Understanding 3D vision as a policy network.

It is often assumed that the brain builds 3D coordinate frames, in retinal coordinates (with binocular disparity giving the third dimension), head-centred, body-centred and world-centred coordinates. This paper questions that assumption and begins to sketch an alternative based on, essentially, a set of reflexes. A 'policy network' is a term used in reinforcement learning to describe the set of actions that are generated by an agent depending on its current state. This is an untypical starting point for describing 3D vision, but a policy network can serve as a useful representation both for the 3D layout of a scene and the location of the observer within it. It avoids 3D reconstruction of the type used in computer vision but is similar to recent representations for navigation generated through reinforcement learning. A policy network for saccades (pure rotations of the camera/eye) is a logical starting point for understanding (i) an ego-centric representation of space (e.g. Marr's (Marr 1982 Vision: a computational investigation into the human representation and processing of visual information) 2[Formula: see text]-D sketch) and (ii) a hierarchical, compositional representation for navigation. The potential neural implementation of policy networks is straightforward; a network with a large range of sensory and task-related inputs such as the cerebellum would be capable of implementing this input/output function. This is not the case for 3D coordinate transformations in the brain: no neurally implementable proposals have yet been put forward that could carry out a transformation of a visual scene from retinal to world-based coordinates. Hence, if the representation underlying 3D vision can be described as a policy network (in which the actions are either saccades or head translations), this would be a significant step towards a neurally plausible model of 3D vision. This article is part of the theme issue 'New approaches to 3D vision'.

Combining cues to judge distance and direction in an immersive virtual reality environment.

When we move, the visual direction of objects in the environment can change substantially. Compared with our understanding of depth perception, the problem the visual system faces in computing this change is relatively poorly understood. Here, we tested the extent to which participants' judgments of visual direction could be predicted by standard cue combination rules. Participants were tested in virtual reality using a head-mounted display. In a simulated room, they judged the position of an object at one location, before walking to another location in the room and judging, in a second interval, whether an object was at the expected visual direction of the first. By manipulating the scale of the room across intervals, which was subjectively invisible to observers, we put two classes of cue into conflict, one that depends only on visual information and one that uses proprioceptive information to scale any reconstruction of the scene. We find that the sensitivity to changes in one class of cue while keeping the other constant provides a good prediction of performance when both cues vary, consistent with the standard cue combination framework. Nevertheless, by comparing judgments of visual direction with those of distance, we show that judgments of visual direction and distance are mutually inconsistent. We discuss why there is no need for any contradiction between these two conclusions.

Route selection in non-Euclidean virtual environments.

The way people choose routes through unfamiliar environments provides clues about the underlying representation they use. One way to test the nature of observers' representation is to manipulate the structure of the scene as they move through it and measure which aspects of performance are significantly affected and which are not. We recorded the routes that participants took in virtual mazes to reach previously-viewed targets. The mazes were either physically realizable or impossible (the latter contained 'wormholes' that altered the layout of the scene without any visible change at that moment). We found that participants could usually find the shortest route between remembered objects even in physically impossible environments, despite the gross failures in pointing that an earlier study showed are evident in the physically impossible environment. In the physically impossible conditions, the choice made at a junction was influenced to a greater extent by whether that choice had, in the past, led to the discovery of a target (compared to a shortest-distance prediction). In the physically realizable mazes, on the other hand, junction choices were determined more by the shortest distance to the target. This pattern of results is compatible with the idea of a graph-like representation of space that can include information about previous success or failure for traversing each edge and also information about the distance between nodes. Our results suggest that complexity of the maze may dictate which of these is more important in influencing navigational choices.

Lessons from reinforcement learning for biological representations of space.

Neuroscientists postulate 3D representations in the brain in a variety of different coordinate frames (e.g. 'head-centred', 'hand-centred' and 'world-based'). Recent advances in reinforcement learning demonstrate a quite different approach that may provide a more promising model for biological representations underlying spatial perception and navigation. In this paper, we focus on reinforcement learning methods that reward an agent for arriving at a target image without any attempt to build up a 3D 'map'. We test the ability of this type of representation to support geometrically consistent spatial tasks such as interpolating between learned locations using decoding of feature vectors. We introduce a hand-crafted representation that has, by design, a high degree of geometric consistency and demonstrate that, in this case, information about the persistence of features as the camera translates (e.g. distant features persist) can improve performance on the geometric tasks. These examples avoid Cartesian (in this case, 2D) representations of space. Non-Cartesian, learned representations provide an important stimulus in neuroscience to the search for alternatives to a 'cognitive map'.

