Szpak, Z.Chojnacki, W.Van Den Hengel, A.2017-09-202017-09-202015Proceedings / CVPR, IEEE Computer Society Conference on Computer Vision and Pattern Recognition. IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2015, vol.07-12-June-2015, pp.2132-214197814673696401063-6919http://hdl.handle.net/2440/107900The estimation of multiple homographies between two piecewise planar views of a rigid scene is often assumed to be a solved problem. We show that contrary to popular opinion various crucial aspects of the task have not been adequately emphasised. We are motivated by a growing body of literature in robust multi-structure estimation that purports to solve the multi-homography estimation prob- lem but in fact does not. We demonstrate that the estima- tion of multiple homographies is an ill-solved problem by deriving new constraints that a set of mutually compatible homographies must satisfy, and by showing that homogra- phies estimated with prevailing methods fail to satisfy the requisite constraints on real-world data. We also explain why incompatible homographies imply inconsistent epipo- lar geometries. The arguments and experiments presented in this paper signal the need for a new generation of robust multi-structure estimation methods that have the capacity to enforce constraints on projective entities such as homog- raphy matrices.en© 2015 IEEEConference paper003004527010.1109/CVPR.2015.72988250003879592020172-s2.0-84959216353222257Szpak, Z. [0000-0002-0694-4622]Chojnacki, W. [0000-0001-7782-1956]Van Den Hengel, A. [0000-0003-3027-8364]