Revisiting Viewing Graph Solvability: an Effective Approach Based on Cycle Consistency
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21730%2F25%3A00364429" target="_blank" >RIV/68407700:21730/25:00364429 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1109/TPAMI.2022.3212595" target="_blank" >https://doi.org/10.1109/TPAMI.2022.3212595</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1109/TPAMI.2022.3212595" target="_blank" >10.1109/TPAMI.2022.3212595</a>
Alternative languages
Result language
angličtina
Original language name
Revisiting Viewing Graph Solvability: an Effective Approach Based on Cycle Consistency
Original language description
In the structure from motion, the viewing graph is a graph where the vertices correspond to cameras (or images) and the edges represent the fundamental matrices. We provide a new formulation and an algorithm for determining whether a viewing graph is solvable, i.e., uniquely determines a set of projective cameras. The known theoretical conditions either do not fully characterize the solvability of all viewing graphs, or are extremely difficult to compute because they involve solving a system of polynomial equations with a large number of unknowns. The main result of this paper is a method to reduce the number of unknowns by exploiting cycle consistency. We advance the understanding of solvability by (i) finishing the classification of all minimal graphs up to 9 nodes, (ii) extending the practical verification of solvability to minimal graphs with up to 90 nodes, (iii) finally answering an open research question by showing that finite solvability is not equivalent to solvability, and (iv) formally drawing the connection with the calibrated case (i.e., parallel rigidity). Finally, we present an experiment on real data that shows that unsolvable graphs may appear in practice.
Czech name
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Czech description
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Classification
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)
Result continuities
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)
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
IEEE Transactions on Pattern Analysis and Machine Intelligence
ISSN
0162-8828
e-ISSN
1939-3539
Volume of the periodical
47
Issue of the periodical within the volume
5
Country of publishing house
US - UNITED STATES
Number of pages
14
Pages from-to
3271-3284
UT code for WoS article
001465416300025
EID of the result in the Scopus database
2-s2.0-105002968533