Space Perception

Abstract

Space perception is the set of processes by which observers recover the three-dimensional layout of the environment and their own position within it from sensory information. Because the two-dimensional retinal image underdetermines the scene that produced it, the visual system combines many depth cues and integrates vision with touch and self-motion to build a stable metric of surrounding space. That space is coded in more than one frame of reference, updated as the observer moves, anchored to environmental geometry, routed through a dorsal cortical pathway specialised for location and action, and stored in a cognitive map supported by place and grid cells. Whether perceived space is Euclidean, and how its many representations combine, remain debated. Three interactive demonstrations model ground-plane distance from the angle of declination, statistically optimal cue combination, and spatial updating during self-motion.

Keywords: space perception, spatial layout, frames of reference, cognitive map

Space perception refers to the recovery of the geometry of the surrounding world, the distances, directions, and shapes of surfaces and objects, together with the observer's own location and orientation within that geometry. The central problem is that the pattern of light on each retina is two-dimensional and ambiguous, consistent with infinitely many arrangements of surfaces in depth, so the perceived third dimension must be constructed by combining partial cues and prior constraints (Cutting & Vishton, 1995). The constructed space is then represented in coordinate frames that must be kept in register as the eyes, head, and body move, and it is used to guide action, to remember where things are, and to find the way back. This article follows space perception from the geometry of the perceived world, through the perception of distance and layout, the frames of reference that encode it, the updating of those frames during movement, reorientation to environmental geometry, the dorsal cortical pathway, and the cognitive map, to the criticisms that qualify each of these accounts.

What Space Perception Is

Space perception is the construction of a representation of the three-dimensional environment from sensory data that do not specify it uniquely. Each eye receives a flat projection of the scene, and any point in that projection could have arisen from a surface at any distance along the line of sight, so depth is not given in the image but must be inferred (Cutting & Vishton, 1995). The perceptual system resolves this ambiguity by exploiting regularities that ordinarily hold in the world, such as the ground being roughly horizontal, light coming from above, and the two eyes viewing the scene from slightly different vantage points, and by combining the many partial sources of information that each constrain the layout.

The problem has two connected parts. The first is metric: recovering how far away surfaces are and how large and how oriented they are, which requires converting angular information on the retina into distances and sizes in the world. The second is referential: specifying positions relative to some origin and set of axes, a frame of reference, and keeping that specification stable as the observer and the objects move. A perceived layout is therefore not a single image but a set of related representations, some tied to the body and some tied to the environment, that together support seeing where things are, reaching for them, walking to them, and remembering their locations. The sections that follow treat these components in turn, beginning with the geometry of the space that perception delivers.

The Geometry of Visual Space

The space that observers perceive is not a faithful copy of physical space. When the perceived distances and angles among points are measured directly, they depart systematically from their physical values, so that perceived visual space is best described by a non-Euclidean geometry whose curvature changes with viewing conditions (Wagner, 1985). In particular, extents oriented in depth, away from the observer, are perceptually compressed relative to extents of the same physical length laid out frontally, so a square on the ground viewed obliquely is seen as a trapezoid shortened in the depth direction. This foreshortening grows with distance and is one reason the metric of perceived space is only loosely tied to the metric of the world.

The compression can be traced in part to how binocular information specifies distance. The angle by which the two eyes converge on a target, and the small differences between the two retinal images, provide metric depth only when scaled by an estimate of absolute distance, and that estimate is biased, so binocular distance perception follows the physical distance with a gain that is less than one and that falls off with range (Foley, 1980). Because the scaling error accumulates in depth but not across the frontal plane, distances in depth are underestimated and the perceived layout is warped. Figure 1 shows the resulting compression schematically, and the theme runs through the next section: the metric of perceived space is a construction that combines fallible cues, each weighted by how reliable it is.

Perceiving Distance and Layout

No single cue specifies distance across the full range at which observers act, so the perception of layout rests on many cues that dominate at different scales. Binocular disparity and convergence are informative within a few metres, motion parallax and relative size across intermediate distances, and occlusion and height in the visual field across the whole range, with each cue's relative potency shifting as a function of distance (Cutting & Vishton, 1995). For an object resting on the ground plane, a particularly powerful cue is its angle of declination below the horizon: given an estimate of eye height, the horizontal distance to the object follows directly from that angle, which is the geometry the first demonstration makes explicit.

