  Planar markers are useful in robotics and computer vision for mapping and
localisation. Given a detected marker in an image, a frequent task is to
estimate the 6DOF pose of the marker relative to the camera, which is an
instance of planar pose estimation (PPE). Although there are mature techniques,
PPE suffers from a fundamental ambiguity problem, in that there can be more
than one plausible pose solutions for a PPE instance. Especially when
localisation of the marker corners is noisy, it is often difficult to
disambiguate the pose solutions based on reprojection error alone. Previous
methods choose between the possible solutions using a heuristic criteria, or
simply ignore ambiguous markers.
  We propose to resolve the ambiguities by examining the consistencies of a set
of markers across multiple views. Our specific contributions include a novel
rotation averaging formulation that incorporates long-range dependencies
between possible marker orientation solutions that arise from PPE ambiguities.
We analyse the combinatorial complexity of the problem, and develop a novel
lifted algorithm to effectively resolve marker pose ambiguities, without
discarding any marker observations. Results on real and synthetic data show
that our method is able to handle highly ambiguous inputs, and provides more
accurate and/or complete marker-based mapping and localisation.
