In this paper we examine how Self-Organizing Maps (SOMs) can be used in detecting and describing emergent ontological relations between semantic objects and object classes in a visual database. The ontological relations we have studied include co-existence, taxonomies of visual and semantic similarity and spatial relationships. The used database contains 2618 images, each of which belongs to one or more of ten predefined semantic classes. 1

A directional map (or spatial template, fuzzy landscape) is an image where the value of each pixel represents the degree to which the pixel satisfies some directional relationship (e.g., right, left, above, below) to some reference object (i.e., a given set of pixels). There exists a simple quantitative model of such relationships, and the computation of direc-tional maps is usually based on algorithmic implementations of this model. We show here that the model has important flaws, and we respond to the issue with a new, promising approach: all directional maps induced by the reference object are generated from a force field that the object (which is seen as a physical entity) creates around itself. Preliminary experiments illustrate and show the interest of the approach. Index Terms — Directional relationships, object localiza-tion, directional maps, force fields, spatial templates