Computational studies of the extraction of visual spatial information from binocular and motion cues

This paper reviews some of the contributions that work in computational vision has made to the study of biological vision systems. We concentrate on two areas where there has been strong interaction between computational and experimental studies: the use of binocular stereo to recover the distances to surfaces in space, and the recovery of the three-dimensional shape of objects from relative motion in the image. With regard to stereo, we consider models proposed for solving the stereo correspondence problem, focussing on the way in which physical properties of the world constrain possible methods of solution. We also show how critical observations regarding human stereo vision have helped to shape these models. With regard to the recovery of structure from motion, we focus on how the constraint of object rigidity has been used in computational models of this process.     

Visual space distortion

We are surrounded by surfaces that we perceive by visual means. Understanding the basic principles behind this perceptual process is a central theme in visual psychology, psychophysics, and computational vision. In many of the computational models employed in the past, it has been assumed that a metric representation of physical space can be derived by visual means. Psychophysical experiments, as well as computational considerations, can convince us that the perception of space and shape has a much more complicated nature, and that only a distorted version of actual, physical space can be computed. This paper develops a computational geometric model that explains why such distortion might take place. The basic idea is that, both in stereo and motion, we perceive the world from multiple views. Given the rigid transformation between the views and the properties of the image correspondence, the depth of the scene can be obtained. Even a slight error in the rigid transformation parameters causes distortion of the computed depth of the scene. The unified framework introduced here describes this distortion in computational terms. We characterize the space of distortions by its level sets, that is, we characterize the systematic distortion via a family of iso-distortion surfaces which describes the locus over which depths are distorted by some multiplicative factor. Given that humans' estimation of egomotion or estimation of the extrinsic parameters of the stereo apparatus is likely to be imprecise, the framework is used to explain a number of psychophysical experiments on the perception of depth from motion or stereo. Received: 9 January 1997 / Accepted in revised form: 8 July 1997     

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     

Non-Bayesian contour synthesis

Recent research has witnessed an explosive increase in models that treat percepts as optimal probabilistic inference. The ubiquity of partial camouflage and occlusion in natural scenes, and the demonstrated capacity of the visual system to synthesize coherent contours and surfaces from fragmented image data, has inspired numerous attempts to model visual interpolation processes as rational inference. Here, we report striking new forms of visual interpolation that generate highly improbable percepts. We present motion displays depicting simple occlusion sequences that elicit vivid percepts of illusory contours (ICs) in displays for which they play no necessary explanatory role. These ICs define a second, redundant occluding surface, even though all of the image data can be fully explained by an occluding surface that is clearly visible. The formation of ICs in these images therefore entails an extraordinarily improbable co-occurrence of two occluding surfaces that arise from the same local occlusion events. The perceived strength of the ICs depends on simple low-level image properties, which suggests that they emerge as the outputs of mechanisms that automatically synthesize contours from the pattern of occlusion and disocclusion of local contour segments. These percepts challenge attempts to model visual interpolation as a form of rational inference and suggest the need to consider a broader space of computational problems and/or implementation level constraints to understand their genesis.     

Binocular fusion in Panum''''s limiting case of stereopsis obeys the uniqueness constraint

In the information processing procedure of stereo vision, the uniqueness constraint has been used as one of the constraints to solve the "correspondence problem". While the uniqueness constraint is valid in most cases, whether it is still valid in some particular stimulus configuration (such as Panum's limiting case) has been a problem of widespread debate for a long time. To investigate the problem, we adopted the Panum's limiting case as its basic stimulus configuration, and delved into the phenomenon of binocular fusion from two distinct aspects: visual direction and orientation disparity. The results show that in Panum's limiting case binocular fusion does not comply with the rules governing regular binocular fusion as far as visual direction and orientation disparity are concerned. This indicates that double fusion does not happen in Panum's limiting case and that the uniqueness constraint is still valid.     

Binocular fusion in Panum’s limiting case of stereopsis obeys the uniqueness constraint

In the information processing procedure of stereo vision, the uniqueness constraint has been used as one of the constraints to solve the “correspondence problem”. While the uniqueness constraint is valid in most cases, whether it is still valid in some particular stimulus configuration (such as Panum’s limiting case) has been a problem of widespread debate for a long time. To investigate the problem, we adopted the Panum’s limiting case as its basic stimulus configuration, and delved into the phenomenon of binocular fusion from two distinct aspects: visual direction and orientation disparity. The results show that in Panum’s limiting case binocular fusion does not comply with the rules governing regular binocular fusion as far as visual direction and orientation disparity are concerned. This indicates that double fusion does not happen in Panum’s limiting case and that the uniqueness constraint is still valid.     

