T-splines have recently been introduced to represent objects of arbitrary shapes using a smaller number of control points than the conventional non-uniform rational B-splines (NURBS) or B-spline representatizons in computer-aided design, computer graphics and reverse engineering. They are flexible in representing complex surface shapes and economic in terms of parameters as they enable local refinement. This property is a great advantage when dense, scattered and noisy point clouds are approximated using least squares fitting, such as those from a terrestrial laser scanner (TLS). Unfortunately, when it comes to assessing the goodness of fit of the surface approximation with a real dataset, only a noisy point cloud can be approximated: (i) a low root mean squared error (RMSE) can be linked with an overfitting, i.e., a fitting of the noise, and should be correspondingly avoided, and (ii) a high RMSE is synonymous with a lack of details. To address the challenge of judging the approximation, the reference surface should be entirely known: this can be solved by printing a mathematically defined T-splines reference surface in three dimensions (3D) and modeling the artefacts induced by the 3D printing. Once scanned under different configurations, it is possible to assess the goodness of fit of the approximation for a noisy and potentially gappy point cloud and compare it with the traditional but less flexible NURBS. The advantages of T-splines local refinement open the door for further applications within a geodetic context such as rigorous statistical testing of deformation. Two different scans from a slightly deformed object were approximated; we found that more than 40% of the computational time could be saved without affecting the goodness of fit of the surface approximation by using the same mesh for the two epochs.
<p><strong>Abstract.</strong> In recent years, the requirements in the industrial production of elongated objects, e.g., aircraft, have been increased. An essential aspect of the production process is the 3D object detection as well as the qualitative assessment of the captured data. On the one hand high accuracy requirements with a 3D standard deviation of &sigma;<sub>3D</sub>&thinsp;=&thinsp;1&thinsp;mm have to be fulfilled, on the other hand an efficient 3D object capturing is needed. In terms of efficiency, kinematic terrestrial laser scanning (k-TLS) has proven its strength in the recent years. It can be seen as an alternative and is even more powerful than to the well established static terrestrial laser scanning (s-TLS). In order to perform a high accurate 3D object capturing with k-TLS, the 3D object capturing of the initial sensor, the (geo-)referencing of the mobile platform, the synchronisation of all sensors and the system calibration, which means the determination of six extrinsic parameters have to be performed with suitable accuracy. Within this contribution we focus on the system calibration. Therefore an approach based on known reference geometries, here planes, is used (Strübing and Neumann, 2013). As a result, the lever arm and boresight angles are determined. Hereby the number as well as the position and orientation of the reference geometries is of importance. Therefore, an optimal arrangement has to be found. Here a sensitive analysis based on uncertainty propagation is used. A selective search of an optimised arrangement is carried out by a genetic algorithm. Within some examples we demonstrate some theoretical aspects and how an optimisation of the reference geometry arrangement can be achieved.</p>
Terrestrial laser scanners (TLS) capture a large number of 3D points rapidly, with high precision and spatial resolution. These scanners are used for applications as diverse as modeling architectural or engineering structures, but also high-resolution mapping of terrain. The noise of the observations cannot be assumed to be strictly corresponding to white noise: besides being heteroscedastic, correlations between observations are likely to appear due to the high scanning rate. Unfortunately, if the variance can sometimes be modeled based on physical or empirical considerations, the latter are more often neglected. Trustworthy knowledge is, however, mandatory to avoid the overestimation of the precision of the point cloud and, potentially, the non-detection of deformation between scans recorded at different epochs using statistical testing strategies. The TLS point clouds can be approximated with parametric surfaces, such as planes, using the Gauss–Helmert model, or the newly introduced T-splines surfaces. In both cases, the goal is to minimize the squared distance between the observations and the approximated surfaces in order to estimate parameters, such as normal vector or control points. In this contribution, we will show how the residuals of the surface approximation can be used to derive the correlation structure of the noise of the observations. We will estimate the correlation parameters using the Whittle maximum likelihood and use comparable simulations and real data to validate our methodology. Using the least-squares adjustment as a “filter of the geometry” paves the way for the determination of a correlation model for many sensors recording 3D point clouds.
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