Series

Epipolar — the series

3 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. 1234512345a point is chosen hereand must be on this linematch to its own epipolar line: 1.4e-13 px5 of 44 correspondences drawn

    A point is a line over there

    Knowing where a mark sits in one photograph does not say where it sits in the other. It says which line it is on, which removes one of the two unknowns and leaves one — and the five lines drawn here meet at a point to within a thirtieth of a billionth of a pixel.

    part 1 · twoviews
  2. left pictureright picture12341234cross-ratio 3.012836 left · 3.012836 rightagree to 8e-12

    The two pencils keep one number

    Four lines through the image of the other eye in one picture, and the four epipolar lines they become in the other. The angles between them change by up to 11.4°; their cross-ratio is 3.012836 on both sides, to eight parts in a trillion. Three pairs of lines fix the map between the pencils, and the fourth is predicted to a third of a billionth of a pixel.

    part 2 · twoviews
  3. left, rectifiedright, rectifiedrows agree to 1.1e-13 px · points to 3.1e-14 mturned 0° about the baseline

    Rectification is a family, not an operation

    Turn both pictures of a pair so their epipolar lines become shared rows. A turn about the line between the eyes and a focal length are left free, and every choice puts all 44 matches on common rows to a tenth of a trillionth of a pixel and every point back where it was. What the choices disagree about is the pixels — one stretches its pictures unevenly by 1.77, another by 4.86.

    part 3 · twoviews

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