Keypoint-based registration of TLS point clouds using a statistical matching approach

2.1 Aim of the registration

The basic aim of pairwise point cloud registration is to determine the relative position (t _x , t _y , t _z ) and orientation (α, β, γ) from a point cloud to be registered in the start reference frame S to a target point cloud in the reference frame T (s. Figure 1). Mathematically, the transformation of a point x from the reference frame S to the reference frame T can be described with the help of a Helmert transformation [22] without a scale factor:

with

where α describes the rotation around the x-axis, β the rotation around the y-axis and γ the rotation around the z-axis. The superscript denotes to which reference frame the point x refers. The estimation of a scale factor is not necessary as long as the same scanner is used for both stations. The mathematical aim of the registration is the estimation of the six transformation parameters between the reference frames S and T .

Figure 1:

Illustration of the three translational (t _x , t _y , t _z ) and three rotational (α, β, γ) registration parameters.

2.2 Registration methods

As mentioned in the introduction, there are a variety of different solution approaches for determining the registration parameters. For better clarity, not all methods will be discussed in the same detail, focusing more on the methods relevant to this work.

A common distinction is made between coarse and fine registrations [23–26]. Apart from the aforementioned use of additional sensors, such as GPS or initial measurement units [11, 27], geometric features, e.g. keypoints [14, 15, 28], lines [29, 30] or surfaces [31], [32], [33], have also been increasingly used for coarse registration in recent years. Those features are extracted based on the recorded point clouds themselves. Subsequently, the features of the point clouds are described in feature vectors based on their local neighborhood and then matched to each other based on the feature vectors. The point detectors and descriptors operate either directly in 3D space [34–37] or in a 2D space derived from the three-dimensional one (e.g. images) [38], [39], [40]. The disadvantage of 3D operators is that they can only be applied to very small or thin point clouds so far due to computational requirements. They currently also suffer from problems with irregular distributed point clouds [41, 42].

Thus, in order to process dense point clouds, image representations are often derived from the point clouds. Afterwards, image feature detectors and descriptors that have been used in image processing for many years are also used for the scan registration [28, 42, 43]. As image representation of the point cloud either ortho images are used [41, 44], which however require a digital surface model, virtual images [45] or panorama images [38, 46]. Since almost all terrestrial laser scanners are polar measuring systems, the panorama image is the most obvious and is thus often used in the existing literature [14, 18, 43, 47], [48], [49]. The pixel values of the panorama images represent either the measured distance of the scan points (range panorama image), the reflected signal intensity of the laser (intensity panorama image) or are linked to camera data and represent the color (RGB panorama image) of the scan points. With the help of the range panorama image, the 2D features can also be converted into three-dimensional features. For example, a 3D keypoint can be calculated from a 2D keypoint with the help of the range panorama image.

In order to use the geometric features for registration, identical image features from different point clouds have to be matched. Due to geometric image distortions or the image changes caused by the different view points of the stations, many descriptors lead to problems with feature matching [42]. This is because the descriptors were mostly developed for images with central projection in the field of image processing [46]. With increasingly smarter descriptors, attempts are being made to overcome this problem [50]. In general, the smaller the image distortions and the smaller the differences due to the change of the view point in the images, the better the image descriptors and the subsequent matching work [46]. With the images acquired from the same position, just different scan faces, laser scanners can even be calibrated [19]. However, this only works because the differences due to the view point are zero.

Finally, it should be mentioned that to avoid the descriptor-based matching problem, approaches based on geometric hashing [51, 52], game theory [53] or the geometry exist. The latter use e.g. the 4-points congruent sets algorithm [54, 55] for registration with extracted 3D-keypoints (K-4PCS) [56] or voxel-based 4-planes congruent sets (V4PCS) [31].

