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Title: Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion
Authors: Byröd, Martin and Kukelova, Zuzana and Josephson, Klas and Pajdla, Tomas and Åström, Kalle
Year: 2008
Document Type:Conference Paper
Conference: Conference on Computer Vision and Pattern Recognition
Conference location: Anchorage, Alaska, USA
Status: Published
Refereed: Yes
Keywords: polynomial equations, localization
BibTeX item:BibTeX
Extra: Code available
Abstract: A number of minimal problems of structure from motion for cameras with radial distortion have recently been studied and solved in some cases. These problems are known to be numerically very challenging and in several cases there exist no known practical algorithm yielding solutions in floating point arithmetic. We make some crucial observations concerning the floating point implementation of Gröbner basis computations and use these new insights to formulate fast and stable algorithms for two minimal problems with radial distortion previously solved in exact rational arithmetic only: (i) simultaneous estimation of essential matrix and a common radial distortion parameter for two partially calibrated views and six image point correspondences and (ii) estimation of fundamental matrix and two different radial distortion parameters for two uncalibrated views and nine image point correspondences. We demonstrate on simulated and real experiments that these two problems can be efficiently solved in floating point arithmetic.




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