No single, stable 3D representation can explain pointing biases in a spatial updating task.

People are able to keep track of objects as they navigate through space, even when objects are out of sight. This requires some kind of representation of the scene and of the observer's location but the form this might take is debated. We tested the accuracy and reliability of observers' estimates of the visual direction of previously-viewed targets. Participants viewed four objects from one location, with binocular vision and small head movements then, without any further sight of the targets, they walked to another location and pointed towards them. All conditions were tested in an immersive virtual environment and some were also carried out in a real scene. Participants made large, consistent pointing errors that are poorly explained by any stable 3D representation. Any explanation based on a 3D representation would have to posit a different layout of the remembered scene depending on the orientation of the obscuring wall at the moment the participant points. Our data show that the mechanisms for updating visual direction of unseen targets are not based on a stable 3D model of the scene, even a distorted one.

The Science Behind Virtual Reality Displays.

Virtual reality (VR) is becoming an increasingly important way to investigate sensory processing. The converse is also true: in order to build good VR technologies, one needs an intimate understanding of how our brain processes sensory information. One of the key advantages of studying perception with VR is that it allows an experimenter to probe perceptual processing in a more naturalistic way than has been possible previously. In VR, one is able to actively explore and interact with the environment, just as one would do in real life. In this article, we review the history of VR displays, including the philosophical origins of VR, before discussing some key challenges involved in generating good VR and how a sense of presence in a virtual environment can be measured. We discuss the importance of multisensory VR and evaluate the experimental tension that exists between artifice and realism when investigating sensory processing.

Comparison of view-based and reconstruction-based models of human navigational strategy.

There is good evidence that simple animals, such as bees, use view-based strategies to return to a familiar location, whereas humans might use a 3-D reconstruction to achieve the same goal. Assuming some noise in the storage and retrieval process, these two types of strategy give rise to different patterns of predicted errors in homing. We describe an experiment that can help distinguish between these models. Participants wore a head-mounted display to carry out a homing task in immersive virtual reality. They viewed three long, thin, vertical poles and had to remember where they were in relation to the poles before being transported (virtually) to a new location in the scene from where they had to walk back to the original location. The experiment was conducted in both a rich-cue scene (a furnished room) and a sparse scene (no background and no floor or ceiling). As one would expect, in a rich-cue environment, the overall error was smaller, and in this case, the ability to separate the models was reduced. However, for the sparse-cue environment, the view-based model outperforms the reconstruction-based model. Specifically, the likelihood of the experimental data is similar to the likelihood of samples drawn from the view-based model (but assessed under both models), and this is not true for samples drawn from the reconstruction-based model.

A moving observer in a three-dimensional world.

For many tasks such as retrieving a previously viewed object, an observer must form a representation of the world at one location and use it at another. A world-based three-dimensional reconstruction of the scene built up from visual information would fulfil this requirement, something computer vision now achieves with great speed and accuracy. However, I argue that it is neither easy nor necessary for the brain to do this. I discuss biologically plausible alternatives, including the possibility of avoiding three-dimensional coordinate frames such as ego-centric and world-based representations. For example, the distance, slant and local shape of surfaces dictate the propensity of visual features to move in the image with respect to one another as the observer's perspective changes (through movement or binocular viewing). Such propensities can be stored without the need for three-dimensional reference frames. The problem of representing a stable scene in the face of continual head and eye movements is an appropriate starting place for understanding the goal of three-dimensional vision, more so, I argue, than the case of a static binocular observer.This article is part of the themed issue 'Vision in our three-dimensional world'.

Using high-fidelity virtual reality to study perception in freely moving observers.

Technological innovations have had a profound influence on how we study the sensory perception in humans and other animals. One example was the introduction of affordable computers, which radically changed the nature of visual experiments. It is clear that vision research is now at cusp of a similar shift, this time driven by the use of commercially available, low-cost, high-fidelity virtual reality (VR). In this review we will focus on: (a) the research questions VR allows experimenters to address and why these research questions are important, (b) the things that need to be considered when using VR to study human perception,

Humans use predictive kinematic models to calibrate visual cues to three-dimensional surface slant.

