Concept

design matrix — where it appears

The matrix of a linear system's coefficients, whose smallest singular values say whether the data determines an answer or merely permits one.

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

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

Five marks and the sixth

Five points determine a conic exactly — five coefficients up to scale, five equations, nothing left over — so a fit through five marks on a photograph is not a fit at all. The sixth mark, withheld, lands on the curve to 1.9e-13 px. And the moment a sixth mark is used, the arithmetic changes character completely: it becomes a least-squares problem, and the residual starts telling you something the five could never say.

foundations · fiveconic

Named alongside it

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

singular values Baseline Circle Conditioning Conic Correspondence degrees of freedom Discriminant Duality Eigenvalues eight-point algorithm Fundamental matrix

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