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

Essential matrix — where it appears

The fundamental matrix with the calibration divided out, so it carries the relative rotation and the direction of the translation and nothing else. It decomposes into four poses, of which visibility selects one — and on a critical surface the same matrix supports two different motions.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

points in front of both camerasR₁, t0 of 44180° from the truthR₁, t reversed0 of 44180° from the truthR₂, t44 of 44chosenR₂, t reversed0 of 44180° from the truththe chosen pose is the true one to 0.0e+0°cheirality, not algebra, picks it

Four cameras fit, and one of them can see

The essential matrix does not determine a camera pair. It determines four, all of which reproject every correspondence exactly, and the thing that picks one is not more algebra — it is the assumption that the photographer could see what was photographed.

twoviews · Cheirality both explain both photographs exactly11.4 m apart, median

The surface two pictures cannot separate

There is a quadric through both camera centres on which two genuinely different motions draw identical pictures. Built explicitly, forty-two marks satisfy both epipolar geometries to 2 × 10⁻¹³ pixels, and the two scenes they reconstruct place the same mark at 15.6 metres and 35.1. The design matrix's nullspace has two dimensions rather than one, which is the seven-point situation arrived at from the other side.

twoviews · Critical horizonthe post, and the post behind the eyecorrect from 14 cm, at 160 mm wideone mark to 6.4e-14 px · off-eye centre 51 px away

The picture contains what is behind the camera

A pinhole maps a direction, and a line has one direction, so a point behind the eye lands on exactly the same mark as its reflection in front — here to 6.4e-14 pixels. The sign the division throws away is why cheirality is a fact supplied from outside the picture rather than measured in it.

foundations · Behind

Named alongside it

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

CheiralityEpipolar geometryFundamental matrixReconstructionreconstruction ambiguityAmbiguityBaselineCamera matrixcentre of projectionCorrespondenceCritical surfaceDegeneracy

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