From the results of the literature mentioned above, it can be seen that the previous methods for feature-based registration are only suitable for coarse registrations. For applications with high accuracy requirements, a fine registration follows. A standard tool for fine registration is the Iterative-Closest-Point-Algorithm (ICP), which was already introduced in its basic form at the beginning of the 90s [12]. It has been further developed until today [13, 57–61]; especially the weighting has been modified [62, 63] and the observations have been substituted by features [64], [65], [66]. However, all these methods have the disadvantages that they either only work well at station distances of a few meters [67] or that the quality assessment is not as clear as it is from the classic geodetic network analysis. For the ICP, often the root mean square error (RMS) is the only quality measure available, whereas for classic geodetic network analysis there are multiple quality assessments, for example, standard deviations of the parameters or redundance components of individual observations [68, 69].

Therefore, the target-based fine registration is still a widespread method of registration [48, 70]. For this, artificial targets are placed in the scan scene, their centers are determined on the basis of geometry or reflected intensities [71] and then used as identical points for registration [72]. With the choice of the scanner, the used laser scanning targets and the geometrical configuration of the targets, the user can influence the quality of the registration. On the one hand, the placement of the targets in the scan scene means an additional effort compared to the other registration methods. On the other hand, the accuracy and reliability of the registration can be evaluated with tools of geodetic network analysis, which creates a high confidence in the data integrity of the registration.

3.1 Overview

From Section 2.2 it is clear that especially for very large and dense point clouds, as we consider here, an image representation of the scan is advantageous for the computational effort. Thus, the first step of our registration algorithm is to convert the point clouds into images. As many other researchers [14, 18, 43, 47], [48], [49], we use the panorama images and search for keypoints in them. The keypoints in the images are detected in the second step of the algorithm using the Förstner operator [73, 74]. Compared to other point detectors such as the Harris Detector [75, 76] or the SUSAN Detector [76], it has the advantage that it provides very precise keypoints [19, 77]. Moreover, for each detected point we also receive the uncertainty of the keypoint in the form of a covariance matrix [73]. The detected keypoints are then extrapolated back into 3D space using the range panorama images.

In the third step, we present a new geometry-based matching approach, which provides point identities between two scanner stations using statistical testing methods. The idea is that given a good initial registration, for example by means of targets, we can test which keypoints, detected from two different viewpoints, are considered identical taking into account their spatial uncertainty. The spatial uncertainty results from the range uncertainty of the scanner, the uncertainty of the keypoint position, the uncertainty of the coarse registration and the later variance component estimation. The matching method avoids the problems that occur when point descriptors are used. In the fourth step, using the keypoint pairs identified as identical, the registration parameters are estimated by means of an adjustment. Finally, the results of the adjustment are used as a new initial registration of the matching step to further improve it. Steps three and four are iterated until the registration parameters converge. The whole process of our registration method is illustrated in Figure 2.

Figure 2:

Processing chain of the new keypoint-based registration.

3.2 Converting point clouds to images

In this work, the panorama images are used to represent point clouds in images. For this, the point clouds, which are usually provided in the manufacturer’s software in Cartesian form, must first be converted into polar coordinates. Without any preregistration, the recorded and exported points of a scanning station refer to the local reference frame of the respective station. The scanned points can be converted from the Catesian form [x, y, z] to polar observations [r, φ, θ] using known trigonometric functions [78].

where r is the measured range, φ the horizontal direction and θ the vertical angle.

In order to convert these spherical coordinates into an image, a grid is created in which the cells represent the polar angles and the gray value represents the reflected laser signal of the individual points. Each pixel of this intensity panorama image, is assigned to a vertical angle by its vertical position and to a horizontal direction by its horizontal position. A detailed description of the conversion of polar coordinates into panorama images can be found in Fangi [38].

For each scanning station, this panorama image can be calculated. In Figure 3 it is shown exemplary for one station. Regions in which no points could be measured, for example the sky (too low reflection) or traffic signs (too high reflection), are filled with NaN-Values (Not-a-Number). These areas are marked in blue in Figure 3.

Figure 3:

Intensity panorama image of a scanner station (bright – low reflected intensity, dark – high reflected intensity).

