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Morphology on Label Images: Flat-Type Operators and Connections

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Abstract

We consider morphological operations on images whose pixel values are considered as labels without ordering between them, except for a least element ⊥ (meaning no label) and a greatest element ⊤(Meaning conflicting labels). Flat dilations and erosions can be defined as in usual grey-level morphology. Since the lattice of label images is not distributive, non-flat operators can be obtained by combination of flat ones. Given any connectivity on sets, there is a connection on label images for which the connected components of an image correspond precisely to its flat zones with their labels attached. Some specific applications of label morphology are given.

In the sequel of this paper [20], we will examine geodesic dilations and reconstructions on label images, and show how this variant of mathematical morphology can be applied to the segmentation of moving objects in video sequences [2, 3].

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Authors and Affiliations

  1. LSIIT UMR 7005 CNRS-ULP, Parc d’Innovation, Boulevard Sé bastien Brant, BP 10413, 67412, Illkirch Cedex, France

    Christian Ronse

  2. IRCAD/EITS/VIRTUALS, 1 Place de l’Hôpital, 67091, Strasbourg Cedex, France

    Vincent Agnus

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  1. Christian Ronse
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Correspondence to Christian Ronse.

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Christian Ronse was born in 1954. He studied pure mathematics at the Université Libre de Bruxelles (Licence, 1976) and the University of Oxford (M.Sc., 1977; Ph.D., 1979), specializing in group theory. Between 1979 and 1991 he was Member of Scientific Staff at the Philips Research Laboratory Brussels, where he conducted research on combinatorics of switching circuits, feedback shift registers, discrete geometry, image processing, and mathematical morphology. During the academic year 1991-1992 he worked at the Université Bordeaux-1, where he obtained his Habilitation diploma. Since October 1992, he has been Professor of Computer Science at the Université Louis Pasteur, Strasbourg (promotion to First Class Professorship in 2001), where he contributed to the development of a research group on image analysis, and the teaching of image processing to students at various levels. His scientific interests include imaging theory, mathematical morphology, image segmentation, motion measurement and medical imaging.

Vincent Agnus was born in 1971. He received the M.Sc. degree in discrete mathematics, the M.Sc. and Ph.D. in computer science from the Université Louis Pasteur, Strasbourg, in 1996, 1997 and 2001 respectively. He is presently working as researcher in medical imaging at the Research Institute for Cancer of the Digestive System (IRCAD), Strasbourg. His research interests include medical image analysis, image segmentation and mathematical morphology.

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Ronse, C., Agnus, V. Morphology on Label Images: Flat-Type Operators and Connections. J Math Imaging Vis 22, 283–307 (2005). https://doi.org/10.1007/s10851-005-4895-1

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