Galois/monodromy groups in 3D reconstruction

Result code in 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>

Alternative codes found

RIV/68407700:21730/21:00356034

Result on the web

<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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Result language

angličtina

Original language name

Galois/monodromy groups in 3D reconstruction

Original language description

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.

Czech name

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Czech description

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Type

O - Miscellaneous

CEP classification

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OECD FORD branch

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

Project

<a href="/en/project/EF15_003%2F0000468" target="_blank" >EF15_003/0000468: Intelligent Machine Perception</a><br>

Continuities

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

Publication year

2021

Confidentiality

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