Dilation matrices for nonseparable bidimensional wavelets

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 introd...

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Detalles Bibliográficos
Autor principal: Ruedin, Ana María Clara
Publicado: 2006
Materias:
Dilation
Nonseparable
Quincunx
Wavelet
Eigenvalues and eigenfunctions
Image analysis
Image processing
Mathematical transformations
Dilation matrices
Nonseparable bidimensional wavelet transforms
Artificial intelligence
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03029743_v4179LNCS_n_p91_Ruedin
http://hdl.handle.net/20.500.12110/paper_03029743_v4179LNCS_n_p91_Ruedin
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_03029743_v4179LNCS_n_p91_Ruedin
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spelling paper:paper_03029743_v4179LNCS_n_p91_Ruedin2023-06-08T15:28:25Z Dilation matrices for nonseparable bidimensional wavelets Ruedin, Ana María Clara Dilation Nonseparable Quincunx Wavelet Eigenvalues and eigenfunctions Image analysis Image processing Mathematical transformations Dilation Dilation matrices Nonseparable bidimensional wavelet transforms Quincunx Artificial intelligence 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. © Springer-Verlag Berlin Heidelberg 2006. Fil:Ruedin, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2006 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03029743_v4179LNCS_n_p91_Ruedin http://hdl.handle.net/20.500.12110/paper_03029743_v4179LNCS_n_p91_Ruedin
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Dilation
Nonseparable
Quincunx
Wavelet
Eigenvalues and eigenfunctions
Image analysis
Image processing
Mathematical transformations
Dilation
Dilation matrices
Nonseparable bidimensional wavelet transforms
Quincunx
Artificial intelligence
spellingShingle Dilation
Nonseparable
Quincunx
Wavelet
Eigenvalues and eigenfunctions
Image analysis
Image processing
Mathematical transformations
Dilation
Dilation matrices
Nonseparable bidimensional wavelet transforms
Quincunx
Artificial intelligence
Ruedin, Ana María Clara
Dilation matrices for nonseparable bidimensional wavelets
topic_facet Dilation
Nonseparable
Quincunx
Wavelet
Eigenvalues and eigenfunctions
Image analysis
Image processing
Mathematical transformations
Dilation
Dilation matrices
Nonseparable bidimensional wavelet transforms
Quincunx
Artificial intelligence
description 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. © Springer-Verlag Berlin Heidelberg 2006.
author Ruedin, Ana María Clara
author_facet Ruedin, Ana María Clara
author_sort Ruedin, Ana María Clara
title Dilation matrices for nonseparable bidimensional wavelets
title_short Dilation matrices for nonseparable bidimensional wavelets
title_full Dilation matrices for nonseparable bidimensional wavelets
title_fullStr Dilation matrices for nonseparable bidimensional wavelets
title_full_unstemmed Dilation matrices for nonseparable bidimensional wavelets
title_sort dilation matrices for nonseparable bidimensional wavelets
publishDate 2006
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03029743_v4179LNCS_n_p91_Ruedin
http://hdl.handle.net/20.500.12110/paper_03029743_v4179LNCS_n_p91_Ruedin
work_keys_str_mv AT ruedinanamariaclara dilationmatricesfornonseparablebidimensionalwavelets
_version_ 1768545187995320320

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