Depth Perception¶

Recover egocentric distance, depth order, and three-dimensional scene layout from two-dimensional retinal projections by exploiting binocular disparity, motion, occlusion, perspective, texture, oculomotor state, and their reliability-sensitive combination.

Version: v2 · 2026-09-06 · History
Domain-specific #: 1645
Origin domain: cognitive science
Subdomain: visual perception and psychophysics
Aliases: Visual depth perception

Core Idea¶

Depth perception is the visual capacity to estimate where surfaces and objects lie in three-dimensional space from optical inputs that do not contain depth as a directly labeled coordinate. Each retina receives a two-dimensional projection. The visual system recovers useful spatial structure by exploiting lawful relations between scene geometry and image structure: the difference between the two eyes' images, eye posture, occlusion, relative retinal size, texture compression, linear perspective, shading, motion parallax, and optical expansion. The outputs include egocentric distance from observer to object, relative or ordinal depth among objects, surface slant and curvature, and a more global three-dimensional layout.^[1]^[2]

No single cue is depth perception. Binocular disparity can support stereopsis even when recognizable monocular contours are absent, as Julesz's random-dot stereograms demonstrated.^[3] Motion parallax can generate a compelling depth ordering from viewpoint-contingent image motion without disparity.^[4] Occlusion establishes which surface is in front without specifying the distance between them. Perspective and texture can support layout from one stationary eye, but only under assumptions about parallelism, surface regularity, or object size. Vergence and accommodation are short-range oculomotor cues. Their operating ranges, ambiguities, and noise differ.

The system therefore uses cues conditionally. When several cues bear on one spatial quantity, their influence can change with reliability, viewing distance, task, and conflict. Landy and colleagues formalized cue promotion, dynamic weighting, and robust combination; Knill and Saunders showed that stereo and texture weights in slant judgments tracked subjects' cue reliabilities closely.^[2]^[5] That result does not imply that every depth judgment is an exact Gaussian Bayesian computation. Some cues are correlated, some supply different quantities, some veto impossible interpretations, and some dominate categorically. Reliability-weighted fusion is a strong recurrent component, not a definition of the entire capacity.

The locked identity is:

three-dimensional scene + retinal projections, observer geometry, and dynamic image changes + cue-specific depth estimators + context- and reliability-sensitive reconciliation -> egocentric distance, depth order, surface orientation, or three-dimensional layout judgment.

Depth perception is thus an inference capacity under projection loss, not literal recovery of a complete Euclidean model. It earns its name when an observer's percept, judgment, or visually guided action varies systematically with information that bears on depth and survives controls for mere detection, object identity, or two-dimensional position.

Structural Signature¶

Sig role-phrases:

the distal three-dimensional layout — surfaces and objects with physical distances, depth order, orientations, and shapes in the world
the retinal projections — two-dimensional eye-centered images that preserve some projective relations while omitting an explicit depth coordinate
the observer geometry and state — interocular separation, eye position, accommodation, head motion, and locomotion that determine which cues are available
the depth-cue family — binocular disparity and vergence; occlusion, relative size, perspective, texture, shading, and focus; motion parallax and optical expansion
the cue-specific estimators — operations that convert each cue's image relation into ordinal, relative, or metric spatial information under stated assumptions
the compatibility and reliability profile — the task- and condition-dependent pattern of agreement, conflict, uncertainty, correlation, and valid operating range across cues
the reconciliation process — selection, veto, promotion, or reliability-sensitive combination that produces one usable spatial interpretation
the depth output — an egocentric distance, depth ordering, surface slant, three-dimensional form, or layout estimate with finite precision
the behavioral readout — discrimination, matching, reaching, walking, interception, navigation, or another response that makes the depth estimate testable

Recognition test. A case instantiates depth perception only if optical or oculomotor information changes an estimate or action concerning distance, depth order, surface orientation, or three-dimensional layout. A two-dimensional feature detector, a drawing that merely contains perspective, or a response to object identity is insufficient. Strong evidence manipulates or conflicts depth cues while holding the target and irrelevant image properties controlled, then measures the predicted change in a depth-specific judgment. A single-cue demonstration can qualify; multiple-cue fusion is common but not required.

