By Jens-André Paffenholz
This blog presents an efficient procedure for directly geo-referencing static 3D laser scans. This is a worthwhile way to obtain the required transformation parameters from the local sensor-defined coordinate system to a global system. Therefore, a multi-sensor systems (MSS) is designed with a phase-measuring laser scanner and 3D positional sensors (see Figure 1). By means of at least one eccentrically mounted GNSS antenna on top of the rotating laser scanner one gets a 3D trajectory of the antenna reference point (ARP). The analysis of the resulting trajectory within a recursive state-space filtering approach (e.g., Kalman filter) yields the transformation parameters (position and orientation) and their full variance-covariance matrix. Apart from the geo-referencing of single laser scans the propagation of the transformation parameter variances to the point clouds is possible. Moreover, an improvement of the obtained direct geo-referencing results by means of matching algorithms (like, e.g., Iterative Closest Point (ICP) algorithm) with consideration of the stochastic point cloud information of each single 3D point is feasible.
Figure 1. Sketch of the MSS (at the Geodetic Institute of the Leibniz Universität Hannover) composed of a phase-measuring laser scanner, GNSS equipment and two single-axis inclinometers.
Overview about the enlisted sensors, their specifications and the algorithm for the transformation parameter estimation
The main characteristic of the terrestrial laser scanning (TLS) technique for engineering geodesy is the immediate data acquisition in 3D space. This is realised with a high spatial resolution (a few millimetres for mean distances of approx. 25 m), as well as with a very high frequency (up to 50 profiles per second) in a relative or local sensor-defined coordinate system. The TLS technique can be used in a static or a kinematic mode. Static scanning is characterised by one single fixed translation and orientation of the laser scanner in relation to an absolute or global coordinate system. For kinematic scanning, where the data acquisition is commonly reduced to 2D profiles, the translations and orientations are time-dependent. Hence, the transformation parameters for each profile are different in relation to each other as well as to an absolute or global coordinate system. When a combination of several static scans from different stations into one coordinate system (registration) is required, the transformation parameters for each scan have to be determined. For an additional link to an absolute or global coordinate system (geo-referencing), typically control points in a known geodetic datum are necessary. By the direct observation of the required transformation parameters by means of GNSS equipment and arbitrary navigation sensors, one can solve the registration and geo-referencing in one single step without the need of additional control points.
At the present developmental stage of the MSS (at the Geodetic Institute of the Leibniz Universität Hannover), it is composed of a phase-measuring laser scanner, one eccentrically mounted GNSS antenna and two inclinometers on top of the rotating laser scanner (cf. Figure 1). Hereby, the horizontal rotation of the laser scanner of at least 360 degrees is suitable to derive the position as well as the azimuthal orientation of the laser scanner.
Currently, the GNSS data processing is done in post processing. In general, real-time processing is possible within the purposed geo-referencing procedure. The practicability within the direct geo-referencing procedure due to expected higher variances for the trajectory points of the ARP has to be investigated in the future. However, the short high frequent trajectory of the ARP makes the GNSS analysis a challenging problem which has to be overcome. The overall duration is about 15 min with up to 20 hz data rate. In this approach the alternating antenna orientation with respect to an earth-centred earth-fixed coordinate system will contribute to the error budget due to the right-hand circular polarisation of the satellite signals and the azimuthally varying phase centre corrections (PCC). In addition, near-field effects caused by the antenna adaption (made from aluminium) on the laser scanner, or possibly multipath from the vicinity surrounding the scanner may contribute to the error budget. Investigations of these GNSS related errors yield to no significant impact of the used antenna adaption within a double difference analysis in the observation domain. As expected, the rotated PCC against the original PCC has an effect of up to 5 mm in the observation domain which corresponds to the horizontal offset components of the used GNSS antenna. The analysis in the coordinate domain also indicates an effect of up to 5 mm. The analysis shows that the PCC effect is dominated by the phase centre offset components. One can conclude that within the currently applied epoch-wise GNSS analysis the effect of rotated PCC has no significant impact on the transformation parameters in the geo-referencing procedure. For further details about these investigations please refer to Paffenholz et al. (2011).
The analysis of the 3D ARP trajectory (cf. Figure 2) is performed within an adaptive extended Kalman filter (aEKF). This yields the transformation parameters (position and orientation) alongside their full variance-covariance matrix. The benefits of using a closed form algorithm on the basis of a Kalman filter (KF) are the following: Firstly, the KF allows real-time data processing, and secondly, the parameter estimation will be less sensitive to outliers. To deal with non-linearities in the system and measurement equations, an extended KF (EKF) is used to estimate the transformation parameters of the MSS. Another promising approach for a non-linear state estimation is the combination of Sequential Monte Carlo filtering (also known as particle filter) and an EKF, which was proposed by Alkhatib et al. (2011). The main benefit of the proposed approach is the better performance in case of high-nonlinear state-space equations. An improvement of the dynamic model of the EKF can be achieved by augmenting the EKF with adaptive parameters. These parameters are time invariant and system-specific with well-known initial values. For further details please refer to Paffenholz et al. (2010).
Figure 2. Sample ARP trajectory of a 360 degree rotation of the laser scanner around its vertical axis. Red indicates the original10 hz measurements with a Javad GNSS receiver Delta with Javad GrAnt-G3T antenna. Blue and green indicate the predicted and filtered trajectory within the aEKF approach, respectively.
