Abstract
A formal definition of a combinatorial topology is presented in this paper for the discrete N-dimensional space defined by the An* lattice. The use of this grid instead of the classical ℤn is based on two arguments:
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It is the optimal sampling grid in the sense of Shannon’s sampling theorem in 2 and 3 dimensions,
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It induces the simplest discrete topology definition because its dual is a K-simplex.
Their interest in image processing and in the medical imaging field is presented with some examples.
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Chafia Hamitouche IEEE-EMBS member, received the Ph.D. degree in Signal Processing and Telecommunications from the University of Rennes I, France, in 1991. She joined the Image and Information Processing department of the “Ecole Nationale Supérieure des Télécommunications de Bretagne”, in 1992, where she is Associate Professor in signal and image processing. Dr. Hamitouche is member of the Laboratory for Medical Information Processing – Inserm U650, her research interests include, 3-D medical image analysis, biological shape modeling, determination of new ND sampling grids optimal topologically and in signal processing sense, study of the relationship between morphology and functionality of osteo-articular complexes and more recently, she is involved in Computer Assisted Orthopaedic Surgery.
Luis IbÒez obtained a Physics degree in 1989 from the Universidad Industrial de Santander, at Bucaramanga, Colombia. In 1994 He obtained a Master in Physics from the same University. He followed a Ph.D. program in Signal Processing at the Université de Rennes I at Rennes, France, performing his research activities on the domain of medical image at the Département Image et Traitement de l’Information of the ... cole Nationale Superieure des Télécommunications de Bretagne at Brest, France. In 1999 he joined the Division of Neurosurgery of the Univesity of North Carolina at Chapel Hill and participated as a member of the MIDAG and CADDLab groups. His activity at UNC-CH was related with the development of algorithms for 3D/2D registration applied to image guided surgery. He also participated as developer of the INSIGHT Registration and Segmentation Toolkit sponsored by the National Library of Medicine. He joined Kitware Inc. in February 2002. He has been member of the IEEE-EMBS and IEEE-Computer Societies since 1995.
Professor Christian Roux graduated from the Ecole Normale Supérieure de Cachan in 1978 and obtained the Ph.D. degree from the Institut National Polytechnique de Grenoble in 1980. He is a Professor at the Ecole Nationale Supérieure des Télécommunications de Bretagne, Brest and Director of the Laboratory for Medical Information Processing—Inserm U650. He has been a Visiting Professor at the Medical Image Processing Group, Department of Radiology, University of Pennsylvania, Philadelphia, U.S.A. in 1992–93.
His research interests concern advanced medical image and shape processing, and dynamic shape analysis and modeling for the quantification of forms and functions. He has published around 90 papers, holds 2 patents, and is co-editor of a book entitled Contemporary Perspectives in Three-Dimensional Biomedical Imaging (IOS Press) published in 1997.
He is a former President of the IEEE Engineering in Medicine and Biology Society, was an Associate Editor of the IEEE Transactions on Medical Imaging (1993–2001), and Chairman of its Steering Committee (2002–2004). Dr. Roux is a member of the Editorial Board of the IEEE Series in Biomedical Engineering and of the IEEE Transactions on Information Technology in Biomedicine. He was the General co-chair of IEEE ISBI 2004 Conference and the Chair of the 2004 edition of the IEEE EMBS International Summer School on Biomedical Imaging. Dr Roux is a Fellow of the IEEE, of the American Institute for Medical and Biological Engineering and of the International Academy for Medical and Biological Engineering. He has received the IEEE EMBS Award in 2003. He is member of the Council of the European Alliance for Medical and Biological Engineering and Science.
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Hamitouche, C., Ibáñez, L. & Roux, C. Discrete Topology of (An*) Optimal Sampling Grids. Interest in Image Processing and Visualization. J Math Imaging Vis 23, 401–417 (2005). https://doi.org/10.1007/s10851-005-2030-y
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DOI: https://doi.org/10.1007/s10851-005-2030-y