Neural computation of inner geometric pattern relations

A method for the description of patterns is proposed that is based on the evaluation of their inner geometric relations. They serve as features and are determined through operations that are mathematically formulated by so-called "generalized auto comparison functions", i.e., by measures that express a pattern's "auto-match" under geometric transformations. A subset of these features, namely the similarity features, are treated in greater detail, especially with regard to their invariance properties. The dominant role of spatial relations in the formation process of early visual representations is exemplified and a mechanism for the extraction of relational features from such representations is proposed. The feasibility for self-organization of suitable computing structures is discussed.