Orthogonal spline fitting in range data

Abstract

An orthogonal fitting technique for spline approximation is introduced. The technique takes into account the fact that there is uncertainty in both sides of the input-output relationship. In least squares (LS) spline approximation a computationally costly iterative process is required to refine the parameterization such that the error is orthogonal to the signal. This process may be avoided by using the total LS (TLS) fitting in case the nature of the error in parameterization is random instead of systematic. A lower rank approximation of the signal may be used as an input to the spline fitting process. In particular, if adaptive parameterization based on distances among observations is used a more reliable parameterization can be obtained. The TLS technique yields a lower bias than LS fitting whereas the LS has a lower variance. However, the difference in variance is not significant.