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.<>