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International Conference on Advanced Concepts for Intelligent Vision Systems

ACIVS 2006: Advanced Concepts for Intelligent Vision Systems pp 91–102Cite as

Dilation Matrices for Nonseparable Bidimensional Wavelets

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 4179))

Abstract

For nonseparable bidimensional wavelet transforms, the choice of the dilation matrix is all–important, since it governs the downsampling and upsampling steps, determines the cosets that give the positions of the filters, and defines the elementary set that gives a tesselation of the plane. We introduce nonseparable bidimensional wavelets, and give formulae for the analysis and synthesis of images. We analyze several dilation matrices, and show how the wavelet transform operates visually. We also show some distorsions produced by some of these matrices. We show that the requirement of their eigenvalues being greater than 1 in absolute value is not enough to guarantee their suitability for image processing applications, and discuss other conditions.

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Author information

Authors and Affiliations

  1. Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab. I. CP 1428, Ciudad de Buenos Aires

    Ana Ruedin

Authors
  1. Ana Ruedin
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Editor information

Editors and Affiliations

  1. DGA/D4S/MRIS, 94114, Arcueil, France

    Jacques Blanc-Talon

  2. Ghent University, 9000, Gent, Belgium

    Wilfried Philips

  3. CSIRO ICT Centre, 1710, Sydney, NSW, Australia

    Dan Popescu

  4. University of Antwerp, 2610, Wilrijk, Belgium

    Paul Scheunders

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© 2006 Springer-Verlag Berlin Heidelberg

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Ruedin, A. (2006). Dilation Matrices for Nonseparable Bidimensional Wavelets. In: Blanc-Talon, J., Philips, W., Popescu, D., Scheunders, P. (eds) Advanced Concepts for Intelligent Vision Systems. ACIVS 2006. Lecture Notes in Computer Science, vol 4179. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11864349_9

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  • DOI: https://doi.org/10.1007/11864349_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44630-9

  • Online ISBN: 978-3-540-44632-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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