Optimal Basis Functions in Curved Surface Measurement Using a Priori Information

Unknown curved surface can be estimated by a linear combination of a set of adequate basis functions.This paper determines the optimal basis functions for the estimation of the unknown surface of a powder-body for the case where a priori information is available.The determination is considered from two aspects.The first is the difference depending on the number of the observations available.The second is that depending on whether we consider a pure estimation of the curved surface or an accurate measurement of the unknown volume of the powder-body.