Combined Polynomial and Periodic Moments for the Analysis of Measured 3D Surfaces

This paper presents a new method of modelling and analyzing 3D surface data; for example, acquired using a laser scanning instrument. A new concept of combining periodic (e.g. FFT, DCT) with polynomial moments (e.g. Tchebichef moments) is presented. Whereby, QR decomposition is used to obtain a unary basis, minimizing the numerical effort when modelling surfaces. The new basis, being unary, is optimal from an error propagation point of view. It is shown that the new method can eliminate some of the problems associated with the Gibbs phenomena. The method is fully invertible, in contrast to applying windowing. The method is also applied to real-time modelling of 3D surface encountered to separate the global geometric from, periodic undulations and local anomalies. Real measurement data from an 3D scanning laser instrument is used to demonstrate the method.