A most versatile relative position descriptor
In daily conversation, the relative positions of objects in space are described in terms of spatial relationships: topological (e.g., “is inside”), directional (e.g., “is above”) and distance (e.g., “is far from”) relationships. A relative position descriptor is a quantitative representation of the relative position of two spatial objects, and it is often used as a basis from which models of spatial relationships can be derived. Like colour, texture, and shape descriptors, it is a visual descriptor. Various relative position descriptors have been proposed, and they have found a variety of applications (e.g., graphical symbol retrieval, linguistic scene description, human-robot interaction, map-to-image conflation, land cover classification). In this thesis, we introduce a new relative position descriptor: the Φ-descriptor. It is a fast-to compute, property-loaded tool that has many advantages over its competitors. Our approach borrows ideas from the Radon transform and Allen’s interval algebra. It is based on the concept of the F-histogram and on an original categorization of pairs of consecutive boundary points on a line. A spatial relationship is usually modeled either as a crisp relation, i.e., as a relation, in the standard mathematical sense, or as a fuzzy relation, which is a concept in fuzzy set theory. We show here that the Φ-descriptor can be used to develop crisp and fuzzy models of a large number of relationships. For example, the well-known RCC8 and DE-4IM topological relations are definable in terms of the descriptor; the RCC8 relations can be fuzzified based on the descriptor; the descriptor can be used to model directional relationships, including visual surroundedness. Keywords: Spatial relationships, relative position, relative position descriptor, visual surroundedness.