Solvability of the Viewing Graph Under the Affine Camera Model

In this paper we focus on the viewing graph, which is used to represent cameras (as nodes) and their pairwise relationships (as edges) in the context of Structure from Motion. By analyzing this graph, it is possible to establish if the available pairwise relationships (e.g., fundamental matrices in the uncalibrated case) are theoretically enough to uniquely determine the cameras, in which case the graph is termed "solvable". Previous results considered calibrated and uncalibrated settings, whereas other camera models have not been explored in the context of viewing graph solvability: this work represents the first study under the affine camera model. We provide a characterization of the problem in terms of a linear system, from which we derive a practical method to check affine solvability. We complement this by some theoretical results providing sufficient/necessary conditions for affine solvability, in order to give further insights on the problem. Thanks to our experiments, we analyze synthetic graphs and real graphs coming from structure-from-motion datasets, where we focus on understanding the differences among different camera models (calibrated, uncalibrated and affine) in terms of solvability. In this context, we also raise an open research question and conjecture a possible answer, which is supported by empirical evidence.