Solving polynomial equations for minimal problems in computer vision

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F07%3A03135394" target="_blank" >RIV/68407700:21230/07:03135394 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Solving polynomial equations for minimal problems in computer vision

Original language description

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

Czech name

Solving polynomial equations for minimal problems in computer vision

Czech description

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

Type

D - Article in proceedings

CEP classification

JD - Use of computers, robotics and its application

OECD FORD branch

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Project

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Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2007

Confidentiality

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

Article name in the collection

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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Number of pages

8

Pages from-to

12-19

Publisher name

Verlag der Technischen Universität Graz

Place of publication

Graz

Event location

St. Lambrecht

Event date

Feb 6, 2007

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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