Artículo
Ruedin, A. "Dilation matrices for nonseparable bidimensional wavelets" (2006) 8th International Conference on Advanced Concepts for Intelligent Vision Systems, ACIVS 2006. 4179 LNCS:91-102
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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. © Springer-Verlag Berlin Heidelberg 2006.
Registro:
| Documento: | Artículo |
| Título: | Dilation matrices for nonseparable bidimensional wavelets |
| Autor: | Ruedin, A. |
| Ciudad: | Antwerp |
| Filiación: | Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Pab. I, CP 1428, Ciudad de Buenos Aires, Argentina |
| Palabras clave: | Dilation; Nonseparable; Quincunx; Wavelet; Eigenvalues and eigenfunctions; Image analysis; Image processing; Mathematical transformations; Dilation; Dilation matrices; Nonseparable bidimensional wavelet transforms; Quincunx; Artificial intelligence |
| Año: | 2006 |
| Volumen: | 4179 LNCS |
| Página de inicio: | 91 |
| Página de fin: | 102 |
| Título revista: | 8th International Conference on Advanced Concepts for Intelligent Vision Systems, ACIVS 2006 |
| Título revista abreviado: | Lect. Notes Comput. Sci. |
| ISSN: | 03029743 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03029743_v4179LNCS_n_p91_Ruedin |
Referencias:
- Skodras, A., Christopoulos, C., Ebrahimi, T., Jpeg2000: The upcoming still image compression standard (2001) Pattern Recognition Letters, 22, pp. 1337-1345. , Elsevier
- Cohen, A., Daubechies, I., Non-separable bidimensional wavelet bases (1993) Revista Matematica Iberoamericana, 9, pp. 51-137
- Karoui, A., Vaillancourt, R., Nonseparable biorthogonal wavelet bases of L2(Rn) (1999) CRM Proceedings and Lecture Notes American Math. Society, 18, pp. 135-151
- Kovacevic, J., Vetterli, M., Nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for Rn (1992) IEEE Trans. Inf. Theor., 38, pp. 533-555
- Cabrelli, C., Heil, C., Molter, U., Accuracy of lattice translates of several multi-dimensional refinable functions (1998) J. of Approximation Theory, 95, pp. 5-52
- Cabrelli, C., Heil, C., Molter, U., (1999) Polynomial Reproduction by Refinable Functions, , Ka-Sing Lau
- Ruedin, A.M.C., Construction of nonseparable multiwavelets for nonlinear image compression (2002) Eurasip J. of Applied Signal Proc., 2002 (1), pp. 73-79
- Heil, C., Colella, D., (1994) Dilation Equations and the Smoothness of Compactly Supported Wavelets, , J. Benedetto and M. Frazier, editors, CRC Press
- Ayache, A., Construction of non-separable dyadic compactly supported orthonormal wavelet bases L2(R2) of arbitrarily high regularity (1999) Revista Mat. Iberoamericana, 15, pp. 37-58
- Kovacevic, J., Vetterli, M., New results on multidimensional filter banks and wavelets (1993) Proc. IEEE Int. Symposium on Circuits and Systems
- He, W., Lai, W., Examples of bivariate non-separable continuous compactly supported orthonormal wavelets (2000) IEEE Trans. on Image Processing, 9, pp. 949-953
- Faugère, J.C., De Saint-Martin, F.M., Rouillier, F., Design of regular nonseparable bidimensional wavelets using grobner basis techniques (1998) IEEE Trans. on Signal Processing, 46, pp. 845-856
- Belogay, E., Wang, Y., Arbitrarily smooth orthogonal nonseparable wavelets in R2 (1999) SIAM J. Math. Anal., 30, pp. 678-697
- Ruedin, A., Nonseparable orthogonal multiwavelets with 2 and 3 vanishing moments on the quincunx grid (1999) Proc. SPIE Wavelet Appl. Signal Image Proc. VII, 3813, pp. 455-466
- Ruedin, A.M.C., Balanced nonseparable orthogonal multiwavelets with two and three vanishing moments on the quincunx grid (2000) Proc. SPIE, 4119, pp. 519-527. , Wavelet Appl. Signal Image Proc. VIII
- Entezari, A., Moller, T., Vaisey, J., Subsampling matrices for wavelet decompositions on body centered cubic lattices (2004) IEEE Sign. Proc. Lett., 11, pp. 733-735A4 - Barco; et al.; Eurasip; Ghent University; IEEE Benelux Signal Processing University; Philips Research
Citas:
---------- APA ----------
(2006) . Dilation matrices for nonseparable bidimensional wavelets. 8th International Conference on Advanced Concepts for Intelligent Vision Systems, ACIVS 2006, 4179 LNCS, 91-102.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03029743_v4179LNCS_n_p91_Ruedin [ ]
---------- CHICAGO ----------
Ruedin, A. "Dilation matrices for nonseparable bidimensional wavelets" . 8th International Conference on Advanced Concepts for Intelligent Vision Systems, ACIVS 2006 4179 LNCS (2006) : 91-102.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03029743_v4179LNCS_n_p91_Ruedin [ ]
---------- MLA ----------
Ruedin, A. "Dilation matrices for nonseparable bidimensional wavelets" . 8th International Conference on Advanced Concepts for Intelligent Vision Systems, ACIVS 2006, vol. 4179 LNCS, 2006, pp. 91-102.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03029743_v4179LNCS_n_p91_Ruedin [ ]
---------- VANCOUVER ----------
Ruedin, A. Dilation matrices for nonseparable bidimensional wavelets. Lect. Notes Comput. Sci. 2006;4179 LNCS:91-102.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03029743_v4179LNCS_n_p91_Ruedin [ ]
