The problem of interpreting single images of abstract figures is addressed. It is argued that neither rule-based deductive inference nor model-based matching are satisfactory computational paradigms for this problem. As an alternative, an inductive approach consisting of two parts is presented. The first part involves a scheme, based on differential geometry, for describing the shapes of curves and surfaces, and for generating these descriptions from images. The second part of the approach relies on a criterion for deciding which description, among the candidates allowed by the constraints in the image, is to be preferred. This criterion–minimum entropy–is related to concepts from Gestalt psychology, thermodynamics, and information theory. Several examples are given to illustrate the inductive approach.