In structure-from-motion the viewing graph is a graph where vertices correspond to cameras and edges represent fundamental matrices. We provide a new formulation and an algorithm for establishing whether a viewing graph is solvable, i.e. it uniquely determines a set of projective cameras. Known theoretical conditions either do not fully characterize the solvability of all viewing graphs, or are exceedingly hard to compute for they involve solving a system of polynomial equations with a large number of unknowns. The main result of this paper is a method for reducing the number of unknowns by exploiting the cycle consistency. We advance the understanding of the solvability by (i) finishing the classification of all previously undecided minimal graphs up to 9 nodes, (ii) extending the practical solvability testing up to minimal graphs with up to 90 nodes, and (iii) definitely answering an open research question by showing that the finite solvability is not equivalent to the solvability. Finally, we present an experiment on real data showing that unsolvable graphs are appearing in practical situations.

Viewing Graph Solvability via Cycle Consistency / Arrigoni, Federica; Fusiello, Andrea; Ricci, Elisa; Pajdla, Tomas. - (2021), pp. 5520-5529. (Intervento presentato al convegno ICCV tenutosi a Virtual nel 11-17, October 2021) [10.1109/ICCV48922.2021.00549].

Viewing Graph Solvability via Cycle Consistency

Arrigoni, Federica;Ricci, Elisa;
2021-01-01

Abstract

In structure-from-motion the viewing graph is a graph where vertices correspond to cameras and edges represent fundamental matrices. We provide a new formulation and an algorithm for establishing whether a viewing graph is solvable, i.e. it uniquely determines a set of projective cameras. Known theoretical conditions either do not fully characterize the solvability of all viewing graphs, or are exceedingly hard to compute for they involve solving a system of polynomial equations with a large number of unknowns. The main result of this paper is a method for reducing the number of unknowns by exploiting the cycle consistency. We advance the understanding of the solvability by (i) finishing the classification of all previously undecided minimal graphs up to 9 nodes, (ii) extending the practical solvability testing up to minimal graphs with up to 90 nodes, and (iii) definitely answering an open research question by showing that the finite solvability is not equivalent to the solvability. Finally, we present an experiment on real data showing that unsolvable graphs are appearing in practical situations.
2021
2021 IEEE/CVF International Conference on Computer Vision (ICCV)
Montreal, QC, Canada
IEEE
978-1-6654-2812-5
Arrigoni, Federica; Fusiello, Andrea; Ricci, Elisa; Pajdla, Tomas
Viewing Graph Solvability via Cycle Consistency / Arrigoni, Federica; Fusiello, Andrea; Ricci, Elisa; Pajdla, Tomas. - (2021), pp. 5520-5529. (Intervento presentato al convegno ICCV tenutosi a Virtual nel 11-17, October 2021) [10.1109/ICCV48922.2021.00549].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/334730
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