When the sensory consequences of an action are systematically altered our brain can recalibrate the mappings between sensory cues and properties of our environment. This recalibration can be driven by both cue conflicts and altered sensory statistics, but neither mechanism offers a way for cues to be calibrated so they provide accurate information about the world, as sensory cues carry no information as to their own accuracy. Here, we explored whether sensory predictions based on internal physical models could be used to accurately calibrate visual cues to 3D surface slant. Human observers played a 3D kinematic game in which they adjusted the slant of a surface so that a moving ball would bounce off the surface and through a target hoop. In one group, the ball's bounce was manipulated so that the surface behaved as if it had a different slant to that signaled by visual cues. With experience of this altered bounce, observers recalibrated their perception of slant so that it was more consistent with the assumed laws of kinematics and physical behavior of the surface. In another group, making the ball spin in a way that could physically explain its altered bounce eliminated this pattern of recalibration. Importantly, both groups adjusted their behavior in the kinematic game in the same way, experienced the same set of slants, and were not presented with low-level cue conflicts that could drive the recalibration. We conclude that observers use predictive kinematic models to accurately calibrate visual cues to 3D properties of world.

Modelling human visual navigation using multi-view scene reconstruction.

It is often assumed that humans generate a 3D reconstruction of the environment, either in egocentric or world-based coordinates, but the steps involved are unknown. Here, we propose two reconstruction-based models, evaluated using data from two tasks in immersive virtual reality. We model the observer's prediction of landmark location based on standard photogrammetric methods and then combine location predictions to compute likelihood maps of navigation behaviour. In one model, each scene point is treated independently in the reconstruction; in the other, the pertinent variable is the spatial relationship between pairs of points. Participants viewed a simple environment from one location, were transported (virtually) to another part of the scene and were asked to navigate back. Error distributions varied substantially with changes in scene layout; we compared these directly with the likelihood maps to quantify the success of the models. We also measured error distributions when participants manipulated the location of a landmark to match the preceding interval, providing a direct test of the landmark-location stage of the navigation models. Models such as this, which start with scenes and end with a probabilistic prediction of behaviour, are likely to be increasingly useful for understanding 3D vision.

Default perception of high-speed motion.

When human observers are exposed to even slight motion signals followed by brief visual transients--stimuli containing no detectable coherent motion signals--they perceive large and salient illusory jumps. This visually striking effect, which we call "high phi," challenges well-entrenched assumptions about the perception of motion, namely the minimal-motion principle and the breakdown of coherent motion perception with steps above an upper limit called dmax. Our experiments with transients, such as texture randomization or contrast reversal, show that the magnitude of the jump depends on spatial frequency and transient duration--but not on the speed of the inducing motion signals--and the direction of the jump depends on the duration of the inducer. Jump magnitude is robust across jump directions and different types of transient. In addition, when a texture is actually displaced by a large step beyond the upper step size limit of dmax, a breakdown of coherent motion perception is expected; however, in the presence of an inducer, observers again perceive coherent displacements at or just above dmax. In summary, across a large variety of stimuli, we find that when incoherent motion noise is preceded by a small bias, instead of perceiving little or no motion--as suggested by the minimal-motion principle--observers perceive jumps whose amplitude closely follows their own dmax limits.

A demonstration of 'broken' visual space.

It has long been assumed that there is a distorted mapping between real and 'perceived' space, based on demonstrations of systematic errors in judgements of slant, curvature, direction and separation. Here, we have applied a direct test to the notion of a coherent visual space. In an immersive virtual environment, participants judged the relative distance of two squares displayed in separate intervals. On some trials, the virtual scene expanded by a factor of four between intervals although, in line with recent results, participants did not report any noticeable change in the scene. We found that there was no consistent depth ordering of objects that can explain the distance matches participants made in this environment (e.g. A>B>D yet also A

An automated calibration method for non-see-through head mounted displays.

