Automatic fuzzy Cartesian granule feature discovery using genetic programming in image understanding

Variables defined over Cartesian granule feature universes can be viewed as multidimensional linguistic variables. These variable universes are formed over the cross product of words drawn from the fuzzy partitions of the constituent base features. Here we present a constructive induction algorithm, which identifies not only the Cartesian granule feature model but also the concepts/variables in which the model is expressed. The presented constructive induction algorithm combines the genetic programming search paradigm with a rather novel and cheap fitness function, which is based upon semantic discrimination analysis. Parsimony is promoted in this model discovery process, thereby leading to models with better generalisation power and transparency. The approach is demonstrated on an image understanding problem, an area that has traditionally been dominated by quantitative and black box modelling techniques. Overall the discovered Cartesian granule features models when demonstrated on a large test set of outdoor images provides highly accurate image interpretation, using four input features, with over 78% of the image area labelled correctly.