That perceived distances are accurate enough to guide action has been shown by visually directed tasks. When observers view a target on the ground up to about twenty metres away and then walk to it without vision, or point continuously to it while walking a different path, they stop at or point to the correct location, indicating that the perceived egocentric distance is close to veridical over this range even though verbal estimates are biased (Loomis et al., 1992). The perception of layout also draws on more than vision. When vision and touch both specify an object's size or shape, the nervous system combines them by weighting each according to its reliability, so that the combined estimate is more precise than either sense alone and matches the prediction of statistically optimal integration (Ernst & Banks, 2002). The second demonstration models this reliability-weighted combination and shows why the fused estimate is less variable than its components.

Frames of Reference

A perceived location must be expressed relative to something, and space perception uses more than one such origin. An egocentric representation specifies positions relative to the observer, or to a part of the observer such as the eye, head, or hand, whereas an allocentric representation specifies positions relative to the external world, using landmarks or environmental axes as the reference. These are genuinely different codes: the egocentric direction of an object changes whenever the observer turns, while its allocentric position does not, and many spatial tasks require translating between the two (Klatzky, 1998).

The primate posterior parietal cortex is central to this coordinate work. Neurons there represent the locations of targets for looking and reaching, and they combine retinal position with signals about eye and head position so that a target can be encoded in the frame appropriate to the action it will guide (Andersen et al., 1997). Because such transformations require holding a location in a stable frame while the eyes move, the parietal cortex also links spatial representation to attention, updating the represented position of a remembered target across each eye movement so that the world is perceived as stable despite the shifting image (Colby & Goldberg, 1999). Egocentric and allocentric codes are not exclusive alternatives but complementary representations that the brain maintains in parallel and combines according to the task (Burgess, 2006).

Spatial Updating

Because the observer moves, an egocentric representation of where things are goes out of date with every step and turn, and it must be revised continuously. Spatial updating is the process that keeps egocentric directions and distances current during self-motion, using information about the movement, from vision, from the vestibular system, and from proprioception, to compute the new relations between the body and remembered locations. That this updating is automatic and rapid is shown when observers who have learned the positions of surrounding targets are guided, without vision, to a new standpoint: they can point accurately to the targets from the new location, having updated all of the directions together rather than recomputing each one (Rieser, 1989).

The updating appears to operate on an egocentric representation that is transformed as a whole. When people imagine moving to a new position, they are slow and error-prone, but when they actually move, even without sight, their pointing stays fast and accurate, which suggests that real self-motion drives an obligatory transformation of the egocentric layout that imagined movement does not (Wang & Spelke, 2002). On this view, primary spatial representations are transient and egocentric, continually updated by self-motion, while enduring knowledge of a place is stored allocentrically and used to reset the egocentric frame when updating drifts. The interplay between a self-motion-driven egocentric estimate and a landmark-based allocentric estimate, each weighted by its reliability, is a recurring theme in models of how the two frames combine (Burgess, 2006). The third demonstration lets a reader move a simulated observer and watch the egocentric bearing to a fixed landmark update.

Reorientation and Environmental Geometry

When observers become disoriented, they recover their heading using the shape of the surrounding space. Disoriented rats searching for food in a rectangular enclosure distribute their errors in a telling way: they confuse a corner with the geometrically equivalent corner diagonally opposite, as though reorientation relied on the rectangular geometry of the space while ignoring non-geometric features such as distinctive wall colours or odours that would have resolved the ambiguity (Cheng, 1986). The finding suggested a dedicated geometric module that computes heading from the metric shape of the environment.

