Series

Cheirality — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. 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.

    part 2 · twoviews
  2. 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.

    part 3 · twoviews

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