Accurate calibration of a head mounted display (HMD) is essential both for research on the visual system and for realistic interaction with virtual objects. Yet, existing calibration methods are time consuming and depend on human judgements, making them error prone, and are often limited to optical see-through HMDs. Building on our existing approach to HMD calibration Gilson et al. (2008), we show here how it is possible to calibrate a non-see-through HMD. A camera is placed inside a HMD displaying an image of a regular grid, which is captured by the camera. The HMD is then removed and the camera, which remains fixed in position, is used to capture images of a tracked calibration object in multiple positions. The centroids of the markers on the calibration object are recovered and their locations re-expressed in relation to the HMD grid. This allows established camera calibration techniques to be used to recover estimates of the HMD display's intrinsic parameters (width, height, focal length) and extrinsic parameters (optic centre and orientation of the principal ray). We calibrated a HMD in this manner and report the magnitude of the errors between real image features and reprojected features. Our calibration method produces low reprojection errors without the need for error-prone human judgements.

Cue combination for 3D location judgements.

Cue combination rules have often been applied to the perception of surface shape but not to judgements of object location. Here, we used immersive virtual reality to explore the relationship between different cues to distance. Participants viewed a virtual scene and judged the change in distance of an object presented in two intervals, where the scene changed in size between intervals (by a factor of between 0.25 and 4). We measured thresholds for detecting a change in object distance when there were only 'physical' (stereo and motion parallax) or 'texture-based' cues (independent of the scale of the scene) and used these to predict biases in a distance matching task. Under a range of conditions, in which the viewing distance and position of the target relative to other objects was varied, the ratio of 'physical' to 'texture-based' thresholds was a good predictor of biases in the distance matching task. The cue combination approach, which successfully accounts for our data, relies on quite different principles from those underlying traditional models of 3D reconstruction.

Latitude and longitude vertical disparities.

The literature on vertical disparity is complicated by the fact that several different definitions of the term "vertical disparity" are in common use, often without a clear statement about which is intended or a widespread appreciation of the properties of the different definitions. Here, we examine two definitions of retinal vertical disparity: elevation-latitude and elevation-longitude disparities. Near the fixation point, these definitions become equivalent, but in general, they have quite different dependences on object distance and binocular eye posture, which have not previously been spelt out. We present analytical approximations for each type of vertical disparity, valid for more general conditions than previous derivations in the literature: we do not restrict ourselves to objects near the fixation point or near the plane of regard, and we allow for non-zero torsion, cyclovergence, and vertical misalignments of the eyes. We use these expressions to derive estimates of the latitude and longitude vertical disparities expected at each point in the visual field, averaged over all natural viewing. Finally, we present analytical expressions showing how binocular eye position-gaze direction, convergence, torsion, cyclovergence, and vertical misalignment-can be derived from the vertical disparity field and its derivatives at the fovea.

Spatial calibration of an optical see-through head-mounted display.

We present here a method for calibrating an optical see-through head-mounted display (HMD) using techniques usually applied to camera calibration (photogrammetry). Using a camera placed inside the HMD to take pictures simultaneously of a tracked object and features in the HMD display, we could exploit established camera calibration techniques to recover both the intrinsic and extrinsic properties of the HMD (width, height, focal length, optic centre and principal ray of the display). Our method gives low re-projection errors and, unlike existing methods, involves no time-consuming and error-prone human measurements, nor any prior estimates about the HMD geometry.

How soccer players head the ball: a test of Optic Acceleration Cancellation theory with virtual reality.

We measured the movements of soccer players heading a football in a fully immersive virtual reality environment. In mid-flight the ball's trajectory was altered from its normal quasi-parabolic path to a linear one, producing a jump in the rate of change of the angle of elevation of gaze (alpha) from player to ball. One reaction time later the players adjusted their speed so that the rate of change of alpha increased when it had been reduced and reduced it when it had been increased. Since the result of the player's movement was to regain a value of the rate of change close to that before the disturbance, the data suggest that the players have an expectation of, and memory for, the pattern that the rate of change of alpha will follow during the flight. The results support the general claim that players intercepting balls use servo control strategies and are consistent with the particular claim of Optic Acceleration Cancellation theory that the servo strategy is to allow alpha to increase at a steadily decreasing rate.

Marr's vision: twenty-five years on.

It is twenty-five years since the posthumous publication of David Marr's book Vision[1]. Only 35 years old when he died, Marr had already dramatically influenced vision research. His book, and the series of papers that preceded it, have had a lasting impact on the way that researchers approach human and computer vision.