Young children behave the same way. Disoriented toddlers in a small rectangular room search equally at the correct corner and its diagonal opposite, failing to use a brightly coloured wall that uniquely specifies the target, even though they can use that wall in non-disoriented tasks, which indicates that reorientation initially draws on environmental geometry alone (Hermer & Spelke, 1994). With development, and in adults, non-geometric landmark information comes to be combined with geometry, and the strict modularity of the original proposal has been softened into a view in which geometry is a powerful but not exclusive cue to orientation (Wang & Spelke, 2002). Reorientation shows that allocentric spatial knowledge is anchored to the large-scale shape of a place, a theme that recurs in the neural representation of environments.

The Dorsal Cortical Pathway

Spatial vision is served by a cortical pathway distinct from the one that identifies objects. Lesion evidence in monkeys established that visual information leaving the striate cortex divides into two streams: a ventral stream, running toward the temporal lobe, that is needed to identify what an object is, and a dorsal stream, running toward the parietal lobe, that is needed to appreciate where an object is and the spatial relations among objects (Ungerleider & Mishkin, 1982). This what and where distinction gave the spatial functions of perception an anatomical home in the parietal cortex, consistent with the coordinate transformations described earlier (Andersen et al., 1997).

An influential reinterpretation recast the dorsal stream in terms of action rather than spatial awareness as such. On this account the ventral stream builds the perceptual representations that support recognition and conscious judgement, while the dorsal stream computes the moment-to-moment visual information needed to guide movements, so its role is less to know where things are than to control action toward them (Goodale & Milner, 1992). The evidence came from patients with dissociations: some, with ventral damage, could not report an object's size or orientation yet shaped the hand correctly to grasp it, while others, with dorsal damage, could describe an object but misreached for it. Whether the dorsal stream is best characterised as where or as how, the two-stream framework anchors the spatial and action-guiding aspects of perception in a pathway separate from object identification.

The Cognitive Map

Allocentric spatial knowledge has a well-characterised neural substrate in the hippocampal formation. Recording from the hippocampus of freely moving rats revealed place cells, neurons that fire when the animal occupies a particular location in an environment and are silent elsewhere, so that the population provides a maplike code of position that is anchored to the world rather than to the body (O'Keefe & Dostrovsky, 1971). Different environments recruit different place-cell maps, and the code is allocentric, tying the firing to places defined by the surrounding geometry and landmarks.

The metric for this map comes from a further cell type upstream. Grid cells in the medial entorhinal cortex fire whenever the animal is at any vertex of a regular triangular lattice tiling the environment, providing a distance-and-direction coordinate system that could support path integration and the updating of position from self-motion (Hafting et al., 2005). In humans, an allocentric representation of place has a counterpart in the parahippocampal place area, a region that responds strongly to scenes and spatial layouts, such as rooms and landscapes, and much more weakly to isolated objects, consistent with a system specialised for representing the local spatial environment (Epstein & Kanwisher, 1998). Together these findings give the allocentric cognitive map a concrete neural form and connect the perception of space to its storage in memory.

Criticisms and Open Questions

Several of the strong claims in this area have been qualified. The proposal that reorientation depends on an encapsulated geometric module has not held in its strict form: with larger spaces, training, or development, both children and adults readily combine landmark information with geometry, so geometry is better regarded as a highly salient cue than as the output of an impenetrable module (Wang & Spelke, 2002). Likewise the clean separation of a ventral what stream from a dorsal where or how stream is an idealisation; the pathways interact extensively, and parietal cortex contributes to spatial awareness as well as to the guidance of action, so a strictly dichotomous reading overstates the anatomy (Colby & Goldberg, 1999).

A second set of questions concerns the metric of perceived space itself. Because perceived distances in depth are compressed and the compression varies with viewing conditions, there is no single geometry that describes visual space across all tasks, and estimates obtained by different methods, verbal report, visually directed action, and perceptual matching, often disagree (Wagner, 1985). The dissociation between accurate visually directed walking and biased verbal judgements of the same distances suggests that different spatial representations may drive perception and action, so asking how far away something looks may not have one answer (Loomis et al., 1992). The mature view treats space perception not as the delivery of a single veridical model of the world but as a family of task-dependent representations, each constructed from reliability-weighted cues and each accurate enough for the use it serves.

