Bayesian attributed hypergraphs: a unified representation of Bayesian networks and hypergraphs for perceptual grouping

This article introduces a representation known as Bayesian attributed hypergraphs (BAHGs) that are based on the integration of Bayesian networks and attributed hypergraphs. BAHGs are an augmentation to attributed hypergraphs that allow for the management of uncertainty, using Bayesian theory, and can reason about formations from the sensory data using simple graph operators. They allow for the creation of multiple instantiations of Bayesian networks while maintaining single instantiation of nodes that represent the same event. This unification of uncertainty management and attributed hypergraphs removes the need of maintaining and synchronizing between a representation for managing uncertainty and another to manage declarative knowledge. A formalism for the construction of a BAHG for image understanding is presented based on the decomposition by parts methodology and the use of geometric constraints among feature sets. An example is presented that performs perceptual grouping among fragmented 3-D surfaces in an attempt to group the surfaces into corners and continuous surfaces.