THE RELIABILITY ASSESSMENT OF THE TLS REGISTRATION METHODS-THE CASE STUDY OF THE ROYAL CASTLE IN WARSAW

Modern measurement technologies are commonly applied to monitor and preserve the cultural heritage as it is an integral part of modern societies. The Terrestrial Laser Scanning (TLS) method is one of the common technologies investigated by the researchers for accurate data acquisition and processing required for architectural documentation. In recent years, many methods were developed for TLS data registration to improve the processing time and accuracy of the bundle adjustment. The aim of this research is to compare the existing TLS target-based registration methods and compare them with the proposed novel method based on the reliability assessmentthe robustness analysis. The novel feature-based approach also includes 2D detectors, which were applied to the TLS data converted into spherical images. Measurements were carried out at the Royal Castle in Warsaw using TLS Z+F 5006H and total station Leica TCRP1202. The collected data was analysed using existing software Z+F LaserControl, LupoScan and developed the application to perform 2D + 1H / 3D registration. The main results demonstrated that the proposed method for TLS registration removed the outliers that could not be eliminated by the deviation analysis on control and check points. The accuracy of TLS registration increased with a RMSE difference between 0.1mm and 3.7mm in comparison to existing methods. Furthermore, the accuracy of the results from 2D detectors was improved with relative orientation RMSE ≤ 2.1mm and equivalent for control and check points for X, Y, and Z coordinates in comparison to target-based registration. * Corresponding author


INTRODUCTION
Cultural heritage is evidence of the past and became an integral part of modern societies. In order to protect and preserve the cultural heritage object and sites, it is necessary to perform the architectural documentation in the form of 3D point clouds, 3D models, orthoimages and vector drawing (Stylianidis, 2019) for this purpose image and range-based method are used (Abbate et al., 2019;Arif and Essa, 2017;Cipriani et al., 2019;Grussenmeyer and Yasmine, 2004;Hatzopoulos et al., 2017;Heras et al., 2019;Kot et al., 2020;Markiewicz et al., 2020Markiewicz et al., , 2017Remondino and El-Hakim, 2006). The selection of the appropriate method for 3D documentation generation determines the way of surveying data pre-processing (Tobiasz et al., 2019). The aim of this article is to present the investigation of the quality assessment for different TLS registration methods. In this article, the comparison of the existing targetbased registration (implemented in the Z+F LaserControl and LupoScan software) with the proposed novel method based on the reliability assessment (target and feature-based) were performed.

The TLS registration methods overview
The first and one of the most important steps in the TLS data processing pipeline is the registration step. It involves the transformation of the point cloud in the assumed reference system, which may be the stated coordinate system, a local system, or an internal system related to the master scan (Cheng et al., 2018). For large and complex historical objects and sites, it is impossible to obtain only data from one TLS position, and multiple point clouds must be transformed into the assumed reference system. This process relies on the detection of corresponding points, shapes or features in at least two-point clouds, and the exterior orientation parameters are obtained for each scan. These parameters determine the spatial location of the central point of the scanner system in the assumed reference system together with three rotation angles, which are then used to transform the point cloud. For this purpose, the 3D affine transformation is usually applied. However, if there are significant scale differences between the scanner system and the external reference system, it is recommended to apply the 3D similarity transformation (Markiewicz and Zawieska, 2019), which is performed on a minimum of three tie points distributed within the entire analysed area. The most common solution for obtaining the coordinates of control and check points, which are determined in an exterior coordinate system, are classic angular and linear measurements performed with a total station (TS) and an independent alignment of observations including horizontal angles and distances in case of a 2D network and height differences in a 1D network. When the number of tie points is increased, redundant observations are created; therefore, the accuracy of data registration is also increased. This also allows for the elimination of outliers and perform the reliability assessment based on the covariance matrices approach. The relation between the local instrument system and the global reference system is expressed in Equation 1, also known as rigid-body transformation in the least-square method (uncorrelated observations): (1) where v -the deviation between the reference and transformed tie point A -coefficient matrix based on the tie points x -estimated transformation parameters y -the difference between coordinates in the reference system and computed by the transformation matrix Mext -the vector of the coordinates of points in the global system Mint -the vector of the coordinates of points in the local (scanner) reference system T -translation vector -the rotation matrix Several TLS registration methods exist (Durrant-Whyte and Bailey, 2006;Liu, 2006;Nuchter et al., 2007;Sprickerhof et al., 2009;Theiler and Schindler, 2012;Van Genderen, 2011;Vosselman and Maas, 2010), which can be divided into two groups comprising pairwise and multiview registration, depending on the amount of input point clouds (Deng et al., 2018;Dong et al., 2020).

