Minimal solver — where it appears
Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.
Seven marks, three answers
Seven correspondences leave a two-dimensional nullspace, and the requirement that a fundamental matrix be singular is a cubic in the mix — one or three real roots. Here it has three, and all three satisfy every one of the seven marks to 8.9 × 10⁻⁹ pixels. The eighth mark, withheld, separates them by more than an order of magnitude.
The surface two pictures cannot separate
There is a quadric through both camera centres on which two genuinely different motions draw identical pictures. Built explicitly, forty-two marks satisfy both epipolar geometries to 2 × 10⁻¹³ pixels, and the two scenes they reconstruct place the same mark at 15.6 metres and 35.1. The design matrix's nullspace has two dimensions rather than one, which is the seven-point situation arrived at from the other side.
An ambiguity is not an uncertainty
Eight marks to forty cuts a solid scene's pose error from 19.8° to 0.7° and leaves a flat one at 48°. The two failures look identical from inside — a confident answer, a residual at the floor — and they respond to opposite remedies, so telling them apart is worth more than either measurement.
Two matches are enough
A general fundamental matrix has seven free numbers and needs eight correspondences. A mirror pair's has two, and two correspondences fix it — with a straightedge, on a print, by drawing the line from each mark to its reflection and marking where the two cross. Given the same sixteen marks read to four tenths of a pixel, the constrained fit lands 4.8 times closer to the truth than the eight-point algorithm.
Named alongside it
The objects these essays reach for when they reach for this one.
AmbiguityCritical surfaceFundamental matrixreconstruction ambiguityConditioningCorrespondenceDegeneracydegrees of freedomEpipolar geometryEpipoleNullspacedesign matrix