Performing the direct geo-referencing by applying the transformation parameters and calculation of the uncertainty measures of the 3D point cloud
The final step of the purposed direct geo-referencing procedure is to apply the transformation parameters (translation vector as well as at least the azimuthal orientation) to the 3D point cloud. The three spatial rotation parameters can be reduced to the azimuthal orientation in case of a sufficient sensor orientation to the direction of gravity. The left part of Figure 3 shows the transformation result from the local sensor-defined to an absolute coordinate system in the case of two 3D point clouds, each from a different static scanner station (red and blue). The radial distance between the scanner and the object is 15 m and 20 m, respectively. It is obvious, that the two geo-referenced point clouds have a slight misalignment of a few centimetres. Due to the known absolute coordinates of the pillar on the roof of the building (middle part of the figure), one can conclude that the geo-referencing of the blue point cloud is inaccurate. Moreover, the variances for the transformation parameters from the blue station are higher than the variances for the red station. This leads to the conclusion that the estimated transformation parameters for the blue station are not reliable. Nevertheless, this direct geo-referencing can be used as adequate pre-registration for matching algorithms.
To overcome this misalignment the application of matching algorithms, like the ICP algorithm, is worthwhile. As input for the ICP algorithm the pre-registered 3D point clouds are used. The a-priori alignment (within a few centimetres) of the two point clouds is sufficient for the application of the ICP algorithm to find an adequate amount of corresponding points for a reliable estimation of the transformation parameters. The ICP result is shown in the right part of Figure 3. One can clearly see that the matching of the two point clouds was successful. The recent topic of the ongoing research is the consideration of the uncertainties of each point cloud within the ICP algorithm for a further improvement of the matching results.
Figure 3. Left: Applied transformation parameters to two scans from different stations (red and blue). Right: Result after running the ICP algorithm on the pre-registered 3D point clouds (shown in the left part of this figure).
In the current research work uncertainties for each single point cloud are calculated by variance propagation: Combining the uncertainties of the scanner measurements (e.g., manufacturer values for the angle and range measurement accuracy), and the uncertainties of the direct geo-referencing procedure (variance-covariance matrix of the transformation parameters obtained within the aEKF). As mentioned before, these uncertainties should be considered in the ICP algorithm in the ongoing work for a further improvement of the matching results. Bae et al. (2009) already stated that the consideration of positional uncertainties in the point cloud matching will be a worthwhile approach to improve the matching, as well as the interpretation of 3D point clouds. An example for the result of the variance propagation of the scanner and direct geo-referencing uncertainties is illustrated in Figure 4. The figure depicts a stochastic point cloud of the red station (similar 3D point cloud as shown in Figure 3). As measure for the uncertainty the mean of the coordinate uncertainty in a range of 5 mm up to 30 mm is shown.
Figure 4. Stochastic point cloud of red station resulting from variance propagation for the uncertainties of the scanner measurements and the direct geo-referencing procedure. Depicted is the mean of the coordinate uncertainty.
Conclusions and Future Work
This article describes an on-site direct geo-referencing of 3D static laser scans by means of tracking the circular motion of the laser scanner around its vertical axis with 3D positioning sensors. The required transformation parameters from the local to an absolute coordinate system are estimated within a Kalman filter approach. The results show a misalignment for two different static laser scanner stations in a range of a few centimetres. Nevertheless, this is an adequate pre-registration for matching algorithms. Besides the geo-referencing, the uncertainties of the 3D point clouds are calculated by variance propagation. The future work is focused on the consideration of the stochastic point cloud information within matching algorithms (like, e.g., ICP) for an optimal fusion of different (pre-) registered point clouds into one optimal solution.
Alkhatib, Hamza; Paffenholz, Jens-André; Kutterer, Hansjörg (2011): Sequential Monte Carlo Filtering for nonlinear GNSS trajectories. In: Sneeuw; Novák; Crespi and Sansò (Eds.): Proceedings of the VII Hotine-Marussi Symposium on Mathematical Geodesy, Rome, 6-10 June 2009. International Association of Geodesy (IAG). 1st Edition. Berlin, Heidelberg: Springer, (in press).
Bae, Kwang-Ho; Belton, David; Lichti, Derek D. (2009): A Closed-Form Expression of the Positional Uncertainty for 3D Point Clouds. In IEEE Trans. Pattern Analysis and Machine Intelligence 31 (4), pp. 577–590.
Paffenholz, Jens-André; Kersten, Tobias; Schön, Steffen; Kutterer, Hansjörg (2011): Analysis of the Impact of Rotating GNSS Antennae in Kinematic Terrestrial Applications. In: Proceedings of the FIG Working Week 2011. FIG. Marrakech, published on CD only / also available via www.fig.net.
Paffenholz, Jens-André; Alkhatib, Hamza; Kutterer, Hansjörg (2010): Direct geo-referencing of a static terrestrial laser scanner. In JAG 4 (3), 115–126.
Jens-André Paffenholz received his Dipl.-Ing. in Geodesy and Geoinformatics at the Leibniz Universität Hannover. Since 2006 he has been research assistant and since 2008 also PhD candidate at the Geodetic Institute at the Leibniz Universität Hannover, respectively. His current interests are: terrestrial laser scanning, industrial measurement systems, and process automation of measurement systems. The present research focus is: precise direct geo-referencing in terrestrial laser scanning applications.