Binocular fusion in Panum’s limiting case of stereopsis obeys the uniqueness constraint

In the information processing procedure of stereo vision, the uniqueness constraint has been used as one of the constraints to solve the “correspondence problem”. While the uniqueness constraint is valid in most cases, whether it is still valid in some particular stimulus configuration (such as Panum’s limiting case) has been a problem of widespread debate for a long time. To investigate the problem, we adopted the Panum’s limiting case as its basic stimulus configuration, and delved into the phenomenon of binocular fusion from two distinct aspects: visual direction and orientation disparity. The results show that in Panum’s limiting case binocular fusion does not comply with the rules governing regular binocular fusion as far as visual direction and orientation disparity are concerned. This indicates that double fusion does not happen in Panum’s limiting case and that the uniqueness constraint is still valid.     

Globally consistent depth sorting of overlapping 2D surfaces in a model using local recurrent interactions

The human visual system utilizes depth information as a major cue to group together visual items constituting an object and to segregate them from items belonging to other objects in the visual scene. Depth information can be inferred from a variety of different visual cues, such as disparity, occlusions and perspective. Many of these cues provide only local and relative information about the depth of objects. For example, at occlusions, T-junctions indicate the local relative depth precedence of surface patches. However, in order to obtain a globally consistent interpretation of the depth relations between the surfaces and objects in a visual scene, a mechanism is necessary that globally propagates such local and relative information. We present a computational framework in which depth information derived from T-junctions is propagated along surface contours using local recurrent interactions between neighboring neurons. We demonstrate that within this framework a globally consistent depth sorting of overlapping surfaces can be obtained on the basis of local interactions. Unlike previous approaches in which locally restricted cell interactions could merely distinguish between two depths (figure and ground), our model can also represent several intermediate depth positions. Our approach is an extension of a previous model of recurrent V1–V2 interaction for contour processing and illusory contour formation. Based on the contour representation created by this model, a recursive scheme of local interactions subsequently achieves a globally consistent depth sorting of several overlapping surfaces. Within this framework, the induction of illusory contours by the model of recurrent V1–V2 interaction gives rise to the figure-ground segmentation of illusory figures such as a Kanizsa square.     

Disambiguating Multi–Modal Scene Representations Using Perceptual Grouping Constraints

In its early stages, the visual system suffers from a lot of ambiguity and noise that severely limits the performance of early vision algorithms. This article presents feedback mechanisms between early visual processes, such as perceptual grouping, stereopsis and depth reconstruction, that allow the system to reduce this ambiguity and improve early representation of visual information. In the first part, the article proposes a local perceptual grouping algorithm that — in addition to commonly used geometric information — makes use of a novel multi–modal measure between local edge/line features. The grouping information is then used to: 1) disambiguate stereopsis by enforcing that stereo matches preserve groups; and 2) correct the reconstruction error due to the image pixel sampling using a linear interpolation over the groups. The integration of mutual feedback between early vision processes is shown to reduce considerably ambiguity and noise without the need for global constraints.     

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.     

Exploring variation in fitness surfaces over time or space

As the number of studies estimating selection on multiple traits has increased in recent years, fitness surfaces have become a fundamental tool for understanding multivariate selection and evolution. However, rigorous statistical comparisons of multivariate selection surfaces over time or space have been limited to parametric analyses of selection coefficients estimated using a quadratic regression model. Although parametric comparisons are useful when selection is approximately linear or quadratic in nature, they are limited when confronting the complex nature of rugged fitness surfaces. Here, I present a novel solution to comparing nonparametric fitness surfaces over time or space. Using a Tucker3 tensor decomposition, which is essentially a higher order principal components analysis, I show how major features of fitness surfaces can be compared statistically. Combined with a bootstrap algorithm, I develop three statistical tests that identify (1) differences in the shape of nonparametric fitness surfaces, (2) differences in the contribution of each surface to variation in fitness across time or space, and (3) specific areas of the surfaces (trait combinations) that vary significantly over time or space. I illustrate the tensor decomposition and statistical analyses using idealized fitness surfaces.     

Cortical connections and early visual function: intra- and inter-columnar processing.

