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  • We present a method for solving systems of polynomial equations appearing in computer vision. This method is based on polynomial eigenvalue solvers and is more straightforward and easier to implement than the state-of-the-art Grobner basis method since eigenvalue problems are well studied, easy to understand, and efficient and robust algorithms for solving these problems are available. We provide a characterization of problems that can be efficiently solved as polynomial eigenvalue problems (PEPs) and present a resultant-based method for transforming a system of polynomial equations to a polynomial eigenvalue problem. We propose techniques that can be used to reduce the size of the computed polynomial eigenvalue problems. To show the applicability of the proposed polynomial eigenvalue method, we present the polynomial eigenvalue solutions to several important minimal relative pose problems.
  • We present a method for solving systems of polynomial equations appearing in computer vision. This method is based on polynomial eigenvalue solvers and is more straightforward and easier to implement than the state-of-the-art Grobner basis method since eigenvalue problems are well studied, easy to understand, and efficient and robust algorithms for solving these problems are available. We provide a characterization of problems that can be efficiently solved as polynomial eigenvalue problems (PEPs) and present a resultant-based method for transforming a system of polynomial equations to a polynomial eigenvalue problem. We propose techniques that can be used to reduce the size of the computed polynomial eigenvalue problems. To show the applicability of the proposed polynomial eigenvalue method, we present the polynomial eigenvalue solutions to several important minimal relative pose problems. (en)
Title
  • Polynomial Eigenvalue Solutions to Minimal Problems in Computer Vision
  • Polynomial Eigenvalue Solutions to Minimal Problems in Computer Vision (en)
skos:prefLabel
  • Polynomial Eigenvalue Solutions to Minimal Problems in Computer Vision
  • Polynomial Eigenvalue Solutions to Minimal Problems in Computer Vision (en)
skos:notation
  • RIV/68407700:21230/12:00196130!RIV13-MSM-21230___
http://linked.open...avai/predkladatel
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(7E10046), Z(MSM6840770038)
http://linked.open...iv/cisloPeriodika
  • 7
http://linked.open...vai/riv/dodaniDat
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http://linked.open...iv/duvernostUdaju
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http://linked.open...dnocenehoVysledku
  • 159587
http://linked.open...ai/riv/idVysledku
  • RIV/68407700:21230/12:00196130
http://linked.open...riv/jazykVysledku
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  • Structure from motion; relative camera pose; minimal problems; polynomial eigenvalue problems (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [7212847817D2]
http://linked.open...i/riv/nazevZdroje
  • IEEE Transactions on Pattern Analysis and Machine Intelligence
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
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http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 34
http://linked.open...iv/tvurceVysledku
  • Kúkelová, Zuzana
  • Pajdla, Tomáš
  • Bujnak, M.
http://linked.open...ain/vavai/riv/wos
  • 000304138300010
http://linked.open...n/vavai/riv/zamer
issn
  • 0162-8828
number of pages
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  • 21230
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