Freeform Surface Filtering Using the Lifting Wavelet Transform

Texture measurement for simple geometric surfaces is well established. Many surface filtration techniques using Fourier, Gaussian, wavelets, etc., have been proposed over the past decades. These filtration techniques cannot be applied to today's complex freeform surfaces, which have non-Euclidean geometries in nature, without distortion of the results. Introducing the lifting scheme opens the opportunity to extend the wavelet analysis to include irregular complex surface geometries. In this paper, a method of filtering those complex freeform surfaces presented by triangular meshes based on the lifting wavelet has been proposed. The proposed algorithm generalises the traditional lifting scheme to any freeform surface represented by any type of triangular mesh; regular, semi-regular or irregular mesh. This technique consists of five major stages; split, predict, update, simplify (down-sampling) and merge (up-sampling). All of these techniques are discussed and explained in the paper. Results and discussion of the application of this method to simulated and measured data are presented.