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

Cheirality — where it appears

The requirement that a reconstructed point lie in front of the camera that saw it. A pinhole maps a direction, so a point and its reflection through the eye leave one mark, and this is the fact brought from outside the picture to choose among reconstructions that fit the marks equally well.

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 the true planefirst number of the plane, from the true valuesecond44 points in front: 31.9 % of the slicethe third number held at its true value

Seeing the scene fences in the plane at infinity

A reconstruction made without the calibration does not know which of its planes is infinitely far away. Requiring every point to lie in front of both cameras rules out every candidate that would tear the courtyard, and what is left is a convex region — 32 per cent of a generous slice — that always holds the true plane and never shrinks to it.

twoviews · Cheirality 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.

Camera matrixEssential matrixreconstruction ambiguityBaselinecentre of projectionConvex hullCorrespondenceDepthEpipolar geometryFundamental matrixHomographyPlane at infinity

All concepts