This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (
Fine registration of point clouds plays an important role in data analysis in Terrestrial Laser Scanning (TLS). This work proposes a blocktopoint fine registration approach to correct the errors of point clouds from TLS and of geodetic networks observed using total stations. Based on a reference coordinate system, the blocktopoint estimation is performed to obtain representative points. Then, fine registration with a sixparameter transformation is performed with the help of an Iterative Closest Point (ICP) method. For comparisons, fine registration with a sevenparameter transformation is introduced by applying a Singular Value Decomposition (SVD) algorithm. The proposed method not only corrects the registration errors between a geodetic network and the scans, but also considers the errors among the scans. The proposed method was tested on real TLS data of a dam surface, and the results showed that distance discrepancies of estimated representative points between scans were reduced by approximately 60%.
Terrestrial Laser Scanning (TLS) is a powerful geodetic tool ideal for supporting a wide spectrum of applications in many different environments, e.g., [
Previous work about registration methods can be found in the following literature. A Least Squares 3D (LS3D) surface matching [
Recently, Grant
For TLS applied in structural monitoring tasks, a uniform framework needs to be established to describe the object surface and to compare the deformation of an object surface between different epochs. Object surfaces could be recognized in the following two methods: those that segment points based on criteria, like the proximity of points, and those that directly estimate surface parameters [
Previous work for TLS applied in structural monitoring tasks was often performed in the following two steps (e.g., [
For the rigid body transformation, an ICP algorithm proposed by Besl and McKay [
Under a similar assumption that both observations and a datum are contaminated by errors, a SVD algorithm can be used to compute similarity transformation parameters within an ErrorsInVariables (EIV) model [
In the research demonstrated in this paper, the fine registration in TLS applications is processed by first transforming the point clouds into a reference coordinate system, followed by blocktopoint estimation; then, the fine registration is performed based on the estimated representative points. The next section of this paper will present the proposed method. Section 3 displays a real application in a scanning task of a dam surface. The conclusion and future work are presented finally.
In this paper, we present a new methodology that extends the work of Eling [
The proposed method is presented in three steps (
To obtain a complete representation of an object surface, all the point clouds from two or more scans need to be transformed from their local scanner coordinate systems into a reference coordinate system, where the reference coordinate system can either be a local coordinate system or be a global coordinate system. The transformation parameters can be determined from identical points in both coordinate systems. The similarity transformation of the coordinates from one coordinate system to another coordinate system is defined as:
The unknown parameters could be solved by the iterative Gauss–Helmert model [
If there are no systematic errors, the expected distance discrepancies between multiple scans would be zero. However, in practical applications, this is never the case. For example, as demonstrated by [
The registration of point clouds could be achieved, e.g., by applying the ICP method [
A quadratic form could be used by evaluation of determinants and then testing the form parameters to describe the object surface [
The parameters from
The extended form matrix is identified:
Based on the estimated parameters of quadratic form estimation, the segmentation is performed in a spherical coordinate system according to the horizontal angles and the vertical angles. The coordinates,
According to the point clouds in a block, the leastsquares method is used to estimate the representative point in this block. Because both the block size and curvature of the block surface are small, the point clouds in one block usually are distributed on a plane surface. Thus, the normal vectors,
In the transformation model in step 1, the registration errors between the scanner stations and the reference coordinate system are adjusted, but the errors among the multiple scans are not included. In order to detect and decrease the distance discrepancies among these multiple scans, a rigid body movement and a similarity transformation are used. The ICP method is commonly used to estimate the rigid body movement parameters. For a comparison with the rigid body movement, the similarity transformation is applied with the help of the SVD algorithm.
The red points in
In the process of the ICP method, one of the datasets is considered as a reference coordinate system. The other dataset is moved to the reference coordinate system. The rigid body movement function can be generally expressed as [
Two aspects should be concerned when the ICP method is applied: computation time and proper initial values. Two strategies were employed to speed up the computation time and improve data quality: (1) reduction of the number of the matching points through the quadratic form estimation; and (2) speeding up the accuracy of the datasets by providing proper initial values.
One issue in applying the ICP algorithm is that it requires proper initial approximations for convergence to the local minimum. With the introduction of blocktopoint estimation, good initial values could be obtained. Another issue occurs when two data regions overlap. Adopting the quadratic form estimation and segmentation methods throws out the points that are unique to each dataset. This means the remaining points are only those that are visible in both scans and have correspondences. Therefore, the two datasets iterated in the ICP algorithm are entirely overlapping regions. This means that the distance discrepancies existing between the scanner stations may be decreased. Note that in [
For a comparison with the sixparameter transformation, the sevenparameter transformation is estimated by using the SVD algorithm. A standard algorithm (see Algorithm 3 in [
Setting
Setting
The scale,
The translation vector Δ
The observations could either be corresponding points or be corresponding patches. The significant difference of the sixparameter transformation and the sevenparameter transformation in this paper lies especially in the estimation of the scale factor. Note that the performance of the ICP method and SVD algorithm introduced in this paper does not imply the abilities of the algorithms themselves, but rather, their corresponding fine registration patterns: the rigid body movement and the similarity transformation, respectively. In the step of fine registration, the magnitudes of errors between the scans are small, because in step 1, a good quality of transformation parameters has been obtained.
