Multi-view orientation estimation using Bingham mixture models

This paper describes a multi-view pose estimation system, that is exploiting the mobility of a depth sensor through mounting it onto a robotic manipulator. Given a pose estimation algorithm that performs feature extraction and matching to a model database, we investigate the probabilistic modeling of the pose space as well as the measurement uncertainty, to be used in a sequential state estimation approach. Uncertainties in 3d position can be modeled in a parametric way by 3d Gaussians, but the space of rotations in 3d - the special orthogonal group SO(3) - requires approaches from directional statistics. A convenient representation for orientations are unit quaternions over which the Bingham distribution defines a parametric probability density function. The Bingham distribution also correctly accounts for the sign symmetry of orientation quaternions and leave degrees of freedom unconstrained (which is especially useful if an object is rotationally symmetric, with no unique quaternion describing its orientation). In our experiments we test different sequential fusion methods, optimize their parameters, and investigate how the derived filter performs in a case with high uncertainties.