While it is widely assumed that the long-range horizontal connections in V1 are present to support contour integration, there has been only limited consideration of other possible relationships between anatomy and physiology (the horizontal connections) and visual function beyond contour integration. We introduce the possibility of other relationships directly from the perspective of computation and differential geometry by identifying orientation columns in visual physiology with the (unit) tangent bundle in differential geometry. This suggests abstracting early vision in a space that incorporates both position and orientation, from which we show that the physiology is capable of supporting a number of functional computations beyond contour integration, including texture-flow and shading-flow integration, as well as certain relationships between them. The geometric abstraction emphasizes the role of curvature, which necessitates a coupled investigation into how it might be estimated. The result is an elaboration of layer-to-layer interactions within an orientation column, with non-linearities possibly implemented by shunting inhibition. Finally, we show how the same computational framework naturally lends itself to solving stereo correspondence, with binocular tangents abstracting curves in space.     

Spatial analysis of marine categorical information using indicator kriging applied to georeferenced video mosaics of the deep-sea Håkon Mosby Mud Volcano

The exact area calculation of irregularly distributed data is in the focus of all territorial geochemical balancing methods or definition of protection zones. Especially in the deep-sea environment the interpolation of measurements into surfaces represents an important gain of information, because of cost- and time-intensive data acquisition. The geostatistical interpolation method indicator kriging therefore is applied for an accurate mapping of the spatial distribution of benthic communities following a categorical classification scheme at the deep-sea submarine Håkon Mosby Mud Volcano. Georeferenced video mosaics were obtained during several dives by the Remotely Operated Vehicle Victor6000 in a water depth of 1260 m. Mud volcanoes are considered as significant source locations for methane indicated by unique chemoautotrophic communities as Beggiatoa mats and pogonophoran tube worms. For the detection and quantification of their spatial distribution 2840 georeferenced video mosaics were analysed by visual inspection. Polygons, digitised on the georeferenced images within a GIS, build the data basis for geostatistically interpolated mono-parametric surface maps. Indicator kriging is applied to the centroids of the polygons calculating surface maps. The quality assessment of the surface maps is conducted by leave-one-out cross-validation evaluating the fit of the indicator kriging variograms by using statistical mean values. Furthermore, the estimate was evaluated by a validation dataset of the visual inspection of 530 video mosaics not included within the interpolation, thus, proving the interpolated surfaces independently. With regard to both validating mechanisms, we attained satisfying results and we provided each category applied for the identification of biogeochemical habitats with a percentage probability value of occurrence.     

Dynamic texture spreading: probing the mechanisms of surface interpolation

Dynamic texture spreading is a filling-in phenomenon where a colored pattern perceptually spreads onto an area confined by virtual contours in a multi-aperture motion display. The spreading effect is qualitatively similar to static texture spreading but widely surpasses it in strength, making it particularly suited for quantitative studies of visual interpolation processes. We first carried out two experiments to establish with objective tasks that texture spreading is a genuine representation of surface qualities and thus goes beyond mere contour interpolation. Two subsequent experiments serve to relate the phenomenon to ongoing discussions about potentially responsible mechanisms for spatiotemporal integration. With a phenomenological method, we examined to what extent simple sensory persistence might be causally involved in the effect under consideration. Most of our findings are consistent with the idea of sensory persistence, and indicate that information fragments are integrated over a time window of about 100 to 180 ms to form a complete surface representation.     

A model of binocular stereopsis including a global consistency constraint

 The binocular correspondence problem was solved by implementing the uniqueness constraint and the continuity constraint, as proposed by Marr and Poggio [Marr D, PoggioT (1976) Science 194: 283–287]. However, these constraints are not sufficient to define the proper correspondence uniquely. With these constraints, random-dot stereograms (RDSs), consisting of the periodic textures in each image, are treated as a correspondence of surfaces composed of patches of alternating values of disparity. This is quite different from the surface we perceive through the RDSs, that is a surface characterized by a single depth. Because these constraints are local, they cannot produce the global optimum of correspondence. To obtain the global optimum of correspondence, we propose a model of binocular stereopsis in which a global measure of correspondence is explicitly employed. The model consists of two hierarchical systems. First, the lower system processes various correspondences based on the uniqueness constraint. Second, the higher system provides a global measure of correspondence for the disparity in question. The higher system uniquely determines the global optimum of correspondence in the lower system through the recurrent loop between hierarchical systems. The convergence of the recurrent loop is determined by the consistency between the hierarchical systems. The condition is termed the `global consistency constraint. Received: 27 August 1998 / Accepted in revised form: 8 November 1999     