What It Is Not¶

Not stereopsis alone. Stereopsis is depth from binocular disparity. Monocular observers and stereoblind observers can still use occlusion, perspective, texture, motion, and familiar size, though with a different precision profile.
Not a flat image's perspective construction. Perspective is a projective relation or representational technique. Depth perception is the observer-side recovery of spatial layout, for which perspective is one possible cue.
Not the Kinetic Depth Effect as a whole. The Kinetic Depth Effect recovers three-dimensional form from changing two-dimensional structure under motion and rigidity constraints. It is one dynamic subtype within the larger cue family.^[6]
Not an exact range finder. Many depth cues yield order or relative slant rather than metric distance. A vivid three-dimensional percept can be systematically compressed, biased, or scale-ambiguous.
Not guaranteed veridical reconstruction. Cue conflicts, false perspective, unusual scale, display geometry, or an invalid prior can produce a stable but wrong depth percept.
Not time-to-contact by itself. Optical expansion can support both depth and approach judgments, but time-to-contact additionally depends on relative velocity; equal distance with different approach speeds gives different contact times.
Not object recognition or figure-ground assignment. Recognizing what an object is or segregating it from background can help interpretation, but neither establishes where it lies in depth.
Not a universal fixed cue hierarchy. Disparity does not always dominate texture, nor vision motion, nor binocular over monocular information. Influence changes with cue reliability and task.^[2]^[5]

Scope of Application¶

Depth perception has a bounded but broad habitat wherever visual organisms or visual displays support judgments of three-dimensional layout.

Binocular vision and stereopsis: retinal disparity, correspondence, fusion limits, and stereoacuity support near-space depth and surface-shape judgments.
Monocular and pictorial space: occlusion, relative size, texture gradient, perspective, shading, blur, and familiar size support depth in natural scenes and pictures.
Active and dynamic vision: observer translation produces motion parallax; object or surface motion can reveal structure; optical expansion informs approach and spatial change.^[4]^[6]
Visually guided action: reaching, grasping, stepping, locomotion, driving, and interception use depth estimates, though action-specific calibration may differ from explicit verbal judgment.
Clinical binocular vision: strabismus and amblyopia can disrupt binocular cooperation, stereopsis, ocular motor function, and fine visuomotor performance; treatment and assessment therefore cannot be reduced to monocular acuity alone.^[7]
Stereoscopic and immersive displays: disparity can specify simulated depth while focal distance remains at the screen, creating cue conflicts that affect performance and comfort.^[8]
Comparative vision: species with different eye placement and movement strategies exploit different cue portfolios; the conservative claim is shared depth-sensitive behavior, not identical human phenomenology.
Machine and biological comparison: computer vision also reconstructs depth, but algorithms and sensors instantiate a neighboring inverse problem. The encyclopedia identity here remains biological visual perception unless a claim explicitly concerns observer behavior or perceptual organization.

Clarity¶

Four distinctions prevent the cue list from becoming a bag of loosely related effects.

First, egocentric distance, relative depth, and three-dimensional shape are different outputs. Occlusion can establish that A is in front of B without saying how far either is from the observer. Binocular disparity can specify local relative depth around fixation more precisely than absolute range. Texture and perspective may constrain surface slant while leaving global scale uncertain. A study must name which output its response measures.

Second, an image correlate becomes a cue only under a mapping and assumptions. Smaller retinal size means farther only when physical size is known or treated as comparable. Converging lines indicate depth under assumptions about parallel lines and projection. Shading indicates relief only under assumptions about illumination and reflectance. The assumptions are not optional decoration; they explain both ordinary success and controlled illusion.

Third, cue availability is not cue use. A display may contain disparity, texture, and perspective while a participant relies primarily on one. Cue-conflict experiments estimate use by placing cues in controlled disagreement and measuring the perceptual compromise. A cue's influence can also change when noise, distance, attention, or task changes.^[2]

Fourth, precision and accuracy are distinct. Repeated judgments may cluster tightly around a biased depth value, or average near the true value with high variability. Cue integration predicts precision gains under conditions such as partially independent noise and calibrated reliability; it does not guarantee accuracy when all cues share a bias or when the scene violates the assumed generative model.

Manages Complexity¶

Depth perception converts a long cue inventory into an auditable workflow.

Declare the spatial target: distance, order, slant, shape, or layout.
Specify observer and scene geometry: viewing distance, eye separation, fixation, head motion, object scale, and surface structure.
Inventory available cues: distinguish binocular, monocular-static, oculomotor, and dynamic information.
State each cue's assumptions and range: for example, familiar size needs a size prior; disparity loses metric leverage with distance; motion parallax requires observer-motion information.
Measure single-cue precision where possible: isolate disparity, texture, motion, or another cue rather than presuming its influence from presence.
Create cue agreement and conflict conditions: perturb one cue while holding others stable to recover weights, vetoes, or nonlinear interactions.
Separate perceptual output from response method: verbal reports, matching, reaching, and locomotion can add different motor or decision transformations.
Intervene at the failed role: restore a missing binocular input, add a robust monocular cue, recalibrate a display, reduce conflict, or redesign the task around the observer's available cue set.

