Ergodic Algorithms on Special Euclidean Groups for ATR
S. Srivastava, Michael I. Miller, Ulf Grenander · Birkhäuser Boston eBooks · 1997
This paper describes a technique for estimating motions of rigid targets based on the deformable template representations of complex scenes. The efficient modeling of representations for variabilities manifested by objects, shapes and scenes supporting invariant recognition is crucial. There are several kinds of variabilities fundamental to these representations: (i) the variability in target pose and placement , and (ii) variability in target numbers and identities . To model the first variability, templates are constructed from two-dimensional CAD surfaces representing the rigid objects. Using the deformable template approach, these templates are varied via the basic rigid transformations involving the translation and rotation groups. Since complex scenes are composed of multiple moving targets, the complete scene transformations are finite Cartesian products of these Lie groups. Given a set of observations of a particular scene the inference constitutes generating minimum mean squared error (MMSE) estimates and, hence, optimizing on the curved geometry of Lie manifolds. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.