Wave Interference for Pattern Description Selen Atasoy 1,2 , Diana Mateus 2 , Andreas Georgiou 1 , Nassir Navab 2 , and Guang-Zhong Yang 1 1 Visual Information Processing Group, Imperial College London, UK {catasoy, a.georgiou, g.z.yang}@imperial.ac.uk 2 Computer Aided Medical Procedures and Augmented Reality, Technical University of Munich, Germany {atasoy, mateus, navab}@in.tum.de Abstract. This paper presents a novel compact description of a pat- tern based on the interference of circular waves. The proposed approach, called “interference description”, leads to a representation of the pat- tern, where the spatial relations of its constituent parts are intrinsically taken into account. Due to the intrinsic characteristics of the interference phenomenon, this description includes more information than a simple sum of individual parts. Therefore it is suitable for representing the in- terrelations of different pattern components. We illustrate that the pro- posed description satisfies some of the key Gestalt properties of human perception such as invariance, emergence and reification, which are also desirable for efficient pattern description. We further present a method for matching the proposed interference descriptions of different patterns. In a series of experiments, we demonstrate the effectiveness of our de- scription for several computer vision tasks such as pattern recognition, shape matching and retrieval. 1 Introduction Many tasks in computer vision require describing a structure by the contextual relations of its consitituents. Recognition of patterns where the dominant struc- ture is due to global layout rather than its individual texture elements such as the triangle images in Figure 1a-c and peace symbols in Figure 10a, patterns with missing contours such as the Kanizsa triangle in Figure 1d and Figure 5b and patterns with large homogeneous regions such as the shape images in Fig- ure 9, necessitate the description of contextual relations within a structure in an efficient yet distinct manner. The captured information has to be discriminative enough to distinguish between structures with small but contextually impor- tant differences and be robust enough to missing information. In this paper, we introduce a method based on wave interference that efficiently describes the contextual relations between the constituent parts of a structure. Interference of several waves that originate from different parts of a struc- ture leads to a new wave profile, namely the interference pattern (Figure 2). This interference profile is computed as the superposition of all constituent circular waves and has two relevant properties for describing a structure. Firstly, the