This workflow localizes error. A poor stereo judgment may reflect weak disparity sensitivity, a correspondence failure, excessive disparity, conflict with focus, or a response-scale problem. Those failures call for different repairs. “Bad depth perception” is too coarse; the signature identifies the cue, assumption, reconciliation step, or readout that failed.

Abstract Reasoning¶

The geometry explains why depth is both recoverable and underdetermined. A point at distance Z projects to an eye-centered angular position; moving the viewpoint or adding a second eye changes that projection in a distance-dependent way. For small lateral observer motion v, image angular velocity is approximately proportional to v/Z, so nearer points move faster across the visual field than farther points. Rogers and Graham isolated this transformation in random-dot displays and obtained compelling, quantitatively ordered depth without other depth cues.^[4]

Binocular disparity likewise compares the two projections. Around a fixation distance Z0, horizontal disparity for a point at distance Z is approximately proportional to interocular separation times (1/Z - 1/Z0) under the small-angle approximation. The sign gives near-versus-far relative to fixation; magnitude supplies relative depth within a useful range. Julesz's random-dot stereograms showed that disparity can support depth even when each monocular image lacks recognizable form boundaries.^[3]

When two approximately independent cues estimate the same scalar depth D with variances sigma_1^2 and sigma_2^2, a reliability-weighted model gives

D_hat = w_1 D_1 + w_2 D_2, where w_i = (1/sigma_i^2) / [(1/sigma_1^2) + (1/sigma_2^2)].

Suppose stereo estimates a surface at 60 cm with sigma_s = 2 cm, while texture estimates 66 cm with sigma_t = 4 cm. Precisions are 1/4 and 1/16, so weights are 0.8 and 0.2; the fused estimate is 61.2 cm. The combined standard deviation is sqrt(1/(1/4 + 1/16)), approximately 1.79 cm, narrower than either input. This is an illustrative computation, not a claim that every depth cue pair satisfies independence or Gaussian noise. Correlated cues, categorical occlusion, incompatible quantities, and out-of-range estimators require a different model.^[2]^[5]

The intervention logic follows from the same analysis. If a cue is precise but biased, reduce its influence by recalibration rather than by adding more copies of it. If two cues share error, do not count them as independent evidence. If a cue is only ordinal, do not force it to supply metric distance. If conflict reveals a fixed winner despite changing reliabilities, investigate veto, causal-inference, or task-strategy accounts rather than calling the result optimal fusion.

Knowledge Transfer¶

Within vision science, the full framework transfers literally from stereopsis to pictorial space, motion-defined structure, clinical binocular function, and stereoscopic displays. The scene, projection, cue-specific operation, depth estimate, and behavioral readout remain the same roles even as the available cue changes. A researcher trained on stereo-texture conflicts can apply the same isolation and perturbation logic to motion-texture or disparity-focus conflicts.

Beyond biological vision, the transfer is shared abstract mechanism, not permission to rename every reconstruction problem “depth perception.” The portable skeleton belongs chiefly to Projection and Bayesian Cue Integration. A camera or retina maps richer spatial structure into a lower-dimensional image; a reconstruction process uses side information and constraints; multiple noisy estimators may be combined by reliability. Those relations recur in robotics, remote sensing, and statistical estimation. What does not transfer automatically is stereopsis, vergence, accommodation, perceptual experience, cue promotion, visual adaptation, or the behavioral calibration of an organism.

This boundary is useful. Computer-vision depth estimation can suggest experiments about cue failure, but agreement between an algorithm and human judgments does not establish a shared biological mechanism. Conversely, a human illusion can expose ambiguity in the image without showing that every machine system will make the same error. The legitimate cross-domain lesson is to identify information lost in projection, state the assumptions used to reconstruct it, measure estimator reliability, and test conflicts. The name Depth Perception remains at home in vision because its operative units are visual cues and perceivers, not arbitrary data and estimators.

