Employing variance component estimation for point cloud based geometric surface representation by B-splines

Abstract

When it comes to the significance assessment of interepochal displacements, great reliance on the stochastic information related to the point clouds introduced in the estimation of the geometric representation of the analysed surface is present. Possible uncertainty sources in point clouds are instrument-, environment- or object sided. Further, the chosen mathematical model for point cloud approximation may introduce an uncertainty budget ascribed as model uncertainty. The present contribution employs variance component estimation (VCE) in the course of geometric point cloud approximation with tensor product B-spline surfaces. A method using the BIQUE-estimation of the variance components is used. It enables considering overlapping variance components. Here, those are related to measurement and model uncertainties. The aim of the article is to investigate whether a realistic estimation of the components can be achieved by means of the VCE in particular with regard to the separation between measurement and model uncertainty. The former include the distance and angular components whilst the model uncertainty is set up using covariance functions. For that, a B-spline surface with comparably superior complexity, whilst describing an identical geometric surface course as the functionally employed surface representation, is generated. Artificial altering of the more complex surface establishes the model uncertainty as distance between equally parametrized sampled points. Results based on simulated data show that variance components are separable and estimable if the model uncertainty exceeds measurement uncertainty, and only points affected by model deviations are included in the VCM setup.