A Case Against Kruppa's Equations for Camera Self-Calibration

Peter Sturm 1
1 MOVI - Modeling, localization, recognition and interpretation in computer vision
GRAVIR - IMAG - Graphisme, Vision et Robotique, Inria Grenoble - Rhône-Alpes, CNRS - Centre National de la Recherche Scientifique : FR71
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. The author previously (1997, 1999) studied these critical motion sequences and showed 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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Submitted on : Tuesday, October 12, 2010 - 2:16:31 PM
Last modification on : Thursday, January 11, 2018 - 6:20:04 AM

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Peter Sturm. A Case Against Kruppa's Equations for Camera Self-Calibration. IEEE Transactions on Pattern Analysis and Machine Intelligence, Institute of Electrical and Electronics Engineers, 2000, 22 (10), pp.1199-1204. ⟨10.1109/34.879804⟩. ⟨inria-00525669⟩

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