Outlier — where it appears
Named by 12 essays across 3 fields — each of them below, with the objects they name alongside it.
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.
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.
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.
A railing matched one along stands underground
Match every post of a railing to the next one along and two photographs build a perfect railing at 19.8 metres instead of 9.0 — straight, evenly spaced, every post on both its rays. Nothing near it can say so. What convicts it is what it stands on: its feet are 1.32 metres under the ground, and one ground mark read to a pixel shows every foot a whole period out from sixty metres away. Its length helps only through its ends, and once those leave the frame, counting matches prefers the wrong railing.
A facade matched a column out comes forward, not back
A railing matched one post along is rebuilt 2.2 times further away. A facade of windows 2.4 metres apart cannot be: a one-column shift that way needs a negative disparity, and the only mistake left in front of the cameras brings the facade to 6.3 metres from twenty, a third its size, hanging 1.1 metres off the ground with nothing under it to sink into. Its corners hold it only if the wall is assumed flat. Two corners then convict it at every period; one corner and a drainpipe need the pipe half a metre in for windows and four and a half for a fine repeat.
A raised eye reads the storeys as the pair read the columns
Put a third camera 3.5 metres above the left one and its epipolar lines run up the facade: the storeys repeat along them as the columns repeated along the level pair's rows, the roofline and the foot carry depth where the corners did, and a raise shorter than a storey can only pull the windows nearer. The three pictures together refuse the level pair's one-column mistake at every raise except those where the storey over the raise equals the period over the baseline — 1.375 and 2.75 metres here — and even there the facade's lowest storey lands on the ground.
A wall's twist can be tested against the error the adjustment reports
A wall reconstructed from two groups of cameras either side of it is likeliest to come out twisted, and the adjustment that found it also reports how far to believe the twist. The report is honest — a flat wall's twist clears twice its stated error one time in twenty, at every layout — so the question is only how large a real twist must be to be seen. Ten marks in two rows state ±5.05 millimetres and see a five-millimetre twist seventeen times in a hundred; fifteen in three rows state ±2.31 and see it fifty-six. The test goes wrong only when its error is assumed rather than measured, and a mismatched mark big enough to fake a twist always shows in its own residual.
A climbing eye names the column mistake, if it knows how high it is
A level pair that matches a facade a column out rebuilds it nearer, and a third camera climbing above the left one watches the rebuilt windows slide down its picture at 98 pixels a metre for every column of the mistake. Read against the real windows, that slide is a ruler: a metre of climb from level names a one-, two-, three- or four-column mistake every time. What it costs is not frames but knowledge — the climb must begin before the rebuilt facade slides off the lattice, and the camera must know its own height to about a quarter storey over the mistake's slide, 34 centimetres for one column and 9 for four.
A staircase winds the mistake round the lattice
A third camera climbing a stair along a facade sees a stereo pair's column mistake slide through its picture along the stair's own direction, wrapping at the columns across and the storeys up — a line wound round a torus. Such a line comes back onto a real window only when the stair's rise over its run is a ratio of whole storeys to whole columns; a degree off the diagonal, no two readings come within 3 px. The stair names the mistake from one frame, as a vertical climb does, but its readings sit twice as far apart in a frame, so a camera that knows where it is only to 10 cm still names it 95 times in 100 against 82, and a 30° stair keeps naming it a metre and a half along, where a vertical climb has lost half.
A turn at the landing makes the mistake a scale, and a scale is weak evidence
On a straight stair along a facade, a stereo pair's column mistake slides through a third camera's picture as one offset shared by every window. Turn the stair towards the wall at a landing and the offset stops being shared: the rebuilt facade's picture becomes the real one's scaled about the point the camera is walking towards, a different scale for every mistake, so no picture on that flight is blind. But the scale grows as the walk over the rebuilt facade's distance, and 10 cm towards the wall separates the one-column reading from the honest one by 1.8 px where 10 cm along the stair gives 9.8. Turning the camera in place adds nothing at all. What the turn does buy is tolerance: an error in how far towards the wall the camera has come costs almost nothing, for the same reason.
The scale names the mistake when the camera has lost its place along the wall
A third camera that knows how far it has paced towards a facade, and nothing about where along or up the wall it stands, still names a stereo pair's column mistake from one picture. Any offset at all refutes the honest reading, which predicts none from anywhere; and once the unknown place is fitted away as one uniform slide, what is left is the rebuilt facade's scale, which each mistake predicts differently. Five centimetres towards the wall names the mistake 95 times in 100 at half a pixel, ten centimetres every time — where a camera that believes it knows its place and is 20 cm out manages 77. The distance has to be paced, though: a rangefinder or the windows' known spacing would have named the mistake by themselves.
A crooked stick hides in a quarter pixel, and its residual finds it only below a tenth
Eight sticks stand in still water, one of them bowed three millimetres and the rest one, and a refraction fit holds every stick to a straight line. Read exactly, the bad stick carries the largest share of the fit's residual in about seven sets of ten. Read to a quarter pixel, as a careful photograph is, it carries it in one set of five, barely more than chance: a millimetre of bow moves the index more than the reading error does and leaves its rays missing by a twelfth of a quarter pixel. The residual stays blind until the bad stick is bowed five or ten millimetres, and dropping the stick it ranks worst does nothing measurable for the index.
Named alongside it
The objects these essays reach for when they reach for this one.
Correspondencerobust estimationTriangulationDegenerate configurationEpipolar lineResidualleast squaresBaselineDisparityFocal lengthFundamental matrixSampling