Galois/monodromy groups in 3D reconstruction

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F21%3A00356034" target="_blank" >RIV/68407700:21230/21:00356034 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/68407700:21730/21:00356034

Výsledek na webu

<a href="https://meetings.ams.org/math/jmm2021/meetingapp.cgi/Paper/2557" target="_blank" >https://meetings.ams.org/math/jmm2021/meetingapp.cgi/Paper/2557</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Galois/monodromy groups in 3D reconstruction

Popis výsledku v původním jazyce

In computer vision, the study of minimal problems is critical for many 3D reconstruction tasks. Solving minimal problems comes down to solving systems of polynomial equations of a very particular structure. ``Structure" of minimal problems may be understood in terms of the Galois/monodromy group of an associated branched cover. We compute these groups for many examples using numerical homotopy continuation methods. Classical problems such as five-point relative pose, planar calibrated homography estimation, and perspective absolute pose give rise to imprimitive Galois groups, and solutions to these problems typically exploit a corresponding decomposition of the associated branched cover. Beside analyzing these cases, we find also several novel minimal problems whose Galois groups are imprimitive and may be reasonable to solve in practical applications.

Název v anglickém jazyce

Galois/monodromy groups in 3D reconstruction

Popis výsledku anglicky

In computer vision, the study of minimal problems is critical for many 3D reconstruction tasks. Solving minimal problems comes down to solving systems of polynomial equations of a very particular structure. ``Structure" of minimal problems may be understood in terms of the Galois/monodromy group of an associated branched cover. We compute these groups for many examples using numerical homotopy continuation methods. Classical problems such as five-point relative pose, planar calibrated homography estimation, and perspective absolute pose give rise to imprimitive Galois groups, and solutions to these problems typically exploit a corresponding decomposition of the associated branched cover. Beside analyzing these cases, we find also several novel minimal problems whose Galois groups are imprimitive and may be reasonable to solve in practical applications.

Druh

O - Ostatní výsledky

CEP obor

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OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/EF15_003%2F0000468" target="_blank" >EF15_003/0000468: Inteligentní strojové vnímání</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

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