motion. This article will focus on a central case, for understanding of motion parallax in spacious real-world environments, of monocular visual cues observable during pure horizontal translation of the eye through a stationary environment. We suggest that the global optokinetic stimulus associated with visual motion parallax must converge in significant fashion with vestibular and proprioceptive pathways that carry signals related to self-motion. Suggestions of experiments to test some of the predictions of this study are made.     

Shape Variation in the Dermatocranium of the Greater Short-Horned Lizard <Emphasis Type="Italic">Phrynosoma hernandesi</Emphasis> (Reptilia: Squamata: Phrynosomatidae)

Dermatocranial shape and horn morphology display great disparity among the species of Phrynosoma. Ontogenetic change in dermatocranial shape in a series of 79 specimens of the short-horned Phrynosoma hernandesi (54F: 25M) was examined using geometric morphometric techniques. A multivariate ANCOVA of Procrustes residuals with sex as a factor and ln(centroid size) as the covariate indicated sexual shape dimorphism. Separate multivariate regressions of Procrustes residuals on ln(centroid size) for each sex indicated that allometry accounts for ~52–54% of the total sample shape variance. Comparisons of ontogenetic shape change between sexes indicate that sexual shape dimorphism is minimal and of uncertain biological significance. Groupings of multivariate regression coefficients by magnitude and sign suggest that allometric integration of the dermatocranium is not uniform over the dermatocranium. Principal component analysis of the landmark configurations corrected for sex and allometry yields a first principal component which describes shape variance concentrated in the posterolateral and posterior regions of the dermatocranium, and again is indicative of non-uniform shape variation over the dermatocranium. Our findings for P. hernandesi indicate that the adult shape of the dermatocranium may contribute to a passive defence against predation. We hypothesize that the complexity in dermatocranial shape demonstrated here for P. hernandesi indicates parcellation of shape variance, which may contribute to explanations of the pronounced dermatocranial disparity exhibited by the species of Phrynosoma.     

A model for the origin and properties of flicker-induced geometric phosphenes

We present a model for flicker phosphenes, the spontaneous appearance of geometric patterns in the visual field when a subject is exposed to diffuse flickering light. We suggest that the phenomenon results from interaction of cortical lateral inhibition with resonant periodic stimuli. We find that the best temporal frequency for eliciting phosphenes is a multiple of intrinsic (damped) oscillatory rhythms in the cortex. We show how both the quantitative and qualitative aspects of the patterns change with frequency of stimulation and provide an explanation for these differences. We use Floquet theory combined with the theory of pattern formation to derive the parameter regimes where the phosphenes occur. We use symmetric bifurcation theory to show why low frequency flicker should produce hexagonal patterns while high frequency produces pinwheels, targets, and spirals.     

频差在立体视觉信息加工中的作用 Ⅱ、频差“克服”视差

双眼立体视觉机制至今不很清楚,存在不少争论,研究它具有深远意义。我们的兴趣是从心理物理、电生理和理论模型三方面开展工作,最终目标是试图搞清楚视觉立体信息处理类机制。本文主要利用心理物理学方法研究频差克差视差的问题。我们利用自己研制的一种多功能立体图形发生器产生左边为非均匀条纹、右边为均匀条纹的一系列具有不同视差的立体图对。在感知到“阶梯”后,用三种方法使得“阶梯”感变平:①改变均匀条纹的频率,②改变均匀条纹与被试的距离,③改变非均匀条纹与被试者的距离。从而实现了频差“克服”视差。我们的结果支持用频差来解释双眼倾斜现象,它使我们相信频差是视差在初级视系统中的表象形式。     

频差在立体视觉信息加工中的作用 Ⅱ、频差“克服”视差

双眼立体视觉机制至今不很清楚,存在不少争论,研究它具有深远意义。我们的兴趣是从心理物理、电生理和理论模型三方面开展工作,最终目标是试图搞清楚视觉立体信息处理类机制。本文主要利用心理物理学方法研究频差克差视差的问题。我们利用自己研制的一种多功能立体图形发生器产生左边为非均匀条纹、右边为均匀条纹的一系列具有不同视差的立体图对。在感知到“阶梯”后,用三种方法使得“阶梯”感变平:①改变均匀条纹的频率,②改变均匀条纹与被试的距离,③改变非均匀条纹与被试者的距离。从而实现了频差“克服”视差。我们的结果支持用频差来解释双眼倾斜现象,它使我们相信频差是视差在初级视系统中的表象形式。