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ECCV
2004
Springer

What Do Four Points in Two Calibrated Images Tell Us about the Epipoles?

10 years 1 months ago
What Do Four Points in Two Calibrated Images Tell Us about the Epipoles?
Suppose that two perspective views of four world points are given, that the intrinsic parameters are known, but the camera poses and the world point positions are not. We prove that the epipole in each view is then constrained to lie on a curve of degree ten. We give the equation for the curve and establish many of the curve's properties. For example, we show that the curve has four branches through each of the image points and that it has four additional points on each conic of the pencil of conics through the four image points. We show how to compute the four curve points on each conic in closed form. We show that orientation constraints allow only parts of the curve and find that there are impossible configurations of four corresponding point pairs. We give a novel algorithm that solves for the essential matrix given three corresponding points and one epipole. We then use the theory to describe a solution, using a 1-parameter search, to the notoriously difficult problem of solv...
David Nistér, Frederik Schaffalitzky
Added 15 Oct 2009
Updated 15 Oct 2009
Type Conference
Year 2004
Where ECCV
Authors David Nistér, Frederik Schaffalitzky
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