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  • Many vision tasks require efficient solvers of systems of polynomial equations. Epipolar geometry and relative camera pose computation are tasks which can be formulated as minimal problems which lead to solving systems of algebraic equations. Often, these systems are not trivial and therefore special algorithms have to be designed to achieve numerical robustness and computational efficiency. In this work we suggest improvements of current techniques for solving systems of polynomial equations suitable for some vision problems. We introduce two tricks. The first trick helps to reduce the number of variables and degrees of the equations. The second trick can be used to replace computationally complex construction of Gröbner basis by a simpler procedure. We demonstrate benefits of our technique by providing a solution to the problem of estimating radial distortion and epipolar geometry from eight correspondences in two images. Unlike previous algorithms, which were able to solve the probl
  • Many vision tasks require efficient solvers of systems of polynomial equations. Epipolar geometry and relative camera pose computation are tasks which can be formulated as minimal problems which lead to solving systems of algebraic equations. Often, these systems are not trivial and therefore special algorithms have to be designed to achieve numerical robustness and computational efficiency. In this work we suggest improvements of current techniques for solving systems of polynomial equations suitable for some vision problems. We introduce two tricks. The first trick helps to reduce the number of variables and degrees of the equations. The second trick can be used to replace computationally complex construction of Gröbner basis by a simpler procedure. We demonstrate benefits of our technique by providing a solution to the problem of estimating radial distortion and epipolar geometry from eight correspondences in two images. Unlike previous algorithms, which were able to solve the probl (en)
  • Many vision tasks require efficient solvers of systems of polynomial equations. Epipolar geometry and relative camera pose computation are tasks which can be formulated as minimal problems which lead to solving systems of algebraic equations. Often, these systems are not trivial and therefore special algorithms have to be designed to achieve numerical robustness and computational efficiency. In this work we suggest improvements of current techniques for solving systems of polynomial equations suitable for some vision problems. We introduce two tricks. The first trick helps to reduce the number of variables and degrees of the equations. The second trick can be used to replace computationally complex construction of Gröbner basis by a simpler procedure. We demonstrate benefits of our technique by providing a solution to the problem of estimating radial distortion and epipolar geometry from eight correspondences in two images. Unlike previous algorithms, which were able to solve the probl (cs)
Title
  • Solving polynomial equations for minimal problems in computer vision
  • Solving polynomial equations for minimal problems in computer vision (en)
  • Solving polynomial equations for minimal problems in computer vision (cs)
skos:prefLabel
  • Solving polynomial equations for minimal problems in computer vision
  • Solving polynomial equations for minimal problems in computer vision (en)
  • Solving polynomial equations for minimal problems in computer vision (cs)
skos:notation
  • RIV/68407700:21230/07:03135394!RIV08-MSM-21230___
http://linked.open.../vavai/riv/strany
  • 12;19
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • Z(MSM6840770038)
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 450986
http://linked.open...ai/riv/idVysledku
  • RIV/68407700:21230/07:03135394
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • Gröbner basis; minimal problems; radial distortion (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...ontrolniKodProRIV
  • [4E31F2D11211]
http://linked.open...v/mistoKonaniAkce
  • St. Lambrecht
http://linked.open...i/riv/mistoVydani
  • Graz
http://linked.open...i/riv/nazevZdroje
  • CVWW 2007: Proceedings of the 12th Computer Vision Winter Workshop
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...UplatneniVysledku
http://linked.open...iv/tvurceVysledku
  • Kúkelová, Zuzana
  • Pajdla, Tomáš
http://linked.open...vavai/riv/typAkce
http://linked.open.../riv/zahajeniAkce
http://linked.open...n/vavai/riv/zamer
number of pages
http://purl.org/ne...btex#hasPublisher
  • Verlag der Technischen Universität Graz
https://schema.org/isbn
  • 978-3-902465-60-3
http://localhost/t...ganizacniJednotka
  • 21230
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