5 - Multi-scalar Filtration Methodologies

Abstract

This chapter provides information to the multi-scalar filtration methodologies. Applications to multi-scalar surfaces are investigated. The theory of the lifting wavelet model is relatively new, simple and natural. The wavelet filtering process comprises three steps. The first is to decompose a surface original signal z(x,y) to a sequence of subsets that transfers space based information into scale based information which represents both the frequencies of z(x,y) and their location in scalar space. Following this, the next step is to separate and capture the different frequency components involved in z(x,y) within selected transmission bands, and finally the different frequency surfaces can be reconstructed in the spatial domain. The wavelet transform algorithm is much easier and faster than conventional filtering methods, and the transform procedure only embraces three stages: plus, minus, and application of the weighting algorithm. All computations are carded out in-place through rows and columns, no extended memory is needed and the algorithm procedure is much faster than normal filtration methods. The wavelet methods and the corresponding algorithms allow a better understanding of the 3D surface. The different frequency components of surfaces can be considered and retrieved with the excellent refinement accuracy in the light of these algorithms. For industrial application purposes, the method has considerable merits.