Examples¶

Canonical: random-dot stereograms isolate binocular disparity¶

Julesz generated paired random-dot images that were individually pattern-like and lacked recognizable monocular object contours. A region in one eye's image was shifted horizontally relative to the corresponding region in the other. When the two images were fused binocularly, observers perceived the shifted region at a different depth. The construction isolated binocular disparity: the depth boundary was not recoverable from either monocular image alone, yet emerged from correspondence between them.^[3]

Mapped back: the distal layout was an experimentally specified near-or-far patch; two retinal projections carried controlled disparity; observer geometry permitted binocular correspondence; the cue-specific estimator recovered relative depth; competing monocular cues were suppressed; and the behavioral report made the three-dimensional percept testable. The intervention is equally explicit: alter disparity magnitude or sign and the perceived relative depth should change accordingly, within fusion limits.

Applied / In Practice: disparity-focus conflict in a stereoscopic display¶

A conventional stereoscopic display presents separate left- and right-eye images whose disparity specifies a simulated object in front of or behind the screen. The light, however, still comes from the physical screen, so accommodation remains tied to screen distance while disparity drives vergence toward the simulated distance. Hoffman and colleagues used displays that allowed these cues to be consistent or conflicting and found that conflict hindered visual performance and increased fatigue.^[8]

Mapped back: the virtual scene supplied intended depth; the two eye images supplied disparity; the fixed focal surface supplied a conflicting focus cue; their reliability and compatibility profile altered the reconciled percept and viewing cost; and task performance and fatigue supplied readouts. The design intervention is not “add more 3D.” It is to reduce disparity-focus separation, constrain content to a tolerable depth range, or use a display architecture that better aligns focal and vergence demands.

Structural Tensions¶

T1: Redundancy versus conflict. Multiple cues make depth robust when one becomes noisy, but the same redundancy creates a reconciliation problem when cues disagree. A fused compromise can improve precision in ordinary scenes and become a systematic illusion in a manipulated display. Diagnostic: When the cues are placed in conflict, does the judgment track a reliability-sensitive compromise, a categorical veto, or one invariantly dominant cue?

T2: Metric accuracy versus ordinal robustness. Occlusion and motion can support reliable front-versus-back order even when absolute distance is poorly calibrated. Demanding metric output from an ordinal cue makes a successful system look defective; accepting only ordinal output can hide errors that matter for reaching or navigation. Diagnostic: Does the task require ordering, relative separation, or calibrated egocentric distance, and is the chosen cue capable of that quantity?

T3: Learned assumptions versus current optical evidence. Familiar size, likely lighting, rigidity, and surface regularity stabilize an underdetermined image, but they can overpower unusual yet genuine evidence. The same prior that resolves ordinary scenes produces error in forced perspective or atypical scale. Diagnostic: Does changing the assumed scene statistics reverse the depth judgment while the immediate image relation remains constant?

T4: Stereoscopic richness versus monocular sufficiency. Binocular disparity supports fine relative depth, but equating depth perception with stereopsis erases the extensive monocular and dynamic portfolio. Conversely, demonstrating monocular depth does not show that binocular loss is inconsequential for precision or visuomotor function. Diagnostic: Which depth judgments degrade after disparity is removed, and which remain supported by motion, occlusion, texture, or perspective?

T5: Active sensing versus experimental isolation. Head and body movement create informative parallax and close the perception-action loop, while laboratory fixation isolates cues cleanly. Isolation improves causal attribution but can remove the very action-generated information used in natural behavior. Diagnostic: Does the effect survive when observers can move, and does allowing movement introduce a new cue rather than merely improve attention?

T6: Simulated depth versus physiological consistency. A display can generate vivid disparity-defined depth while forcing accommodation to remain at the screen. Increasing simulated depth may strengthen the intended percept and simultaneously increase cue conflict and fatigue. Diagnostic: Are disparity, focus, perspective, and motion specifying compatible distances over the display's intended viewing range?

T7: Autonomous visual construct versus reduction to parent primes. Projection explains why depth is missing from each retinal image, and Bayesian Cue Integration explains one recurring fusion rule, yet neither supplies the visual cue taxonomy, stereoscopic correspondence, ocular geometry, psychophysical readouts, or clinical failures. Diagnostic: Can the case be diagnosed and repaired using only generic projection and weighting language, or must one know which visual cue and spatial output failed? The former belongs to the parents; the latter retains Depth Perception as an autonomous domain node.

Structural–Framed Character¶

Depth Perception is mixed-structural, domain-anchored on the structural–framed spectrum. Its inverse-from-projection and cue-reconciliation skeleton is structurally clear, but the node's identity depends on the visual architecture and experimental practices that make a cue a depth cue.