Motion perception and motion estimation by total-least squares

A computational model of motion perception is proposed. The model, which is gradient-based, adheres to the neural constraint that transmitted signals are positive-valued functions by posing the estimation of image motion as a quadratic programming problem combined with total-least squares: a model that assumes that image signals are contaminated by noise in both the spatial and temporal dimensions. By shrinking motion estimates with a regularizer whose subtractive effect introduces a contrast dependent speed threshold into motion computations, it is shown that the total-least squares model when posed as a quadratic programming problem, is capable of explaining both increases and decreases in perceived speed as these effects were reported by Thompson (1982) to vary as a function of image contrast and temporal frequency. The correlation that exists between the model's contrast speed response and results reported from visual psychophysics is consistent with the view that the visual system assumes that image signals may be contaminated by noise in both the spatial and the temporal domain, and that visual motion is influenced by the consequence of these assumptions.     

Visuo-tactile representation of near-the-body space.

Here we report findings from neuropsychological investigations showing the existence, in humans, of intersensory integrative systems representing space through the multisensory coding of visual and tactile events. In addition, these findings show that visuo-tactile integration may take place in a privileged manner within a limited sector of space closely surrounding the body surface, i.e., the near-peripersonal space. They also demonstrate that the representation of near-peripersonal space is not static, as objects in the out-of-reach space can be processed as nearer, depending upon the (illusory) visual information about hand position in space, and the use of tools as physical extensions of the reachable space. Finally, new evidence is provided suggesting the multisensory coding of peripersonal space can be achieved through bottom-up processing that, at least in some instances, is not necessarily modulated by more "cognitive" top-down processing, such as the expectation regarding the possibility of being touched. These findings are entirely consistent with the functional properties of multisensory neuronal structures coding near-peripersonal space in monkeys, as well as with behavioral, and neuroimaging evidence for the cross-modal coding of space in normal subjects. This high level of convergence ultimately favors the idea that multisensory space coding is achieved through similar multimodal structures in both humans and non-human primates.     

Common Cortical Loci Are Activated during Visuospatial Interpolation and Orientation Discrimination Judgements

There is a wealth of literature on the role of short-range interactions between low-level orientation-tuned filters in the perception of discontinuous contours. However, little is known about how spatial information is integrated across more distant regions of the visual field in the absence of explicit local orientation cues, a process referred to here as visuospatial interpolation (VSI). To examine the neural correlates of VSI high field functional magnetic resonance imaging was used to study brain activity while observers either judged the alignment of three Gabor patches by a process of interpolation or discriminated the local orientation of the individual patches. Relative to a fixation baseline the two tasks activated a largely over-lapping network of regions within the occipito-temporal, occipito-parietal and frontal cortices. Activated clusters specific to the orientation task (orientation>interpolation) included the caudal intraparietal sulcus, an area whose role in orientation encoding per se has been hotly disputed. Surprisingly, there were few task-specific activations associated with visuospatial interpolation (VSI>orientation) suggesting that largely common cortical loci were activated by the two experimental tasks. These data are consistent with previous studies that suggest higher level grouping processes -putatively involved in VSI- are automatically engaged when the spatial properties of a stimulus (e.g. size, orientation or relative position) are used to make a judgement.     

Evolutionary stasis, constraint and other terminology describing evolutionary patterns

Current use of terms to describe evolutionary patterns is vague and inconsistent. In this paper, logical definitions of terms that describe specific evolutionary patterns are proposed. Evolutionary inertia is defined in a manner analogous to inertia in physics. A character in a static state of evolutionary inertia represents evolutionary stasis while a character showing consistent directional evolutionary change represents evolutionary thrust. I argue that evolutionary stasis should serve as the null hypothesis in all character evolution studies. Deviations from this null model consistent with alternative hypotheses (e.g. random drift, adaptation) can then give us insight into evolutionary processes. Failure to reject a null hypothesis of evolutionary stasis should not be used as a serious explanation of data. The term evolutionary constraint is appropriate only when a selective advantage for a character state transition is established but this transition is prevented by specific, identified factors. One type of evolutionary constraint discussed is evolutionary momentum. A final pattern of evolutionary change discussed is closely related to evolutionary thrust and is referred to as evolutionary acceleration. I provide examples of how this set of definitions can improve our ability to communicate interpretations of evolutionary patterns.