The reliability assessmentthe covariance matrix analysis approach
The theory of reliability is commonly used to diagnose outliers in the surveying data, while this article will explore the use of this method for the determination of outliers in the tie points (used for TLS registration). The proposed approach will compensate the orientation quality based on the local reliability criteria, which enables to determine if the pair of tie points are correctly matched. The proposed method of quality assessment will not only focus on the RMSE on control and check points evaluation, but it will take into account the points spatial distribution. Based on the least square method (Equation 1), the formula for local reliability criteria is determined (Equation 3), which is called the "disorder-response" dependency and is one of the basic elements of reliability theory (Baarda, 1968;Rofatto et al., 2020). A detailed description of these equations was presented by Prószyński (1994).
where: Rreliability matrix of the tie points Iidentity matrix Acoefficient matrix based on the tie points To analyse the internal reliability factors, the diagonal value of the matrix R must be tested. The matrix R is an orthogonal projection operator, where the range of values on diagonal are between 〈0,1〉. According to the definition of internal reliability, {R}ii=0 when this tie point is completely uncontrolled. However, when {R}ii≅1-tie point is fully controllable by other tie points. It is stated that the spatial tie points are well distributed in terms of reliability when the internal reliability criteria for each tie point is {R}ii>0.5.

The test site description -Royal Castle in Warsaw
The subject of the analysis is the basement rooms located on the lowest floor of the Tin-Roofed Palace (Figure 1), which is now an integral part of the architectural complex of the Royal Castle in Warsaw. This part of the Royal Castle is an original one and wasn't destroyed during the Warsaw Uprising in 1944. The palace adjoined the Castle building from the south and was finally incorporated into it by erecting Royal Library in the years 1779-82, situated on the northern wing of the palace. The cellars are the part of its main body, on the west side, and belong to the oldest construction phase. These are the remains of the first known building in this area -the house of Wawrzyniec Reffus, the royal armourer. The history of the tenement house dates to the mid -17th century when between 1651 and 1655, a grand patrician house was built on this plot. In the years 2004-2008, the palace underwent a major renovation but without the basement. The restoration of these rooms has been postponed (The Royal Castle in Warsaw, 2021). While preparing for the future renovation works, it was decided to take a non-invasion inventory of the interiors, such as TLS surveying ( Figure 2).

Data acquisition and pre-processing
The initial data acquisition process was divided into two parts (1) TLS measurement with Z+F 5006h with resolution 6.1mm/ 10m and (2) Total Station measurement with Leica TCRP 1202 with angular accuracy 2sec., linear accuracy 2mm +2ppm. The TLS data acquired 4-point clouds with angular resolution 360 o /320 o at 4 different hight of station position. The total station acquired data from 2 measurement stations and at 2-time series to ensure the accuracy, reliability of the data and removal of errors. The ground control points were used for the TLS checkboard, and retroreflective targets were used for Total Station (TS) to determine the reference system. In order to validate the reference system, two approaches were used: (1) the free network adjustment of observation for all points in one bundle adjustment and (2) the two-stage adjustment: (a) first order network determination bases on retroreflective targets and (b) network adjustment in reference to first order network.

Relative registrationquality assessment
For semi-automatic marked point measurement and registration, the commercial software Z+F Laser Control and LupoScan were used. For fully automatic tie point detection, the featurebased method was used, which contains the following steps: (1) convert TLS data into the spherical image with depth map, (2) detect keypoints with SIFT, ASIFT, FAST and AFAST algorithm, (3) keypoint description (2D SIFT descriptor) and descriptor matching, (4) outliers detection and geometrical verification with relative parameters computation (RANSAC method) and (5) automatic division of detected tie points into the control and check and final registration based on intersection method.

