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A Case Against Kruppa's Equations for Camera Self-Calibration
October 2000 (vol. 22 no. 10)
pp. 1199-1204

Abstract—We consider the self-calibration problem for perspective cameras and especially the classical Kruppa equation approach. It is known that for several common types of camera motion, self-calibration is degenerate, which manifests itself through the existence of ambiguous solutions. In a previous paper, we have studied these critical motion sequences and have revealed their importance for practical applications. Here, we reveal a type of camera motion that is not critical for the generic self-calibration problem, but for which the Kruppa equation approach fails. This is the case if the optical centers of all cameras lie on a sphere and if the optical axes pass through the sphere's center, a very natural situation for 3D object modeling from images. Results of simulated experiments demonstrate the instability of numerical self-calibration algorithms in near-degenerate configurations.

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Index Terms:
Self-calibration, calibration, euclidean reconstruction, Kruppa equations, critical motions, degeneracy, absolute conic.
Peter Sturm, "A Case Against Kruppa's Equations for Camera Self-Calibration," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 22, no. 10, pp. 1199-1204, Oct. 2000, doi:10.1109/34.879804
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