Wavelets Defined Over Non Nested Tetrahedral Grids: A Theoretical Approach
Keywords:non nested multiresolution analysis, irregular tetrahedralizations, nested multiresolution analysis, wavelets
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.