About: Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion

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Description	A number of minimal problems of structure from motion for cameras with radial distortion have recently been solved. These problems are known to be numerically very challenging and in several cases there were no practical algorithms yielding solutions in FP. We make some crucial observations concerning the floating point implementation of Groebner 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. A number of minimal problems of structure from motion for cameras with radial distortion have recently been solved. These problems are known to be numerically very challenging and in several cases there were no practical algorithms yielding solutions in FP. We make some crucial observations concerning the floating point implementation of Groebner 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. (en)
Title	Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion (en)
skos:prefLabel	Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion (en)
skos:notation	RIV/68407700:21230/10:00162858!RIV11-MSM-21230___
http://linked.open...avai/riv/aktivita	P R Z
http://linked.open...avai/riv/aktivity	P(7E09062), R, Z(MSM6840770038)
http://linked.open...iv/cisloPeriodika	2
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Kúkelová, Zuzana Pajdla, Tomáš
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	České vysoké učení technické v Praze / Fakulta elektrotechnická
http://linked.open...dnocenehoVysledku	258817
http://linked.open...ai/riv/idVysledku	RIV/68407700:21230/10:00162858
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	radial distortion calibration; minimal problems; Groebner basis (en)
http://linked.open.../riv/klicoveSlovo	minimal problems Groebner basis radial distortion calibration
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[C9E17B3D17CE]
http://linked.open...i/riv/nazevZdroje	Computer Vision and Image Understanding
http://linked.open...in/vavai/riv/obor	JD
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	5 (xsd:int)
http://linked.open...vavai/riv/projekt	Planetary Robotics Vision Ground Processing
http://linked.open...UplatneniVysledku	2010
http://linked.open...v/svazekPeriodika	114
http://linked.open...iv/tvurceVysledku	Kúkelová, Zuzana Pajdla, Tomáš Byröd, M. Josephson, K. Äström, K.
http://linked.open...ain/vavai/riv/wos	000274337400007
http://linked.open...n/vavai/riv/zamer	Decision Making and Control for Manufacturing III
issn	1077-3142
number of pages	11 (xsd:int)
http://localhost/t...ganizacniJednotka	21230
is http://linked.open...avai/riv/vysledek of	Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion

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