Calibration of a Moving Camera Using a Planar Pattern: A Centre Line-Based Approach for Varying Focal Length

P Gurdjos and R Payrissat

This paper deals with the problem of calibrating a (moving) camera with varying focal length, from n views of a planar pattern with a known Euclidean structure. The main issue under discussion is to find a new method whose complexity does not dramatically increase with the number n of views, contrary to existing methods. Our contribution is to relate this calibration problem to the Centre Line (CL) constraint, that is the principal point locus when planar figures are in perpective correspondence, in accordance with Poncelet's theorem. We demonstrate that the CL equation is irrespective of the focal length and holds for each view, with only three unknown parameters whose values are constant in the images. We define its analytic equation with coefficients computed from the world-plane to image homography matrices. An important aspect is that we can make use of it as a linear cost function that expresses a geometric error (instead of algebraic errors in existing methods). We explain why an ``optimal'' solution can be obtained when pixels are rectangular. The simulations on synthetic data and an application with real images confirm the two strong points of our method with respect to existing ones: a lower computation cost and a better system conditioning that permits to obtain more accurate results.

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