Linear solvability in the viewing graph

Authors:
Alessandro Rudi;Matia Pizzoli;Fiora Pirri
Affiliations:
Department of Computer and System Sciences, Sapienza University of Rome;Department of Computer and System Sciences, Sapienza University of Rome;Department of Computer and System Sciences, Sapienza University of Rome
Venue:
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part III
Year:
2010

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Abstract

The Viewing Graph [1] represents several views linked by the corresponding fundamental matrices, estimated pairwise. Given a Viewing Graph, the tuples of consistent camera matrices form a family that we call the Solution Set. This paper provides a theoretical framework that formalizes different properties of the topology, linear solvability and number of solutions of multi-camera systems. We systematically characterize the topology of the Viewing Graph in terms of its solution set by means of the associated algebraic bilinear system. Based on this characterization, we provide conditions about the linearity and the number of solutions and define an inductively constructible set of topologies which admit a unique linear solution. Camera matrices can thus be retrieved efficiently and large viewing graphs can be handled in a recursive fashion. The results apply to problems such as the projective reconstruction from multiple views or the calibration of camera networks.