The size of the raster cells, or number of pixels, determines the resolution of the images. To avoid data loss and interpolation, we decided to adjust the image resolution to the scanning resolution by default. This means that since the angular resolution of all scans in this paper is 3.1 mm at 10 m distance to the scanner (corresponds to 64″), the image resolution is chosen so that one pixel is also 64″. With a horizontal scan coverage of 360° and a vertical scan coverage of 0°–140° (as in Figure 3), this corresponds to a panorama image of 19,980 × 8325 pixels. The vertical angle ends at 140° and not 180°, because of the constructional blind spot below the scanner. Since this extreme resolution will lead to problems with the computing power of regular computers, the panorama image is divided into partial subimages, each representing an angular range of 10° × 10°. A single subimage thus has a resolution of 555 × 555 pixels and can be used for further processing.

3.3 Detecting keypoints

As described in Section 2, the Förstner operator [74] is applied to detect keypoints. The idea of the Förstner operator is to find prominent points with the help of the gradient images of gray value images. For this, the inverse proportionality between the gradient image and the uncertainty of pixels is used. Pixels, which have a high gradient in all directions (e.g. corners), have small eigenvalues of the covariance matrix. When the largest eigenvalue of the covariance matrix of the pixel under consideration is below a defined threshold and there are no pixels with smaller eigenvalues in the local neighborhood, then it is a keypoint. As a result of the Förstner operator, the 2D keypoints including their uncertainty in form of covariance matrices are obtained, which can be converted from pixel to angle values using the known angular grid. For a detailed description of the Förstner operator, please refer to the existing literature [73, 74].

We apply the Förstner operator to all subimages of the intensity panorama image with the parameter settings from Table 1. The pixel size of the gradient filter, integration filter as well as the precision threshold were chosen depending on the mean vertical angle θ ̂ of the currently considered subimage j and are specified in the unit pixel [px]. Thus, the distortions caused by the panorama image are partially compensated. Figure 4 shows the intensity panorama image with all the detected keypoints. Since the Förstner operator cannot handle NaN values, the image areas in which no measurements could be made are assumed to be white.

Figure 4:

All keypoints detected with the Förstner operator in the intensity panorama image of an exemplary scanner station.

At this exemplary station, a total of 38,440 points are found. This number depends strongly on the surroundings. The number of keypoints in the later datasets presented in Section 4 varies between 32,304 and 99,231 keypoints per station. Furthermore, it can be seen from Figure 4 that a large number of keypoints is located in the vegetation, for instance bushes.

Figure 5 shows three enlarged subimages with their detected keypoints. On the left subimage, it can be seen that the keypoints are detected at locations that are plausible for the human observer. The middle subimage shows that there are also cases where the keypoints are very close to each other. On the right subimage, it can be seen that many keypoints are found in the bushes and trees due to varying intensities.

Figure 5:

Detailed views of detected keypoints for three subimages of Figure 4.

The detected 2D keypoints are transformed back into the 3D space. For this, the distances from the range panorama image are assigned to each keypoint and thus the three dimensional polar observations of the keypoints are obtained. The required range panorama image is calculated analogously to the intensity panorama image. Furthermore, covariance matrices can be created for each 3D keypoint. For the angular precision, the covariance matrix of the keypoints from the Förstner operator is used and for the precision of the distance the manufacturer’s data. The angles and distances are assumed to be uncorrelated.

The polar observations are finally converted into Cartesian coordinates x using the inverse equations of Eqs. (3)–(5) and also the covariance matrices Σ _xx are calculated in the Cartesian 3D space using variance propagation.

3.4 Statistical matching

The previous processing steps refer to the data from only one station at a time. That is different in this step: Now, the detected keypoints of two stations are to be matched with each other. The purpose of the matching process is to find keypoints that represent identical points in the real world. Usually different descriptors are used to match these keypoints. Since this does not work reliably due to the strongly varying viewing angles [18], we introduce a new statistical matching method in the following, which is based solely on the geometric position of the points as well as on their spatial uncertainty.

