Least squares 3D surface and curve matching

Abstract

The automatic co-registration of point clouds, representing 3D surfaces, is a relevant problem in 3D modeling. This multiple registration problem can be defined as a surface matching task. We treat it as least squares matching of overlapping surfaces. The surface may have been digitized/sampled point by point using a laser scanner device, a photogrammetric method or other surface measurement techniques. Our proposed method estimates the transformation parameters of one or more 3D search surfaces with respect to a 3D template surface, using the Generalized Gauss-Markoff model, minimizing the sum of squares of the Euclidean distances between the surfaces. This formulation gives the opportunity of matching arbitrarily oriented 3D surface patches. It fully considers 3D geometry. Besides the mathematical model and execution aspects we address the further extensions of the basic model. We also show how this method can be used for curve matching in 3D space and matching of curves to surfaces. Some practical examples based on the registration of close-range laser scanner and photogrammetric point clouds are presented for the demonstration of the method. This surface matching technique is a generalization of the least squares image matching concept and offers high flexibility for any kind of 3D surface correspondence problem, as well as statistical tools for the analysis of the quality of final matching results. D

Error in target-based georeferencing and registration in terrestrial laser scanning

“…An overview of the surface matching strategies can be found in Gruen and Akca (2005). The ICP method is more widely used for registration.…”

Co-registration and bias corrections of satellite elevation data sets for quantifying glacier thickness change

“…Other studies have corrected DEMs using single or multiple linear regression corrections between elevation and the location and terrain parameters (Gorokhovich and Voustianiouk, 2006;Bolch et al, 2008;Peduzzi et al, 2010). In terrestrial and airborne laser scanning, 3-D Least Squares Matching (LSM) is used to minimize the Euclidean distances between the points of point clouds, often allowing not only for shifts but also for rotations and scales between the two or more datasets (Gruen and Akca, 2005;Miller et al, 2009). Another commonly applied correction to DEMs is an elevation dependent bias adjustment (Berthier et al, 2004(Berthier et al, , 2007Paul and Haeberli, 2008;Kääb, 2008) which may have significant implications for glacier elevation changes because glaciers spread a range of altitudes which define their ablation and accumulation areas.…”

On the detection of systematic errors in terrestrial laser scanning data

“…The iterative closest point (ICP) algorithm was investigated by Besl Yang and Medioni [18], and Zhang [21]. The pros and cons of the ICP approach have been illustrated by Gruen and Akca [7]. The basic version of the ICP method is based on the search for pairs of nearest points in the two sets, and estimates a rigid transformation.…”