Elements of a Gestalt algebra: Steps towards understanding images and scenes

A mathematical structure is sketched that is meant to capture the regularities and hierarchies in the structure of images. The approach is motivated by difficulties arising from aerial image analysis of urban terrain. It is not feasible to list and model all possibilities for things such as buildings that occur in such data. Emanating from the Gestalt-theory of perception an abstract algebra of operations on image objects is defined and the formal properties are discussed. It is intended to build a future software system on such formalisms that will realize only those gestalt models that are evident from the data and can build and recognize structures of previously unseen and unexpected structure.