We denote the keypoints of the start station to be registered as X S S , the keypoints of the target station as X T T . Again, the superscript indicates which reference frame the points currently refer to, the index indicates which frame the observations originally referred to or from which system the observations were recorded.

The idea of our statistical matching method is to find keypoints in X T and X S , which are so close to each other in the real world that they are assumed to be identical with regard to their spatial uncertainties. For the calculation of the keypoint distances, however, a good initial registration is necessary, which is given by the pure target-based registration.

The matching process can be divided into three parts:

1. The keypoints of both stations still refer to their respective local reference frames T and S . With the help of initial registration parameters and Eq. (1), the keypoints of the start reference frame X S S can be transformed into the target reference frame X S T , so that the keypoints of both stations refer to the same reference frame. In order to avoid mismatches later, good initial transformation parameters are necessary, which are already known from the artificial laser scanning targets and the pure target-based registration. Besides the keypoints themselves, the covariance matrices of the keypoints X S are also strictly propagated from reference frame S to T . Due to the uncertainty of the initial registration, the variances of X S T increase compared to X S S .

   Figure 6 shows a synthetic 2D-example of three keypoints detected from both stations after the transformation in the common reference frame T . For better visualisation the confidence ellipses in this example are drawn highly enlarged. From these ellipses it is visible that the variances of the points X S T are larger than the position uncertainties of the points X T T due to the uncertainty of the registration. Also, the more circular form of the ellipses of X S T is caused by the variance propagation of the initial registration uncertainty to the keypoints of the Station S .

2. For each keypoint in X T T , the nearest keypoint in X S T is searched. To implement this efficiently for several thousand keypoints, we use a kd-tree. In Figure 6, the nearest neighbors are visualised with black lines.

3. Based on a statistical test, we examine if a pair of nearest neighbors is the same point considering their spatial uncertainties. Therefore, we testwith the hypothesis H₀ if the difference vector

between the ith keypoint of X T T and the nearest jth keypoint of X S T is equal to zero:

Figure 6:

Synthetic 2D example to illustrate the statistical geometry-based keypoint matching.

The covariance matrix of the difference vector is calculated Σ d d i = Σ x x S , j + Σ xx S , i , assuming that the two covariance matrices of the keypoints i and j are uncorrelated. Considering this variance propagated matrix, the test variable

can be calculated, which is X² distributed by the degree of freedom f. In our case f = 3, since the three differences of the difference vector are calculated from six observations.

If the test magnitude is less than or equal to the quantile value of the X² distribution of a given probability level (95 % in this paper), the pair of nearest neighbors are assumed to be the same point. If the test variable is bigger, the tested keypoints are assumed to be significantly different and are not considered further in the following. In the synthetic example from Figure 6, the test reveals that the keypoints at the top right are not the same; the keypoints at the top left and bottom are tested as identical.

This method is applied to the scan discussed in the Section 3.3 and the scan from one more station. The initial registration is calculated using three common artificial targets. The distance between the two stations is about 16.6 m. Figure 7 shows the matched points for the station to be registered. In total 124 points from both stations were identified as identical with the help of the statistical tests.

Figure 7:

Visualization of the keypoints, which are identified as identical with the method of statistical keypoints matching and are used for registration.

As expected, keypoints are assigned to each other especially at corners and edges of buildings and their extensions. Compared to Figure 4, the percentage of keypoints in the shrubs and trees is drastically reduced. Nevertheless, some keypoints are matched, which are located in the vegetation. A detailed analysis shows that these are either obviously stable and prominent structures, such as branch forks, or individual matches where points accidentally lie so close to each other that they are assumed to be identical. Whether these few mismatches have a negative effect on the registration is judged later on the basis of the evaluation datasets in Section 4.