Worked Example

The first demonstration models distance to an object on the ground from the angle of declination of the line of sight below the horizon. For an observer whose eye is at height h above a flat ground plane, an object on the ground at horizontal distance d is seen along a line depressed by an angle gamma below the horizontal, where the tangent of gamma equals h divided by d. Solving for distance gives d equal to h divided by the tangent of gamma. With an eye height of 1.6 metres, a declination of 5 degrees gives d equal to 1.6 divided by tan 5 degrees, or 1.6 divided by 0.0875, which is about 18.3 metres. A declination of 10 degrees gives 1.6 divided by 0.1763, about 9.1 metres, and 20 degrees gives 1.6 divided by 0.3640, about 4.4 metres. Equal increments of declination therefore correspond to shrinking increments of distance as the object nears the horizon, which is the geometric root of the depth compression in Figure 1.

The second demonstration models the optimal combination of two cues to the same quantity, such as the size of an object signalled by both vision and touch. If vision provides an estimate with variance sigma-v squared and touch an estimate with variance sigma-h squared, the statistically optimal combined estimate is a weighted average in which each cue's weight is proportional to its reliability, the reciprocal of its variance. Taking a visual standard deviation of 0.5 and a haptic standard deviation of 1.0, in arbitrary units, the visual variance is 0.25 and the haptic variance is 1.0. The visual weight is the reciprocal of 0.25 divided by the sum of the reciprocals of 0.25 and 1.0, that is 4 divided by 5, or 0.8, and the haptic weight is 0.2. The variance of the combined estimate is the product of the two variances divided by their sum, 0.25 times 1.0 divided by 1.25, which equals 0.2, so the combined standard deviation is about 0.447. Because 0.447 is smaller than either 0.5 or 1.0, combining the two senses yields an estimate more precise than either alone, which is the signature of optimal integration.

Discussion

Space perception is best understood not as a single achievement but as a coordinated set of solutions to the problem that the world's geometry is not given in the senses. The visual system reconstructs a metric layout from cues that are individually ambiguous, and it does so by weighting each cue and each sense by its reliability, an inferential strategy that also governs how vision and touch, and how self-motion and landmarks, are fused. The resulting space is represented in several frames at once, egocentric frames tied to the body for guiding action and allocentric frames tied to the world for memory and navigation, and the perceptual system spends considerable effort keeping these frames in register as the eyes, head, and body move. Table 1 sets the principal components of space perception side by side with the representation each involves and the evidence that most sharply characterises it.

Read this way, space perception connects low-level cue processing to high-level navigation within a single inferential story. The metric of perceived space is fallible and task-dependent, compressed in depth and reshaped by viewing conditions, yet it is accurate enough to let observers reach, walk, and find their way, because the same reliability-weighting that fuses cues also lets the system fall back on whichever representation is most trustworthy at the moment. What perception delivers is not a perfect map but a working one, continually rebuilt from partial evidence and kept aligned with the world just well enough for action.

Glossary

Allocentric representation.

A coding of spatial position relative to the external world, using landmarks or environmental axes rather than the observer as the reference.

Angle of declination.

The angle by which the line of sight to an object on the ground is depressed below the horizon, a cue from which distance can be recovered given eye height.

Binocular disparity.

The small difference between the two eyes' images of a scene, which provides information about relative depth.

Cognitive map.

An allocentric internal representation of the spatial layout of an environment, supporting navigation and memory for locations.

Cue integration.

The combination of multiple sources of spatial information, often weighted by reliability so the fused estimate is more precise than any single cue.

Dorsal stream.

The cortical visual pathway running from the striate cortex toward the parietal lobe, associated with spatial location and the visual guidance of action.

Egocentric representation.

A coding of spatial position relative to the observer or a part of the observer, such as the eye, head, or hand.

Frame of reference.

The origin and set of axes with respect to which spatial positions are specified.

Geometric module.

A proposed mechanism that recovers heading from the metric shape of the surrounding space, originally held to ignore non-geometric cues.

Grid cell.

A neuron in the medial entorhinal cortex that fires at the vertices of a regular triangular lattice tiling the environment, providing a metric for space.

Parahippocampal place area.

A human brain region that responds strongly to scenes and spatial layouts and weakly to isolated objects.

