A Direct Approach to Viewing Graph Solvability

Federica Arrigoni*, Andrea Fusiello, Tomas Pajdla ;

"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."