The efficient generation of compact models for the representations of objects, shapes and scenes supporting invariant recognition , which accommodate the infinity of poses manifest by motions during scene evolution is crucial. To model the first, templates are constructed from the 2-dimensional surfaces representing the rigid objects. These are made flexible via the introduction of basic transformations involving both rigid motions of translation and rotation, as well as non-rigid motions such as scale. These transformations form Lie group actions on the templates. Since complex scenes are composed of multiple templates, the transformations are products of subgroups of the generalized linear group.
Inference constitutes optimization on the curved geometry of Lie manifolds.
The full inference or hypothesis space becomes a countable disconnected unions of these Cartesian product groups with the model order and model type variables to be inferred as well. We take a Bayesian approach seeking the conditional mean estimates of the representation element given the oberved data. The prior is based on previous knowledge on expected scenes. In rigid target recognition, the prior on target trajectories is based on Newtonian dynamics. In particular, the transition probabilities converge in the variation norm to P .