Wreath Product 3D Analysis and Movement Affordances: A Neurorobotic Approach

Symmetry-based wreath products have been proposed as a cognitive representation combining actuation and perception as derived from sensorimotor streams. Previous work has described how 2D wreath product shape analysis may be expressed in an appropriate neural network formulation, and here we extend this to include 3D surface analysis. That is, symmetry group operators with sensorimotor semantics are exploited in a neural network computational framework to provide a behaviorally relevant interpretation of a 3D scene. In addition, we describe how this approach provides a high-level abstraction which permits the recognition of similar geometric categories. Finally, we argue that this analysis can be implemented in a straightforward way as a neural network computation.