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 “infinitesimal solvability”, demonstrating its usefulness in understanding real structure from motion graphs; we propose an algorithm for testing infinitesimal solvability and extracting components of unsolvable cases, that is more efficient than previous work; we set up an open question on the connection between infinitesimal solvability and solvability.

A Direct Approach to Viewing Graph Solvability

Fusiello A.;
2025-01-01

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 “infinitesimal solvability”, demonstrating its usefulness in understanding real structure from motion graphs; we propose an algorithm for testing infinitesimal solvability and extracting components of unsolvable cases, that is more efficient than previous work; we set up an open question on the connection between infinitesimal solvability and solvability.
2025
9783031732317
9783031732324
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/1294745
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