Vocabulary travels partially. Projection, estimator, reliability, and reconciliation travel; retinal disparity, stereopsis, vergence, accommodation, motion parallax, and depth judgment do not retain their meanings outside vision.
Evaluative weight is low. “Accurate” and “biased” are comparisons to scene geometry or task criterion, not moral or institutional judgments.
Institutional origin is moderate. The capacity is biological, but its cue taxonomy and operational boundaries are stabilized by psychophysics, ophthalmology, and vision science.
Human-practice binding is low to moderate. Nonhuman animals can display depth-sensitive behavior without a research institution, yet named cue weights and perceptual outputs require an observational and experimental frame.
Import versus recognition is mixed. A reliability-weighted inverse problem is recognized in other fields; importing Depth Perception as such requires a visual observer, optical projection, and depth-specific response.

Its portable skeleton is projection loss followed by constrained, sometimes reliability-sensitive reconstruction. Its character: a strongly structural visual capacity whose specialist cue vocabulary and perceptual validation keep the named abstraction within vision science.

Structural Core vs. Domain Accent¶

This section decides why Depth Perception is a domain-specific abstraction rather than a new prime.

What is skeletal. A richer distal structure is projected into a lower-dimensional observation, so recovery requires side information, constraints, or multiple estimators. When several noisy estimates bear on one quantity, their influence may scale with reliability. This skeleton travels intact as the parent patterns Projection and, in multi-cue cases, Bayesian Cue Integration. It supports general questions: what did the projection discard, which constraints restore identifiability, which estimators share error, and how should reliability affect influence?

What is domain-bound. The distinctive content is the visual mapping between scene geometry and retinal or oculomotor variables: interocular disparity, correspondence, vergence, accommodation, occlusion, relative size, perspective, texture gradient, shading, motion parallax, and optical expansion. The outputs are phenomenological and behavioral spatial judgments made by a visual organism. Fusion limits, stereoacuity, amblyopia, strabismus, head movement, cue promotion, and disparity-focus conflict have no unchanged meaning in a generic inference system. Remove the visual observer and the mapping from optical cue to perceived distance, and the remaining inverse problem is no longer Depth Perception.

Why this does not clear the prime bar. Cross-domain reuse works only after renaming retinal images as measurements, disparity and texture as estimators, and perceptual layout as a latent state. That translation preserves the parents but strips away the candidate's diagnostic and intervention package. A Kalman filter may fuse range sensors using the same mathematics, but it has no stereopsis, vergence, pictorial cue, or perceptual illusion unless those are added by analogy. Within vision, the full identity is recognized across scenes, observers, tasks, and species. Beyond vision, the general lessons belong to Projection and Bayesian Cue Integration. The breadth therefore supports an autonomous domain node, not a substrate-independent prime.

Projection — presupposes. Optical imaging maps three-dimensional scene structure onto two-dimensional retinal surfaces and omits an explicit depth coordinate. Depth perception exists because the observer must recover useful spatial structure from that loss.^[1]
Bayesian Cue Integration — typically contains. When multiple partly independent cues estimate the same depth quantity, their weights can track reliability and their combination can improve precision.^[2]^[5] Single-cue depth remains possible, so this is a characteristic component rather than a universal taxonomic genus.
Perspective — related cue and boundary. Perspective supplies representational geometry from which a perceiver may infer depth. A perspective drawing can exist without being perceived as three-dimensional, and depth can be perceived without linear perspective.
Perception-Action Loop — often manifests. Head movement and locomotion create motion parallax, while the resulting depth estimate guides the next movement. Static pictorial or stereoscopic depth does not require the full loop.
Kinetic Depth Effect — domain subtype, not prime parent. It is the motion-defined recovery of three-dimensional structure from changing two-dimensional projections, one specialist route within the larger depth capacity.^[6]

Relationships to Other Abstractions¶

Current abstraction Depth Perception Domain-specific

Parents (2) — more general patterns this builds on

Depth Perception is part of, typical Bayesian Cue Integration Prime

Bayesian Cue Integration — typically contains. When multiple partly independent cues estimate the same depth quantity, their weights can track reliability and their combination can improve precision.
Depth Perception presupposes Projection Prime

Projection — presupposes. Optical imaging maps three-dimensional scene structure onto two-dimensional retinal surfaces and omits an explicit depth coordinate.

Children (2) — more specific cases that build on this

Double-Nail Illusion Domain-specific is a kind of Depth Perception

related when eye convergence, fixation, head motion, or reaching changes the evidence and reveals or destabilizes the percept.
Looming Domain-specific is a kind of Depth Perception

Depth Perception is the proposed immediate parent: looming is a dynamic, primarily monocular cue for changing egocentric distance and approach.

