Galois/monodromy groups for decomposing minimal problems in 3D reconstruction
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21730%2F22%3A00371867" target="_blank" >RIV/68407700:21730/22:00371867 - isvavai.cz</a>
Výsledek na webu
<a href="https://doi.org/10.1137/21M1422872" target="_blank" >https://doi.org/10.1137/21M1422872</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/21M1422872" target="_blank" >10.1137/21M1422872</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Galois/monodromy groups for decomposing minimal problems in 3D reconstruction
Popis výsledku v původním jazyce
We consider Galois/monodromy groups arising in computer vision applications, with a view towards building more efficient polynomial solvers. The Galois/monodromy group allows us to decide when a given problem decomposes into algebraic subproblems, and whether or not it has any symmetries. Tools from numerical algebraic geometry and computational group theory allow us to apply this framework to classical and novel reconstruction problems. We consider three classical cases—3-point absolute pose, 5-point relative pose, and 4-point homography estimation for calibrated cameras—where the decomposition and symmetries may be naturally understood in terms of the Galois/monodromy group. We then show how our framework can be applied to novel problems from absolute and relative pose estimation. For instance, we discover new symmetries for absolute pose problems involving mixtures of point and line features. We also describe a problem of estimating a pair of calibrated homographies between three images. For this problem of degree 64, we can reduce the degree to 16, the latter better reflecting the intrinsic difficulty of algebraically solving the problem. As a byproduct, we obtain new constraints on compatible homographies, which may be of independent interest.
Název v anglickém jazyce
Galois/monodromy groups for decomposing minimal problems in 3D reconstruction
Popis výsledku anglicky
We consider Galois/monodromy groups arising in computer vision applications, with a view towards building more efficient polynomial solvers. The Galois/monodromy group allows us to decide when a given problem decomposes into algebraic subproblems, and whether or not it has any symmetries. Tools from numerical algebraic geometry and computational group theory allow us to apply this framework to classical and novel reconstruction problems. We consider three classical cases—3-point absolute pose, 5-point relative pose, and 4-point homography estimation for calibrated cameras—where the decomposition and symmetries may be naturally understood in terms of the Galois/monodromy group. We then show how our framework can be applied to novel problems from absolute and relative pose estimation. For instance, we discover new symmetries for absolute pose problems involving mixtures of point and line features. We also describe a problem of estimating a pair of calibrated homographies between three images. For this problem of degree 64, we can reduce the degree to 16, the latter better reflecting the intrinsic difficulty of algebraically solving the problem. As a byproduct, we obtain new constraints on compatible homographies, which may be of independent interest.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Návaznosti výsledku
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)
Ostatní
Rok uplatnění
2022
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
SIAM Journal on Applied Algebra and Geometry
ISSN
2470-6566
e-ISSN
2470-6566
Svazek periodika
6
Číslo periodika v rámci svazku
4
Stát vydavatele periodika
US - Spojené státy americké
Počet stran výsledku
33
Strana od-do
740-772
Kód UT WoS článku
001127815500003
EID výsledku v databázi Scopus
2-s2.0-85146368317