Analysis and classification of surface variation error using a geometry- adapted discrete wavelet transform

Surface wavelet representations [1] are a generalization of classical wavelets on the real line. They allow us to build a multilevel model of spatial data that is defined on an irregular mesh describing a general domain. Such wavelet representations differ from the classical case in that the wavelet filters are spatially variant. Using surface wavelets, one can develop a biorthogonal geometry-adapted Discrete Wavelet Transform (DWT) that has similar analysis properties to the conventional biorthogonal DWT on the real line. In this paper, we propose the use of a geometry-adapted DWT as a simple tool for classifying geometric errors that occur due to variation in manufacturing processes. It might be used, for example, in sheet metal forming, where a clay model of an automobile body needs to conform to the specifications contained in a CAD model. Likewise, it might also be used in numerically controlled machining to classify the source of machining error. We demonstrate that constant, oscillatory and random variations can be easily distinguished through an examination of the wavelet coefficients.