Abstract
In this paper, we present some adaptive wavelet decompositions that can capture the directional nature of images. Our method exploits the properties of seminorms to build lifting structures able to choose between different update filters, the choice being triggered by the local gradient-type features of the input. In order to deal with the variety and wealth of images, one has to be able to use multiple criteria, giving rise to multiple choice of update filters. We establish the conditions under these decisions can be recovered at synthesis, without the need for transmitting overhead information. Thus, we are able to design invertible and non-redundant schemes that discriminate between different geometrical information to efficiently represent images for lossless compression methods.
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The work of Piella is supported by a Marie-Curie Intra-European Fellowships within the 6th European Community Framework Programme.
Gemma Piella received the M.S. degree in electrical engineering from the Polytechnical University of Catalonia (UPC), Barcelona, Spain, and the Ph.D. degree from the University of Amsterdam, The Netherlands, in 2003.
From 2003 to 2004, she was at UPC as a visiting professor. She then stayed at the Ecole Nationale des Telecommunications, Paris, as a Post-doctoral Fellow. Since September 2005 she is at the Technology Department in the Pompeu Fabra University.
Her main research interests include wavelets, geometrical image processing, image fusion and various other aspects of digital image and video processing.
Beatrice Pesquet-Popescu received the engineering degree in telecommunications from the “Politehnica” Institute in Bucharest in 1995 and the Ph.D. thesis from the Ecole Normale Supérieure de Cachan in 1998. In 1998 she was a Research and Teaching Assistant at Université Paris XI and in 1999 she joined Philips Research France, where she worked for two years as a research scientist, then project leader, in scalable video coding. Since Oct. 2000 she is an Associate Professor in multimedia at the Ecole Nationale Supérieure des Télécommunications (ENST).
Her current research interests are in scalable and robust video coding, adaptive wavelets and multimedia applications.
EURASIP gave her a “Best Student Paper Award” in the IEEE Signal Processing Workshop on Higher-Order Statistics in 1997, and in 1998 she received a “Young Investigator Award” granted by the French Physical Society. She is a member of IEEE SPS Multimedia Signal Processing (MMSP) Technical Committee and a Senior Member IEEE. She holds 20 patents in wavelet-based video coding and has authored more than 80 book chapters, journal and conference papers in the field.
Henk Heijmans received his masters degree in mathematics from the Technical University in Eindhoven and his PhD degree from the University of Amsterdam in 1985. Since then he has been in the Centre for Mathematics and Computer Science, Amsterdam, where he had been directing the “signals and images” research theme.
His research interest are focused towards mathematical techniques for image and signal processing, with an emphasis on mathematical morphology and wavelet analysis.
Grégoire Pau was born in Toulouse, France in 1977 and received the M.S. degree in Signal Processing in 2000 from Ecole Centrale de Nantes. From 2000 to 2002, he worked as a Research Engineer at Expway where he actively contributed to the standardization of the MPEG-7 binary format. He is currently a PhD candidate in the Signal and Image Processing Departement of ENST-Telecom Paris. His research interests include subband video coding, motion compensated temporal filtering and adaptive non-linear wavelet transforms.
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Piella, G., Pesquet-Popescu, B., Heijmans, H.J.A.M. et al. Combining Seminorms in Adaptive Lifting Schemes and Applications to Image Analysis and Compression. J Math Imaging Vis 25, 203–226 (2006). https://doi.org/10.1007/s10851-006-6711-y
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DOI: https://doi.org/10.1007/s10851-006-6711-y