Combining Seminorms in Adaptive Lifting Schemes and Applications to Image Analysis and Compression

Authors:
Gemma Piella;Béatrice Pesquet-Popescu;Henk J. Heijmans;Gregoire Pau
Affiliations:
Signal and Image Proc. Dep., Ecole Nationale Supérieure des Télécommunications, Paris, France 75014;Signal and Image Proc. Dep., Ecole Nationale Supérieure des Télécommunications, Paris, France 75014;CWI, Amsterdam, The Netherlands 1090 GB;Signal and Image Proc. Dep., Ecole Nationale Supérieure des Télécommunications, Paris, France 75014
Venue:
Journal of Mathematical Imaging and Vision
Year:
2006

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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.