Solving polynomial equations for minimal problems in computer vision

Kód výsledku v IS VaVaI

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Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Solving polynomial equations for minimal problems in computer vision

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

Solving polynomial equations for minimal problems in computer vision

Popis výsledku anglicky

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

Druh

D - Stať ve sborníku

CEP obor

JD - Využití počítačů, robotika a její aplikace

OECD FORD obor

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Projekt

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Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2007

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

CVWW 2007: Proceedings of the 12th Computer Vision Winter Workshop

ISBN

978-3-902465-60-3

ISSN

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e-ISSN

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Počet stran výsledku

8

Strana od-do

12-19

Název nakladatele

Verlag der Technischen Universität Graz

Místo vydání

Graz

Místo konání akce

St. Lambrecht

Datum konání akce

6. 2. 2007

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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