Abstract. We present a simple framework to compute hyperbolic Voronoi diagrams of finite point sets as affine diagrams. We prove that bisectors in Klein’s non-conformal disk model are hyperplanes that can be interpreted as power bisectors of Euclidean balls. Therefore our method simply consists in computing an equivalent clipped power diagram followed by a mapping transformation depending on the selected representation of the hyperbolic space (e.g., Poincaré conformal disk or upper-plane representations). We discuss on extensions of this approach to weighted and k-order diagrams, and describe their dual triangulations. Finally, we consider two useful primitives on the hyperbolic Voronoi diagrams for designing tailored user interfaces of an image catalog browsing application in the hyperbolic disk: (1) finding nearest neighbors, and (2) computing smallest enclosing balls. 1 Introduction and prior work The birth and spread of science was originally initiated by geometry, the science

tree-structured self-organising maps (TS-SOM), image theft detection Abstract — This paper describes an image browsing and retrieval application called GalSOM. Bitmap images are described by their colour histograms and sorted using an improved variant of the tree-structured self-organising map (TS-SOM) algorithm. The advantages of using such a system are discussed in detail, and their application to the problem of image theft detection is proposed. 1