Wavelets Defined Over Non Nested Tetrahedral Grids: A Theoretical Approach

  • Liliana B. Boscardin Depto. de Matemática, Universidad Nacional del Sur, Bahía Blanca, 8000, Argentina
  • Silvia M. Castro Depto. de Cs. e Ing. de la Computación, Universidad Nacional del Sur, Bahía Blanca, 8000, Argentina
  • Liliana R. Castro Depto. de Matemática, Universidad Nacional del Sur, Bahía Blanca, 8000, Argentina
Keywords: non nested multiresolution analysis, irregular tetrahedralizations, nested multiresolution analysis, wavelets

Abstract

The main contribution of this paper is the definition of wavelets over non nested tetrahedral grids, allowing the representation of functions defined on an a irregular tetrahedralization. In this way, it is possible to represent different attributes of a 3D object such as its color, brightness, density, etc. This representation consists of a set of coefficients corresponding to a coarse resolution followed by a set of detail coefficients that measures the error between two successive approximations. In this work the analysis matrix that allows going from a fine to a coarser resolution and the synthesis matrix needed for going from a coarse resolution to a finer one, are presented. All this is within the framework of non nested tetrahedral grids.

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Published
2019-04-17
How to Cite
Boscardin, L. B., Castro, S. M., & Castro, L. R. (2019). Wavelets Defined Over Non Nested Tetrahedral Grids: A Theoretical Approach. Journal of Computer Science and Technology, 19(01), e02. https://doi.org/10.24215/16666038.19.e02
Section
Original Articles