The reliability assessmentthe robustness analysis
The tie points were examined with regards to accuracy and network reliability. The analysis was performed to assess the methods of data registration to obtain the highest accuracy and robustness (Equation 2 and 3). This step allowed to eliminate outliers and analyse network reliability in the local coordinate system.

Exterior registrationquality assessment
For existing target-based and feature-based methods, the control points were assigned to the exterior coordinate reference system from TS measurements.

Data acquisition and pre-processing
The first step of data processing involves total station data preparation and bundle adjustment using two methods 1) free adjustment, 2) two-stage adjustment. The results demonstrated that there is no significant difference between both methods. The similarity between Average and Median values indicates that the bundle adjustment process for the two methods was performed correctly without the presence of outliers. It is not necessary to perform twice bundle adjustment process (separately for retroreflective points and TLS reference points), but it can be completed in a single step process (free adjustment).  The results (Figure 4) Figure 5. The quality assessment of relative orientation -RSME on marked check points To perform the independent analysis of TLS registration, the quality assessment on marked check points (which were not used to compute transformation parameters) was carried out, and the results are presented in figure 5. The results show ( Figure 5) a similar trend for the X coordinate of the check point where the proposed method offers a lower RMSE value in comparison to existing methods, while the Y and Z coordinates of check points have achieved a similar RMSE value. Results in both figures 4 and 5 have a similar RMSE value, which can confirm that the TLS registration process was completed correctly.

The reliability assessmentthe robustness analysis
On the completion of the first part of data analysis for relative registration and quality assessment with RMSE for control and check points. The next step is to carry out a reliability assessment of tie points (control points). Table 2  As reported in the literature (Prószyński, 1994), the reliability factor must be higher than 0.5 for all points used in the registration process to guarantee the robustness of the TLS point cloud registration. If the reliability factor is below 0.5, then the developed TLS registration could have an uncontrolled point by other points taking part in the bundle adjustment process, which means that it cannot be assessed if it is a deviation value or an outlier. The results presented in Table 2 indicates that one of the values (min) for the existing method is below the required 0.5 and should be eliminated for further data processing. On the other hand, the proposed method achieved very high-reliability factor values for all detectors, confirming the robustness of the method. The TLS registration requires a minimum of 4 control points (Van Genchten, 2008) for point cloud registration. In this research, 6 control points were used for the target-based method. However, the reliability factor for Min remains low. The proposed method uses a detector, which detects a high number of point and improves their robustness to eliminate the outliners.  Figure 6 presents the results of the exterior registration using "free" adjustment on the control points using Z+F, LupoScan 3D, LupoScan 2D+1H (existing methods), SIFT, ASIFT, FAST and AFAST (novel proposed methods). Figure 6. The quality assessment of exterior orientation -RSME on marked control points

Exterior registrationquality assessment
The results ( Figure 6)  The results of the quality assessment on marked check points (which were not used to compute transformation parameters) are presented in figure 7. The results (Figure 7) show a similar trend for X and Y coordinates of check point where the proposed method offers a lower RMSE value in comparison to existing methods, while the Z coordinate of check points are similar for RMSE value. Results in both figures bb and cc have a similar RMSE value, which can confirm that the TLS exterior registration process was completed correctly.

CONCLUSIONS
An important element during an inventory of historical objects is the correct determination of the ground control points uses for TLS point cloud registration in the external reference system. Often, due to external factors (such as the impossibility to mark points or place on the object, complex shape of the object, narrow spaces, i.e.), it is difficult to set points in terms of geometry correctly. Due to that fact, it is necessary to determine the procedure of observation, filtration and validation in the bundle adjustment process based on the extended reliability factors analysis. The results in Table 3 show that differences between RMS on control and check points significantly exceeded the values of measurement errors. Based on the assessment of the feature-based methods, due to a large number of tie point, the RMSE values on control and check points are similar because of their number and distribution. In that case, the reliability factor analysis shows that the detected point allows performing robust relative TLS registration.