3.5 Registration adjustment

In order to estimate the six registration parameters p , the parameters can be linked with the pairs of keypoints l based on the functional model of the Helmert transformation (s. Section 2.1). Eq. (1) can be reformulated to give the conditions c for the registration adjustment

According to Förstner & Wrobel [69], these conditions can be approximated by

with the initial values l ⁰ and p ⁰ and the Jacobian matrices

The contradiction w of the conditions can be calculated with

where v are the residuals of the observations. The uncertainties of the keypoints are accounted for by the covariance matrices of the keypoints Σ _xx . They form the a-priori covariance matrix Σ _ll corresponding to the observation vector l . The estimated registration parameters p ̂ and the estimated residuals of the keypoint observations are obtained by

with the weight matrix W = B ⊺ Σ l l B − 1 . The corresponding a-posteriori covariance matrices

provide the estimated uncertainties of the registration parameters and residuals, respectively.

In addition to the registration parameters, various quality parameters of reliability and accuracy can be determined. A simple measure of reliability is the redundancy R = C − P with C the number of conditions and P the number of parameters. For the example from Section 3.4, the redundancy of the registration with targets is only 3 and the redundancy of registration with keypoints is 498. The clearly larger redundancy of the registration with keypoints compared to the registration with targets only is a first indicator that the registration using keypoints leads to an increase in reliability.

In a more detailed reliability analysis, the minimal detectable errors ∇₀ l [69] is calulated:

with the critical value δ₀ defined by probabilities of false positive and false negative errors, the a-priori standard deviations σ l i and the partial redundancy

of the observations under investigation [69]. This means that outliers in the observations bigger than this value can be detected. The smaller this threshold is, the smaller errors can be detected. In the registration example, ∇₀ l are between 3.8 mm and 8.9 mm in distances and 16″ and 344″ in angles for the keypoint-based registration. For the pure target-based registration, ∇₀ l are between 4.9 mm and 6.8 mm for distances and 35″ and 197″ for angles. Due to the larger number of identical points when registering with keypoints, gross errors in the observations can be found easier. However, there are also keypoints that are further away from the scanner than the artificial targets. For these keypoints the minimal detectable errors is therefore also larger.

These reliability criteria (redundancy, minimal for detectable error) can be calculated theoretically based only on the geometric configuration and without actual observations [68, 69]. Using the observation residuals v (Eq. (15)) from the adjustment, the a-posteriori standard deviations σ ̂ can be estimated separately for the distances r, horizontal directions φ and vertical angles θ with

The estimated standard deviations are afterwards used to adjust the covariance matrix of the observations Σ _ll and the registration adjustment is calculated again [68, 69]. This variance component adjustment is performed until the global test of the registration is accepted and the final a-posteriori standard deviations are obtained. For the exemplary registration, the estimated standard deviations are σ ̂ r = 3.5 m m , σ ̂ φ = 36,9 ″ , and σ ̂ θ = 39,5 ″ . As expected, these standard deviations are significantly larger than the standard deviations of artificial targets, which are less than 1 mm for the distance and less than 10″ for the angles [16, 71].

After the variance component adjustment of the observations, the a-posteriori standard deviations of the six registration parameters can be obtained from the covariance matrix of the parameters (Eq. (16))

where i represents the respective registration parameter.

3.6 Iterative matching and registration

Considering that the result of the matching step depends strongly on the initial registration parameters of the target-based registration and its uncertainty, it is evident that the registration based on keypoints with the smaller uncertainty can also improve the keypoint matching. For this reason, the matching step and the subsequent registration are repeated iteratively. In each iteration, the registration parameters of the previous iteration are used as the new initial registration for the matching. Also, the points which were not matched in the previous iteration are considered again. Thus, the keypoint-based registration becomes more independent of the original target-based registration with each iteration. The matching and registration are repeated until the registration parameters do not change significantly anymore.

