Monocular Pose Estimation

Monocular pose estimation is a more or less well-known subject area, which was rst treated in the 1980s, for example by Lowe [122, 123]. Overviews of the various approaches to pose estimation can be found in [115, 150]. The various algorithms different in the type of information that is known about the object whose pose is to be estimated and in the mathematical formalism that is used to represent the pose itself.

The data that is assumed to be given in all monocular pose estimation algorithms is some geometrical information about the object and the corresponding appearance of the object in the image taken. For example, some typical approaches are to assume knowledge of the location of points and/or lines on an object, and the location of their appearance in an image. Finding these correspondences is known as the correspondence problem, which is by no means trivial. It is usually only tractable if either unique markers are placed on an object or a tracking assumption is made. In the latter case it is assumed that the pose of the object is roughly known and only has to be adapted slightly. Such an assumption is particularly necessary if only a contour model of the object is given [155].

The mathematical framework used for pose estimation is typically matrix algebra. However, there have been approaches using dual quaternions [39, 173], which are isomorphic to motors in conformal geometric algebra. The drawback of using dual quaternions is that within this framework the only representable geometric entities are lines. In the geometric-algebra framework used in this text, any representable geometric entity can be used.