Lifting wavelet for three-dimensional surface analysis

Abstract It is recognised that surface topography is the one of the most important factors affecting the functional performance of components. It is also reported that the wear rate of surfaces in operational service is determined by roughness, waviness and the multi-scalar topographical features of the surfaces, such as random peak/pits and ridge/valleys. These functional topographical features will impact directly on wear mechanical and physical properties of a whole system, especially in joint replacement systems used in bio-engineering. In this situation, a vitally important consideration for the functional characterisation must be the extraction of all topographical events over an interacting surface. It is the purpose of this paper to discuss the possibility of using a ‘lifting Wavelet’ representation for filtration of functional surfaces. The Wavelet and scalar coefficients are only dependant on the measured raw data of a surface and the filtering and lifting factors calculated by a cubic spline interpolation in an interval. The Wavelet transform only embraces three stages, splitting, prediction and updating. The other advantage derived from the new model is that there is no boundary destruction. The implementation of the lifting Wavelet is easy to understand and perform. A group of examples has been selected here to demonstrate the feasibility and applicability of the lifting Wavelet for the characterisation of surfaces.