Visual Plane
every picture states the point it is correct from
Concept

eight-point algorithm — where it appears

The linear method that recovers a fundamental matrix from eight or more correspondences and nothing else. It solves for seven free numbers and repairs the rank afterwards, which is why the coordinates it is run on decide whether the answer is usable at all.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

0.5120.1110100how finely each point is read off the picture (px, log scale)worst epipolar error against the exact geometry (px, log scale)raw pixelscentred and scaled1.1× apart at 0.25 px, 29.9× at 4 pxspread 102 against 2.5e+5

Eight points and the basis they are read in

The linear system that recovers a fundamental matrix is written in whatever coordinates the marks were read in, and pixel coordinates are a bad choice. Centring and scaling them first is worth nothing at a quarter-pixel reading and a factor of thirty at four.

twoviews · Eightpoint the lenstwo marks, a straightedge, no arithmetic2.8e-13 px

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.

mirrors · Mirrorpair

Named alongside it

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

ConditioningCorrespondencedesign matrixFundamental matrixBaselinedegrees of freedomEpipoleMinimal solverNormalisationNullspacesingular valuesStraightedge construction

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