Arrangement: a spatial relation for describing and comparing part embeddings

A qualitative spatial relation called `arrangement´ is proposed. Given an image, the relation describes the sequence in which neighbors of each part are situated around it. The relation captures a perceptual gestalt of the image. An application of the relation to similarity retrieval in medical image databases is discussed. `Arrangement´ is closely related to directional relations and extends the notion of directional relations to parts that have complex shapes. A metric for comparing `arrangements´ is also proposed. The metric is obtained by interpreting `arrangements´ in terms of Voronoi diagrams. The metric enables robust use of the relation in real-world situations