Chapter 2 · Optional lab
The visual lab
Realistic illustrations of the eye and retina, an interactive model of receptive fields and clickable maps of the visual pathways. No scores or assessments – explore for as long as it helps.
Binocular depth
What changes when you move your gaze?
Move the object or change fixation independently. Follow the same point in the two eyes’ visual-direction views and compare its positions relative to gaze.
Left eye · 0.61°
Right eye · -0.61°
Calculated disparity (L − R)Nearer · crossedCalculated vergence angle: 2.44°
- Object point: 1.00 m · To object
- Fixation point: 1.50 m · To fixation
The point is nearer than fixation: it falls right of gaze in the left-eye view and left in the right-eye view. This is crossed disparity in this example.
Upright, gaze-centred visual-direction views — not inverted retinal images. Both use the same fixed scale: right means right in both panels. The point stays the same size to isolate the position difference. The cross marks 0°, the gaze direction.
Top view: a filled point marks the same feature on the object; the cross is the fixation point. Solid lines lead to the object, dashed lines to fixation. Lateral eye spacing is exaggerated; angles in the diagram are not to scale.
These panels explain image differences on an ordinary screen; no special stereo viewing is needed. They do not send separate images to your actual eyes or predict fusion or double vision. More disparity does not mean better depth vision.
The geometry behind the images
This is a central horizontal example: object and fixation lie on the midline. Eye separation is a fixed example value, 0.064 m, not an estimate of your eyes. Only the point’s direction is calculated; we do not model the whole object image, neuronal responses or accommodation.
For each eye, the direction to fixation is subtracted from the direction to the object. Disparity is left minus right direction angle. With these particular upright coordinates, positive means crossed/nearer and negative means uncrossed/farther. Other coordinate choices can reverse the sign, and zero disparity here applies to the fixated midline point – not to every point across a flat region at the same distance. The fixed image scale is −3° to +3°.
aR = −aL
d = aL − aR
Vergence = 2 atan((b/2)/f)
atan gives radians; displayed angles are converted to degrees.
Sources
- Wheatstone, C. (1838). Contributions to the physiology of vision.—Part the first. On some remarkable, and hitherto unobserved, phenomena of binocular vision. Philosophical Transactions of the Royal Society of London, 128, 371–394. DOI: 10.1098/rstl.1838.0019.
Historical geometric experiments with binocular images; obsolete absolute physiological claims are not adopted here.
- Julesz, B. (1964). Binocular depth perception without familiarity cues. Science, 145(3630), 356–362. DOI: 10.1126/science.145.3630.356.
Human random-dot psychophysics: disparity-based depth without prior recognition of familiar objects.
- Cumming, B. G. & Parker, A. J. (2000). Local disparity not perceived depth is signaled by binocular neurons in cortical area V1 of the macaque. Journal of Neuroscience, 20(12), 4758–4767. DOI: 10.1523/JNEUROSCI.20-12-04758.2000.
Macaque V1 single-unit recordings with locally ambiguous gratings; distinguishes local disparity from perceived depth, not human neuronal recordings.
- Hillis, J. M., Watt, S. J., Landy, M. S. & Banks, M. S. (2004). Slant from texture and disparity cues: optimal cue combination. Journal of Vision, 4(12), 967–992. DOI: 10.1167/4.12.1.
Human psychophysics: slant judgments and reliability-weighted texture/disparity combination under the study’s conditions, not universal optimality.
Illustrations and models for learning; not measurements.