Galois/monodromy groups for decomposing minimal problems in 3D reconstruction

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Galois/monodromy groups for decomposing minimal problems in 3D reconstruction
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
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)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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