Visual Plane
every picture states the point it is correct from
Concept

Depth from disparity — where it appears

Depth recovered from how far a point shifts between two views, which is the baseline times the focal length over the distance. Because it is a reciprocal, a fixed error in the picture maps to an interval in the world that is not symmetric and eventually is not bounded.

Named by 5 essays across 4 fields — each of them below, with the objects they name alongside it.

in units of the 1.20 m fixation distance0.0000 cm over 121 azimuths

The depth a pair calls zero

Two eyes verged on a point agree — the same coordinate in both pictures — not on a plane at the fixation distance but on a circle through both eyes and that point. Found by bisection along 121 azimuths and fitted rather than assumed, it is a circle to 0.0000 cm; at 26° off centre it lies 23 cm nearer than a flat wall does.

depth · Horopter 020406012345the baseline between the two eyes (metres)angle between the cone axes (°)42.6°two cones, one ballcentre to 9e-7°

Two pictures of a ball

Two outlines give two tangent cones, and where their axes cross is the ball's centre — with the radius following from either half-angle. There is no correspondence problem, because a ball's outline in one picture and its outline in another are guaranteed to be the same ball; and there is a degeneracy, which is the two eyes and the ball in a line, and the solver refuses it rather than returning something plausible.

metrology · Ballrecovery -10100.5001the screen's radius, log₁₀ metresvertical difference between the eyes, log₁₀ arcminutesa stated fusion limit, 15′eyes 63 mm apart, at each screen's own sitting distanceunder the limit throughout

What the two eyes are sent

A reader's eyes are two seats sixty-three millimetres apart, so a curved screen delivers each of them a different map — and the part of the difference no homography absorbs is binocular evidence of the glass. Turned into a depth it comes back as the screen's own sag, 49 millimetres against 47 on a television, by a route that never saw the radius.

screen · Stereodisplay a wall at 10 m0 px−0.25 m0.25 px+0.17 m0.5 px+0.64 m0.75 px−0.64 m7 m8 m9 m10 m11 m12 m13 m14 mf = 900 px, B = 65 mm, whole pixelsshift 0.150 px puts a shell on the wall

A rectification's free shift is free only near the pair

Sliding a rectified pair's principal points apart adds a constant to every disparity, and a constant changes nothing about where points are — on paper. A whole-pixel reading is not paper. The same slide moves every depth the reading can report, and for a wall ten metres away the choice between the best shift and the worst is 1.71 metres. Near the pair it is millimetres. A matcher with half a pixel of its own error erases the choice, and pays more than the worst shift did.

depth · Disparity -500500.5001distance to the thing being stitched (log₁₀ metres)what the stitch leaves behind (px)2.86 m80 mm baselinezero at one depth each

A rig is right on one surface

Several cameras looking outward have several centres, and no warp registers all of a scene. The residual is a disparity, so the depth the stitch is computed for has an exact optimum — the harmonic midpoint of the depth range, not the middle of it — and the arithmetic middle costs a factor of 2 z_far over the sum, which tends to two.

curved · Stitchdepth

Named alongside it

The objects these essays reach for when they reach for this one.

DisparityBaselineBinocular disparityDemonstrationPicture surfaceReconstructionTriangulationViewing positionAngular sizeBiasCalibrationcentre of projection

All concepts