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Wavelets bases defined over tetrahedra
Keywords:
multiresolution, lifting, volume modeling, waveletsAbstract
In this paper we define two wavelets bases over tetrahedra which are generated by a regular subdivision method. One of them is a basis based on vertices while the other one is a Haar-like basis that form an unconditional basis for Lp (T, Σ, μ), 1 < p < ∞, being μ the Lebesgue measure and Σ the σ - algebra of all tetrahedra generated from a tetrahedron T by the chosen subdivision method. In order to obtain more vanishing moments, the lifting scheme has been applied to both of them
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References
[1] J. Bey, “Tetrahedral Grid Refinement”, Computing, Vol. 55, No. 4, pp. 355-378, 1995.
[2] F. Dong and J. Shi, “Multiresolution Data Modeling for Irregular Data Fields based on Wavelets”, IEEE IV, 1997.
[3] M. Girardi and W. Sweldens, “A New Class of Unbalanced Haar Wavelets that form an Unconditional Basis for Lpon General Measure Spaces, Journal of Fourier Analysis Appl., Vol. 3, pp. 457-474, 1997.
[4] D. J. Holliday and G. M. Nielson, “Progressive volume Models for Rectilinear Data using Tetrahedral Coons Volumes”, http://prism.asu.esu/research/data/publications/paper00pvmnitv.pdf, 2000.
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[11] W, Sweldens, “The Lifting Scheme: A New Philosophy in Biorthogonal Wavelet Constructions”, Proc. of the SPIE, vol. 2569, pp.68-79, 1995.
[12] W, Sweldens, “The Lifting Scheme:Custom-Design Construction of Biorthogonal Wavelets”, Appl. and Computational Harmonic Analysis, Vol.3, pp. 186-200, 1996.
[2] F. Dong and J. Shi, “Multiresolution Data Modeling for Irregular Data Fields based on Wavelets”, IEEE IV, 1997.
[3] M. Girardi and W. Sweldens, “A New Class of Unbalanced Haar Wavelets that form an Unconditional Basis for Lpon General Measure Spaces, Journal of Fourier Analysis Appl., Vol. 3, pp. 457-474, 1997.
[4] D. J. Holliday and G. M. Nielson, “Progressive volume Models for Rectilinear Data using Tetrahedral Coons Volumes”, http://prism.asu.esu/research/data/publications/paper00pvmnitv.pdf, 2000.
[5] R. Lorentz and P. Oswald, “Multilevel Finite Riesz Basis for Sobolev Spaces”, Proc. of the 9th Int. Conference on Domain Decomposition Methods in Sc. and Eng., Domain Decomposition Press, pp. 178-187, 1998.
[6] J. M. Lounsbery, Multiresolution Analysis for Surfaces of Arbitrary Topological Type, PhD. Thesis, University of Washington, Washington, Seattle, 1994.
[7] S. Muraki, “Approximation and Rendering of Volume Data using Wavelet Transforms”, Proc. of Visualization’92, pp. 21-28, 1992.
[8] G. M. Nielson, I. H. Jung and J. Sung, “Haar Wavelets over Triangular Domains with Applications to Multiresolution Models for Flow over a Sphere”, IEEE Visualization ’97, 1997.
[9] P. Schröder and W. Sweldens, “Spherical Wavelets: Efficiently Representing Functions on the Sphere”, ACM Proceedings of SIGGRAPH’95, pp. 161-172, 1995.
[10] E. Stollnitz, T. DeRose and D. Salesin, Wavelets for Computer Graphics: Theory and Applications, Morgan & Kaufmann Publishers Inc., 1996.
[11] W, Sweldens, “The Lifting Scheme: A New Philosophy in Biorthogonal Wavelet Constructions”, Proc. of the SPIE, vol. 2569, pp.68-79, 1995.
[12] W, Sweldens, “The Lifting Scheme:Custom-Design Construction of Biorthogonal Wavelets”, Appl. and Computational Harmonic Analysis, Vol.3, pp. 186-200, 1996.
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Published
2006-04-03
How to Cite
Boscardín, L. B., Castro, L. R., Castro, S. M., & De Giusti, A. E. (2006). Wavelets bases defined over tetrahedra. Journal of Computer Science and Technology, 6(01), p. 46–52. Retrieved from https://journal.info.unlp.edu.ar/JCST/article/view/828
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