Visual stability and space perception in monocular vision: mathematical model

Motion parallax from microscopic head movements during visual fixation

Under normal viewing conditions, adjustments in body posture and involuntary head movements continually shift the eyes in space. Like all translations, these movements may yield depth information in the form of motion parallax, the differential motion on the retina of objects at different distances from the observer. However, studies on depth perception rarely consider the possible contribution of this cue, as the resulting changes in viewpoint appear too small to be of perceptual significance. Here, we quantified the parallax present during fixation in normally standing observers. We measured the trajectories followed by the eyes in space by means of a high-resolution head-tracking system and used an optical model of the eye to reconstruct the stimulus on the observer's retina. We show that, within several meters from the observer, relatively small changes in depth yield changes in the velocity of the retinal stimulus that are well above perceivable thresholds. Furthermore, relative velocities are little influenced by fixation distance, target eccentricity, and the precise oculomotor strategy followed by the observer to maintain fixation. These results demonstrate that the parallax available during normal head-free fixation is a reliable source of depth information, which the visual system may use in a variety of tasks.

Motion perception during selfmotion: The direct versus inferential controversy revisited

According to the traditional inferential theory of perception, percepts of object motion or stationarity stem from an evaluation of afferent retinal signals (which encode image motion) with the help of extraretinal signals (which encode eye movements). According to direct perception theory, on the other hand, the percepts derive from retinally conveyed information only. Neither view is compatible with a perceptual phenomenon that occurs during visually induced sensations of ego motion (vection). A modified version of inferential theory yields a model in which the concept of extraretinal signals is replaced by that of reference signals, which do not encode how the eyes move in their orbits but how they move in space. Hence reference signals are produced not only during eye movements but also during ego motion (i.e., in response to vestibular stimulation and to retinal image flow, which may induce vection). The present theory describes the interface between self-motion and object-motion percepts. An experimental paradigm that allows quantitative measurement of the magnitude and gain of reference signals and the size of the just noticeable difference (JND) between retinal and reference signals reveals that the distinction between direct and inferential theories largely depends on: (1) a mistaken belief that perceptual veridicality is evidence that extraretinal information is not involved, and (2) a failure to distinguish between (the perception of) absolute object motion in space and relative motion of objects with respect to each other. The model corrects these errors, and provides a new, unified framework for interpreting many phenomena in the field of motion perception.

Neural model of first-order and second-order motion perception and magnocellular dynamics

A neural model of motion perception simulates psychophysical data concerning first-order and second-order motion stimuli, including the reversal of perceived motion direction with distance from the stimulus (gamma display), and data about directional judgments as a function of relative spatial phase or spatial and temporal frequency. Many other second-order motion percepts that have ascribed to a second non-Fourier processing stream can also be explained in the model by interactions between ON and OFF cells within a single, neurobiologically interpreted magnocellular processing stream. Yet other percepts may be traced to interactions between form and motion processing streams, rather than to processing within multiple motion processing streams. The model hereby explains why monkeys with lesions of the parvocellular layers, but not of the magnocellular layers, of the lateral geniculate nucleus (LGN) are capable of detecting the correct direction of second-order motion, why most cells in area MT are sensitive to both first-order and second-order motion, and why after 2-amino-4-phosphonobutyrate injection selectively blocks retinal ON bipolar cells, cortical cells are sensitive only to the motion of a moving bright bar's trailing edge. Magnocellular LGN cells show relatively transient responses, whereas parvocellular LGN cells show relatively sustained responses. Correspondingly, the model bases its directional estimates on the outputs of model ON and OFF transient cells that are organized in opponent circuits wherein antagonistic rebounds occur in response to stimulus offset. Center-surround interactions convert these ON and OFF outputs into responses of lightening and darkening cells that are sensitive both to direct inputs and to rebound responses in their receptive field centers and surrounds. The total pattern of activity increments and decrements is used by subsequent processing stages (spatially short-range filters, competitive interactions, spatially long-range filters, and directional grouping cells) to determine the perceived direction of motion.

The angular Velocity associated with the optical flowfield arising from motion through a rigid environment

The instantaneous optical flowfield due to a camera moving through a rigid environment may be compatible with up to three distinct values for the angular velocity, but three is the maximum number that can occur. Each angular velocity is associated with a particular set of relative depths of points in the environment. A method of constructing all flowfields compatible with more than one value of the angular velocity is given.

Multiple interpretations of a pair of images of a surface

It is known that if two optical images of a visually textured surface, projected from finitely separated viewpoints, allow more than one 3D interpretation, then the surface must be part of a quadric passing through the two viewpoints. It is here shown that this quadric is either a plane or a ruled surface of a type first considered by Maybank in a study of ambiguous optic flow fields; and that in the latter case, three is the maximum number of distinct interpretations that the two images can sustain.

Two metric solutions to three-dimensional reconstruction for an eye in pure rotations

A problem in space perception concerns how a mobile observer acquires information about the structure of objects. Earlier research derived the optic-flow equations for an eye undergoing pure rotations. It was suggested that, by utilizing three points and two views, one can recover the distance of points and the motion parameters. The radius of the eyeball was the metric unit. Yet the common view regards this problem as indeterminate. We derived a unique solution in the discrete case, which required three points and two views. However, when we observed a single bright point, a substantial amount of visual stability existed. We therefore derived a solution in the differential approach for a single point, which is based on a distinction that we made between mathematical and visual points. Both solutions were checked with a computer simulation and were found to be accurate, supporting the space perception in navigation (SPIN) theory.

