Gabor Space and the Development of Preattentive Similarity

We show that a certain class of similarity measures, which is based on set-theoretic concepts, and explains many of the characteristics of human similarity assessment, can be interpreted as a distance in a suitable psychological space. This view unifies a number of different measures of similarity that psychological experiments have determined to be active in humans for different classes of stimuli. Based on this, we proceed to sketch a theory of pattern similarity based on the Gabor decomposition. This theory considers stimuli as functions defined on a suitable manifold generated by the action of the Weyl-Heisenberg group on an image. A distance measure is introduced between functions in this manifold by endowing it with a suitable metric tensor. 1 Introduction This paper speculates on some of the ideas we are working on while trying to build a multimedia database based on similarity. The problem is of very wide scope, and takes together issues from the most diverse fields: we have ..