Four epochs of data were measured by [
According to the quadratic form estimation, the object surface was estimated as an elliptical cylinder (
Based on the estimated parameters of the elliptical cylinder, rectangular blocks with small sizes were obtained according to the horizontal angles and the vertical angles of the point clouds. Points in one block were estimated as a representative point. Approximately 12, 000 blocks were segmented on the dam surface. The size of a block is shown in
Similarly stated by [
Setting station 1000 as a reference station, the sixparameter transformation and the sevenparameter transformation are applied, respectively, to detect and decrease the distance discrepancies of representative points between two scans. The distance discrepancy,
Under the same data sources, mean standard deviations of distance discrepancies of representative points in the four epochs are demonstrated in three groups: the results from [
In order to show more detail,
The fine registration with sixparameter transformation was performed with the help of the ICP method in the four epochs. Setting station 1000 as the reference coordinate system, the representative points from station 2000 and station 4000 were transformed into this reference coordinate system. Under the same data source, the mean standard deviation of distance discrepancies is approximately 3.2 mm with the sixparameter transformation (see
In many research projects (e.g., [
Fine registration with sevenparameter transformation was performed for the comparison with the sixparameter transformation. In
In fine registration, the rigid body movement estimated six parameters by applying the ICP method, while for comparisons, the similarity transformation obtained seven parameters by applying the SVD algorithm. The mean standard deviation of distance discrepancies between the scans was decreased by approximately 3.2 mm based on the comparison between sevenparameter fine registration and [
As demonstrated in
Instead of the original point clouds, the computation based on the estimated representative points saves much time. For example, transforming the estimated points from station 2000 to station 1000 takes just under 10 s. The 10 s include the time of searching the explicit representative points and computing the parameters of fine registration. Users who have a high demand for data quality may perform this fine registration step.
For TLS applications, the estimated representative points could be compared in order to test if the corresponding points have significant variations in different epochs. Additionally, the deformation of the object is usually small; thus, the detection and elimination of these systematic errors are indispensable in the task of deformation monitoring, such as a water dam.
This paper was focused on blocktopoint fine registration in Terrestrial Laser Scanning (TLS), which is used for combined evaluation of point clouds from TLS and of geodetic networks observed using total stations. Of specific interest were those methods that utilize corresponding representative points, as they employ the original point clouds for registration (e.g., [
Comparing fine registration with the sixparameter transformation and with the sevenparameter transformation, the sevenparameter transformation worked better, mainly due to the scale factor. Not only the registration errors from the scans to the reference coordinate system were considered, but also the distance discrepancies between the scans were treated. This is meaningful in real applications. In this paper with real TLS data from the Oker dam surface, the mean standard deviation of the distance discrepancies between the scans was decreased by approximately 3.2 mm based on the comparison between sevenparameter fine registration and [
The proposed blocktopoint fine registration can be used in applications for objects with regular shapes. For complicated object surfaces that cannot be described by several parameters, other modeling methods are suggested to describe the object surfaces, such as the NonUniform Rational BSpline (NURBS) model. Future work will try to apply the proposed method to other applications, such as tunnel monitoring tasks.
The work presented in this paper was conducted during my doctoral studies. I am grateful to Hansjörg Kutterer and Ingo Neumann for their guidance and helpful comments. The author would also like to thank Xing Fang for his help and discussion and Dirk Eling for providing the source data.
The author declares no conflict of interest.
Data processing workflow of Terrestrial Laser Scanning (TLS) applied in structural monitoring tasks. ICP, Iterative Closest Point; SVD, Singular Value Decomposition.
Blocktopoint correspondence in fine registration. The red points are the estimated representative points of blocks
(
Elliptic cylinder fitting. (
Distance discrepancies of representative points between two scans in epoch 4 (fine registration with sixparameter transformation)(mm) (the left figure means the variations of distance discrepancies between station 1000 and station 2000; the middle one is the variations of distance discrepancies between station 1000 and station 4000; the right figure denotes the variations of distance discrepancies between station 2000 and station 4000).
Distance discrepancies of representative points between two scans in epoch 4 (fine registration with sevenparameter transformation)(mm) (the left figure means the variations of distance discrepancies between station 1000 and station 2000; the middle one is the variations of distance discrepancies between station 1000 and station 4000; the right figure denotes the variations of distance discrepancies between station 2000 and station 4000).
The estimated parameters of the elliptical cylinder (m).
127.25  227.53  98.06  69.18  68.95 
The size of a block.
0.34 m  0.79 m  0.25 m  0.27 m^{2} 
The mean standard deviation of distance discrepancies of representative points in the four epochs (the second column result comes from [
5 mm  3.2 mm  1.8 mm 
The mean standard deviations and the mean values of the distance discrepancies of representative points between two scans in epoch 4 (


 

2000 to 1000  6.0 mm  2.92 mm/0.09 mm  1.62 mm/−0.09 mm 
4000 to 1000  4.6 mm  3.43 mm/−0.09 mm  1.82 mm/0.35 mm 
4000 to 2000  4.1 mm  3.70 mm/−1.61 mm  2.23 mm /0.14 mm 