A Direct Approach to Viewing Graph Solvability
Abstract
The viewing graph is a useful way to represent uncalibrated cameras and their geometric relationships: nodes correspond to cameras and edges represent fundamental matrices. By analyzing this graph, it is possible to establish if the problem is “solvable” in the sense that there exists a unique (up to a single projective transformation) set of cameras that are compliant with the given fundamental matrices. In this paper, we take several steps forward in the study of viewing graph solvability: we propose a new formulation of the problem that is more direct than previous literature, based on a formula that explicitly links pairs of cameras via their fundamental matrix; we introduce the new concept of “”, demonstrating its usefulness in understanding real structure from motion graphs; we propose an algorithm for testing and extracting components of unsolvable cases, that is more efficient than previous work; we set up an open question on the connection between and solvability.
Cite
Text
Arrigoni et al. "A Direct Approach to Viewing Graph Solvability." Proceedings of the European Conference on Computer Vision (ECCV), 2024. doi:10.1007/978-3-031-73232-4_18Markdown
[Arrigoni et al. "A Direct Approach to Viewing Graph Solvability." Proceedings of the European Conference on Computer Vision (ECCV), 2024.](https://mlanthology.org/eccv/2024/arrigoni2024eccv-direct/) doi:10.1007/978-3-031-73232-4_18BibTeX
@inproceedings{arrigoni2024eccv-direct,
title = {{A Direct Approach to Viewing Graph Solvability}},
author = {Arrigoni, Federica and Fusiello, Andrea and Pajdla, Tomas},
booktitle = {Proceedings of the European Conference on Computer Vision (ECCV)},
year = {2024},
doi = {10.1007/978-3-031-73232-4_18},
url = {https://mlanthology.org/eccv/2024/arrigoni2024eccv-direct/}
}