Optical flow from eye movement with head immobilized: "ocular occlusion" beyond the nose

The point of observation translates with eye movement because it is not coincident with the center of rotation in the eye. "Ocular occlusion" results. The amount of optical structure revealed by eye rotation depends on the distances of the occluding and occluded surfaces. The method of adjustment was used in Expt 1 to investigate the amount of structure detected at distances up to 1 m. In Expt 2, a forced-choice method was used to confirm predictions based on the assumption that the point of observation is in the entrance pupil at 11 mm from the center of rotation. (The location of the point of observation in the eye had not been measured previously.) Experiment 3 investigated the use of ocular occlusion to detect separation of surfaces in depth.

Corneal lens goggles and visual space perception

Night vision goggles are head-mounted, unity-power systems designed to allow the human operator to see and operate at night. Field experience and experimental studies have revealed many drawbacks in conventional designs that impair performance. One major drawback is the poor space perception provided by the goggles. The Hadani et al. [J. Opt. Soc. Am. 70, 60-65 (1980)] model for space perception attributes this drawback to the fact that the conventional designs shift the observer's effective center of perspective approximately 15 cm ahead and also predicts the resulting impairments. An innovative redesign is presented in this paper-the corneal lens goggles (CLG)-which brings the effective center of perspective of the goggles to coincide with the center of perspective of the eyes, thus annulling the optical length of the device. Qualitative and quantitative laboratory studies have compared the performance of the CLG and conventional goggles (type AN/PVS-5). These studies have revealed better visual and visual-motor performance with the CLG. The implications to optical design of the Hadani et al. theory and the CLG concept are discussed.

Scene segmentation from visual motion using global optimization

This paper presents results from computer experiments with an algorithm to perform scene disposition and motion segmentation from visual motion or optic flow. The maximum a posteriori (MAP) criterion is used to formulate what the best segmentation or interpretation of the scene should be, where the scene is assumed to be made up of some fixed number of moving planar surface patches. The Bayesian approach requires, first, specification of prior expectations for the optic flow field, which here is modeled as spatial and temporal Markov random fields; and, secondly, a way of measuring how well the segmentation predicts the measured flow field. The Markov random fields incorporate the physical constraints that objects and their images are probably spatially continuous, and that their images are likely to move quite smoothly across the image plane. To compute the flow predicted by the segmentation, a recent method for reconstructing the motion and orientation of planar surface facets is used. The search for the globally optimal segmentation is performed using simulated annealing.

Monocular depth perception from optical flow by space time signal processing

A theory of monocular depth determination is presented. The effect of finite temporal resolution is incorporated by generalizing the Marr–Hildreth edge detected operator –∇ 2 G ( r ) where ∇ 2 is the Laplacian and G ( r ) is a two-dimensional Gaussian. The constraint that the edge detection operator in space–time should produce zero-crossings at the same place in different channels, i. e. at different resolutions of the Gaussian, led to the conclusion that the Marr–Hildreth operator should be replaced by – □ 2 G ( r , t ) where □ 2 is the d’Alembertian ∇ 2 – (1/ u 2 )(∂ 2 /∂ t 2 ) and G ( r , t ) is a Gaussian in space–time. To ensure that the locations of the zero-crossings are independent of the channel width, G ( r , t ) has to be isotropic in the sense that the velocity u appearing in the defintion of the d’Alembertian must also be used to relate the scales of length and time in G . However, the new operatior –□ 2 G ( r , t ) produces two types of zero-crossing for each isolated edge feature in the image I ( r , t ). One of these, termed the ‘static edge’, corresponds to the position of the image edge at time t as defined by ∇ 2 I ( r , t ) = 0; the other, called a ‘depth zero’, depends only on the relative motion of the observer and object and is usually found only in the periphery of the field of view. When an edge feature is itself in the periphery of the visual field and these zeros coincide, there is an additional cross-over effect. It is shown how these zero-crossings may be used to infer the depth of an object when the observer and object are in relative motion. If an edge feature is near the centre of the image (i. e. near the focus of expansion), the spatial and temporal slopes of the zeros crossing at the static edge may be used to infer the depth, but, if the edge feature is in the periphery of the image, the cross-over effect enables the depth to be obtained immediately. While the former utilizes sharp spatial and temporal resolution to give detailed three-dimensional information, the cross-over effect relies on longer integration times to give a direct measure of the time-to-contact. We propose that both mechanisms could be used to extract depth information in computer vision systems and speculate on how our theory could be used to model depth perception in early visual processing in humans where there is evidence of both monocular perception of the environment in depth and of looming detection in the periphery of the field of view. In addition it is shown how a number of previous models are included in our theory, in particular the directional sensor proposed by Marr & Ullman and a method of depth determination proposed by Prazdny.

Perception of stabilized retinal stimuli in dichoptic viewing conditions

Perception of stabilized retinal stimuli was studied both in monocular and dichoptic viewing conditions. When identical stabilized stimuli of large size and high luminance were presented to both eyes, the phenomena characteristic of monocular perception (rapid fading of perceived images within a few seconds or their episodic disappearance and regeneration) failed to be observed: the visual images were perceived as decaying only gradually and slowly within several minutes. The results suggest that rapid changes and fluctuations of visual images perceived monocularly may be due to the effects of binocular interaction (cooperation/rivalry), episodic darkenings of the visual field seeming to be caused by temporary predominance of the occluded eye.