Place cell.

A hippocampal neuron that fires when the animal occupies a particular location in an environment, forming part of an allocentric map.

Posterior parietal cortex.

A cortical region that represents target locations for looking and reaching and transforms them between reference frames.

Spatial updating.

The revision of egocentric spatial representations during self-motion so that directions and distances to remembered locations remain current.

Vergence.

The inward rotation of the two eyes to fixate a near target, a signal that helps scale binocular depth to absolute distance.

Visual space.

The perceived geometry of the environment, whose metric departs systematically from that of physical space.

Visually directed action.

Movement to a previously seen target performed without ongoing vision, used to measure the accuracy of perceived egocentric distance.

Key Researchers

John O'Keefe (b. 1939). Professor at University College London and the Sainsbury Wellcome Centre; discovered hippocampal place cells and, with the cognitive-map theory, shared the 2014 Nobel Prize in Physiology or Medicine. ORCID - Faculty Page - Wikipedia)

Edvard I. Moser (b. 1962). Director of the Kavli Institute for Systems Neuroscience at NTNU; co-discovered grid cells in the entorhinal cortex and shared the 2014 Nobel Prize. ORCID - Faculty Page - Lab - Google Scholar - Wikipedia

Russell A. Epstein. Professor of Psychology at the University of Pennsylvania; identified the parahippocampal place area as a scene-selective region representing the local spatial environment. ORCID - Faculty Page - Lab - Google Scholar

Melvyn A. Goodale (b. 1943). Founding director of the Brain and Mind Institute at Western University; with A. David Milner, framed the dorsal stream as a system for the visual guidance of action. ORCID - Faculty Page - Google Scholar - Wikipedia

Richard A. Andersen (b. 1950). James G. Boswell Professor of Neuroscience at the California Institute of Technology; mapped multimodal reference frames and coordinate transformations in the posterior parietal cortex. Faculty Page - Lab - Wikipedia)

Roberta L. Klatzky. Professor of Psychology at Carnegie Mellon University; formalised the distinction between egocentric and allocentric spatial representations and their interconnections. ORCID - Faculty Page - Google Scholar - Wikipedia

Jack M. Loomis. Emeritus Professor of Psychological and Brain Sciences at the University of California, Santa Barbara; measured the accuracy of visually directed action to targets in perceived space. Faculty Page - Personal Page - Google Scholar

Frequently Asked Questions

What is space perception?
It is the set of processes by which observers recover the three-dimensional layout of the environment, and their own position within it, from sensory information that does not specify that layout uniquely (Cutting and Vishton, 1995).

Why is depth perception considered a problem?
Because each retinal image is a two-dimensional projection consistent with infinitely many arrangements of surfaces in depth, so the third dimension must be inferred by combining many partial cues rather than read off directly (Cutting and Vishton, 1995).

How does the brain combine different depth cues?
It weights each cue and each sense by its reliability and forms a weighted average, so the combined estimate is more precise than any single source, matching the prediction of statistically optimal integration (Ernst and Banks, 2002).

What is the difference between egocentric and allocentric space?
An egocentric representation locates things relative to the observer, so it changes as the observer moves, whereas an allocentric representation locates things relative to the world and stays fixed as the observer moves (Klatzky, 1998).

What is spatial updating?
It is the continuous revision of egocentric directions and distances to remembered locations during self-motion, shown when people point accurately to targets after being led without vision to a new standpoint (Rieser, 1989).

How do people reorient when they are lost?
They rely heavily on the geometric shape of the surrounding space, so that disoriented children and animals confuse a corner with its diagonally opposite, geometrically equivalent corner (Cheng, 1986).

What are place cells and grid cells?
Place cells are hippocampal neurons that fire at particular locations, and grid cells are entorhinal neurons that fire on a regular lattice, together providing a neural map and metric for allocentric space (Hafting et al., 2005).

Is the dorsal visual stream for where or for how?
It was first described as a where pathway for spatial location, then reinterpreted as a how pathway that computes the visual information guiding action, and current views treat it as doing both (Goodale and Milner, 1992).

References