Hierarchy paths (2) — routes to 2 parentless roots

Depth Perception → Projection → Abstraction

Show alternative path (1)

Neighborhood in Abstraction Space¶

Depth Perception sits in a sparse region of the domain-specific corpus (73^rd percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Depth, Motion & Spatial Perception (7 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-09-08

Not to Be Confused With¶

Stereopsis. Depth from binocular disparity is one route within Depth Perception. Tell: Would the judgment survive monocular viewing using occlusion, texture, perspective, or motion?
Perspective. Perspective is a projection or representational relation; Depth Perception is an observer's spatial inference. Tell: Is the claim about how depth is depicted, or about a perceiver's distance or layout judgment?
Kinetic Depth Effect. This subtype recovers three-dimensional structure from image motion. Tell: Is motion the defining information, or can the case use static or binocular cues?
Perceptual Constancy. Constancy keeps an object's perceived property stable across changing proximal input; depth perception estimates spatial layout itself. Tell: Is the output stable object size or shape despite viewing change, or the object's distance and depth relation?
Figure-Ground Organization. Figure-ground assigns border ownership and foreground status, which can correlate with depth order. Tell: Does the response identify a figure, or estimate which surface is nearer and by how much?
Optical Flow and Time-to-Contact. Flow describes image motion and time-to-contact combines expansion with relative speed. Tell: Is the output an image-velocity field or arrival time, or a spatial distance and layout estimate?
Computer-Vision Depth Estimation. Algorithms recover range from stereo, motion, shading, or learned priors. Tell: Is the claim about an algorithmic map, or about perceptual experience and behavior of a visual organism?
Bayesian Cue Integration. This prime is the precision-weighted combination rule for multiple noisy estimates. Tell: Is the claim the general fusion computation, or the visual cue family and depth-specific capacity that may also operate from a single cue?

References¶

[1] David Marr, Vision: A Computational Investigation into the Human Representation and Processing of Visual Information, W. H. Freeman, 1982. Authoritative computational treatment of vision as recovery of distal structure from retinal images. registry ↩a ↩b

[2] Michael S. Landy, Laurence T. Maloney, Elizabeth B. Johnston, and Mark Young, “Measurement and Modeling of Depth Cue Combination: In Defense of Weak Fusion”, Vision Research 35(3), 1995, pp. 389–412. Authoritative review and model of cue promotion, dynamic weighting, robustness, and experimental perturbation in human depth-cue combination. registry ↩a ↩b ↩c ↩d ↩e ↩f

[3] Bela Julesz, “Binocular Depth Perception of Computer-Generated Patterns”, Bell System Technical Journal 39(5), 1960, pp. 1125–1162. Primary random-dot stereogram experiments isolating binocular disparity as sufficient for vivid relative depth. registry ↩a ↩b ↩c

[4] Brian Rogers and Maureen Graham, “Motion Parallax as an Independent Cue for Depth Perception”, Perception 8(2), 1979, pp. 125–134. Primary random-dot experiments isolating observer-contingent parallax as a compelling and quantitatively ordered depth cue. registry ↩a ↩b ↩c

[5] David C. Knill and Jeffrey A. Saunders, “Do Humans Optimally Integrate Stereo and Texture Information for Judgments of Surface Slant?”, Vision Research 43(24), 2003, pp. 2539–2558. Primary experiments finding cue weights that closely track subjective reliability across surface slants and observers. registry ↩a ↩b ↩c ↩d

[6] Hans Wallach and D. N. O'Connell, “The Kinetic Depth Effect”, Journal of Experimental Psychology 45(4), 1953, pp. 205–217. Primary experiments establishing recovery of three-dimensional form from changing two-dimensional projections. registry ↩a ↩b ↩c

[7] Eileen E. Birch, “Amblyopia and Binocular Vision”, Progress in Retinal and Eye Research 33, 2013, pp. 67–84. Authoritative review connecting binocular dysfunction in amblyopia with visual, ocular-motor, and fine-motor deficits and motivating binocular treatment approaches. registry ↩

[8] David M. Hoffman, Ahna R. Girshick, Kurt Akeley, and Martin S. Banks, “Vergence–Accommodation Conflicts Hinder Visual Performance and Cause Visual Fatigue”, Journal of Vision 8(3), 2008, article 33. Primary display experiments comparing consistent and conflicting vergence and focal cues. registry ↩a ↩b