Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion
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| Titel: | Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion |
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| Autoren: | Kukelova, Zuzana, Byröd, Martin, Josephson, Klas, Pajdla, Tomas, Åström, Karl |
| Weitere Verfasser: | Lund University, Faculty of Science, Centre for Mathematical Sciences, Mathematics (Faculty of Engineering), Lunds universitet, Naturvetenskapliga fakulteten, Matematikcentrum, Matematik LTH, Originator, Lund University, Faculty of Science, Centre for Mathematical Sciences, Research groups at the Centre for Mathematical Sciences, Mathematical Imaging Group, Lunds universitet, Naturvetenskapliga fakulteten, Matematikcentrum, Forskargrupper vid Matematikcentrum, Mathematical Imaging Group, Originator, Lund University, Faculty of Science, Centre for Mathematical Sciences, Research groups at the Centre for Mathematical Sciences, Algebra, Lunds universitet, Naturvetenskapliga fakulteten, Matematikcentrum, Forskargrupper vid Matematikcentrum, Algebra, Originator, Lund University, Profile areas and other strong research environments, Strategic research areas (SRA), ELLIIT: the Linköping-Lund initiative on IT and mobile communication, Lunds universitet, Profilområden och andra starka forskningsmiljöer, Strategiska forskningsområden (SFO), ELLIIT: the Linköping-Lund initiative on IT and mobile communication, Originator |
| Quelle: | Computer Vision and Image Understanding. 114(2):234-244 |
| Schlagwörter: | Natural Sciences, Computer and Information Sciences, Computer graphics and computer vision, Naturvetenskap, Data- och informationsvetenskap (Datateknik), Datorgrafik och datorseende, Mathematical Sciences, Matematik |
| Beschreibung: | 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 were no practical algorithms 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 that these two problems can be efficiently solved in floating point arithmetic in simulated and real experiments. For comparison we have also invented a new non-minimal algorithm for estimating fundamental matrix and two different radial distortion parameters for two uncalibrated views and twelve image point correspondences based on a generalized eigenvalue problem. |
| Dateibeschreibung: | electronic |
| Zugangs-URL: | https://lucris.lub.lu.se/ws/files/2084497/1276956.pdf |
| Datenbank: | SwePub |
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Nájsť tento článok vo Web of Science | 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 were no practical algorithms 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 that these two problems can be efficiently solved in floating point arithmetic in simulated and real experiments. For comparison we have also invented a new non-minimal algorithm for estimating fundamental matrix and two different radial distortion parameters for two uncalibrated views and twelve image point correspondences based on a generalized eigenvalue problem. |
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| ISSN: | 10773142 1090235X |
| DOI: | 10.1016/j.cviu.2008.11.008 |