Revisiting Viewing Graph Solvability: an Effective Approach Based on Cycle Consistency

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Revisiting Viewing Graph Solvability: an Effective Approach Based on Cycle Consistency

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Revisiting Viewing Graph Solvability: an Effective Approach Based on Cycle Consistency

Popis výsledku anglicky

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.

Druh

J_imp - 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)

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)

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

IEEE Transactions on Pattern Analysis and Machine Intelligence

ISSN

0162-8828

e-ISSN

1939-3539

Svazek periodika

47

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

14

Strana od-do

3271-3284

Kód UT WoS článku

001465416300025

EID výsledku v databázi Scopus

2-s2.0-105002968533