Concept

Outlier — where it appears

A measurement that is not a noisy reading of the quantity being fitted but a reading of something else. A fit has nowhere to put it except across every other value, so its damage is general — unless it agrees with the model exactly, and then no test computed from the same data can see it.

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

Also named here as robust estimation — the same set of essays touches all of them, so they are one junction rather than several.

00.50011.50010203040correspondenceepipolar error at every OTHER point, after one match is movedmedian 0.54 pxthe moved oneevery point wrong: median 0.54 px, worst 1.7 pxclean fit 2.3e-13 px

A wrong match is not a small error

Move one correspondence of forty-four by thirty pixels and the recovered geometry is wrong for every other point — the typical one by half a pixel, from a fit that was exact to a part in ten trillion. Least squares has nowhere to put a bad row except across all of them.

depth · Outlier
seen herethe pair's pointexposed by 21.4 pxlines agree to 4e-13 px

A mismatch on its own line needs a third eye

Slide one mark of a correspondence 30 px along the epipolar line the other mark fixes, and every test two photographs can run stays at the arithmetic floor — epipolar distance 2.2e-14 px, the two rays meeting to 1.5e-15 m, reprojection 1.1e-13 px — while the point is reported half a metre too near. A third picture exposes it by 21.4 px from a third eye two metres off the first line of sight, and by exactly nothing from an eye on that line.

depth · Outlier
left pictureright picturethe post it is matched toone image row, drawn as two strips19.8 m instead of 9.0

A third eye that lands on the next post

Match one post of a railing to its neighbour and the pair reports it at 19.8 metres instead of 9.0, with every test two photographs can run at the arithmetic floor. A third picture usually exposes that by hundreds of pixels — but at five azimuths in seventy-eight degrees the wrong point lands within three pixels of another post, and the third view confirms the mistake. Narrow the railing to twenty centimetres and those places cover 28 per cent of the arc.

depth · Outlier

Named alongside it

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

BaselineCorrespondenceResidualrobust estimationFundamental matrixleast squaresTriangulationDegenerate configurationDemonstrationEpipolar lineinstrument limit

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