Concept

Reprojection error — where it appears

4 essays name this object, across 2 fields. What follows is each of them, and the objects they name alongside it.
view 1view 6the scene, in plan — recovered points and cameras over the true onesreprojection 0.332 px · track 2.0e-3264 observations, 168 parameters

The track and the scene together

Six photographs go in and one hundred and sixty-eight numbers come out — every camera's position and orientation and every point's place in space, solved for at once. Nothing in the solve was ever told where a camera or a point was.

manyviews · bundle
midpoint — 2.77 mm gapfrom the left eyefrom the right eyegap 2.77 mm at 7.22 mexact marks: 2.2e-16 m

Two rays that do not meet

Triangulation is described everywhere as the intersection of two rays, and two rays in space do not intersect. Read the same two marks to a whole pixel and they miss by 2.77 mm at seven metres, which is a real length and is the part a residual will not report.

depth · triangulation
-10-50-2-10baseline (m, log scale)worst deviation in the recovered shape (log scale)exact pointsread to 1 pxat 2 mm: 4.7e-9 exact, 2.9e+1 read to 1 px6e+9× apart

A turn of the head is not a step sideways

The textbook says a short baseline makes reconstruction ill-conditioned. Measured, the algebra does not notice — a two-millimetre baseline recovers the courtyard to nine digits from exact marks. What fails is the ratio of baseline to reading error, and it fails without refusing.

depth · baseline
-10-50012345iterationreprojection error (px, log scale)exact marksread to 1 px4.67 px → 0.3324 px in 5 iterationsexact marks reach 1.3e-11 px

Where the adjustment stops

Given exact marks the reprojection error falls to a hundredth of a billionth of a pixel, which is arithmetic. Given the same marks read to a whole pixel it falls to a third of a pixel and stays there, and a solver that reached zero on those would be fitting the rounding.

manyviews · bundle

Named alongside it

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

ResidualBaselinebundle adjustmentCorrespondenceTriangulationcamera trackConditioningConvergenceDegeneracydirect linear transformEntrance pupilEpipole

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