In our registration example, there are 124 matches in the first iteration as described above. Due to the adjustment of the first iteration, the uncertainty of the parameters is slightly reduced by the keypoint-based registration; this means that it is possible in the second iteration to distinguish between identical and non-identical keypoints with a smaller uncertainty and thus only 119 keypoints are matched. After the adjustment in the second iteration, the uncertainty changes of the registration parameters are even smaller. After 5 iterations of matching and registration, the registration parameters do not change any more. Finally, 109 matches are identified and estimated standard deviations of the registration parameters of σ ̂ α = 9.9 ″ , σ ̂ β = 10.2 ″ , σ ̂ γ = 5.7 ″ , σ ̂ t x = 0.44 m m , σ ̂ t y = 0.44 m m and σ ̂ t z = 0.49 m m are achieved. The final estimated variances of the polar observations of the keypoints are σ ̂ r = 3.5 m m , σ ̂ φ = 37 ″ , and σ ̂ θ = 40 ″ .

4.1 Datasets

The first of the two evaluation datasets is the Library dataset. The library of the University of Bonn has a length and width of about 49 m × 42 m. The scans are captured with the Leica ScanStation P50 from 12 stations (S1 – S12) distributed around the building. When choosing the scanner positions, care is taken to ensure stable ground and that the building is scanned with as little shadowing as possible. The station distances in this dataset vary between 16 m and 30 m. All Scans are performed with a resolution of 3.1 mm at 10 m distance from the scanner.

For target-based registration, the targets recommended by the manufacturer are placed at 15 locations so that three identical targets are always scanned from two neighboring stations. Figure 8 shows an image of the library and an overview of the scanner stations and target locations.

Figure 8:

Dataset Library: Image of the scan object and site plan.

The second dataset are scans of a Castle in Bonn (Figure 9), which was built in the 12th century. The two wings of its L-shape have an approximate length of 40 m each. The castle is scanned from 10 scanner stations (S1 – S10) with the Leica ScanStation P50 and a resolution of 3.1 mm at 10 m distance. The positions of the stations are selected according to the usual criteria of target-based registration, as in the dataset Library. The station distances in this dataset vary between 13 m and 27 m.

Figure 9:

Dataset Castle: Image of the scan object and site plan.

The accompanying targets from the manufacturer are again used for the target-based registration. To ensure that all neighboring stations scan enough identical targets, the targets are placed at 16 locations. They as well as the scanner stations are shown in Figure 9.

For both datasets, the pairwise registrations between all consecutive stations are calculated once by means of the artificial targets only, once with the ICP and once by means of the new keypoint-based method. As described above, the results of the target-based method serve as initial values for the keypoint-based registration and are also used as initial values for the ICP registration.

4.2 Evaluation of pairwise registrations

In the following, the single pairwise target-based, ICP and keypoint-based registrations are compared with each other. Firstly, the differences between ICP and keypoint-based registrations are calculated relative to the target-based registration. Since no reference target registration exists for the data sets, no absolute differences can be examined. Secondly, the estimated standard deviations described in Section 2.1 of the observations as well as the standard deviations of the registration parameters are considered. Since these cannot be calculated for the ICP, the ICP is not considered in this comparison.

4.3 Evaluation of registration traverse

In order to demonstrate the benefit of the precision gain of the keypoint-based registration, we now compare a traverse of several pairwise registrations. In nearly all scanning projects as well as in our two evaluation datasets, it is necessary to scan from more than two scanner stations to fully capture the entire scan object. In these cases, multiple pairwise registrations are linked together and even small differences in the precision of the registration become more apparent. To illustrate this effect as much as possible, the traverse in the two data sets are considered as dead traverse. So, all pairwise registrations (S1–S12, resp. S1–S10) are linked with each other. In case of perfect registrations, the position and orientation of the target frame of the first registration and the start frame of the last registration should not differ. However, due to the imperfections in the individual registrations, this does not happen and a so-called loop closure error can be calculated for the target-based, ICP and keypoint-based registrations. In addition, variance propagation is used to propagate the standard deviations of the single registrations over the whole chain of registrations.

4.3.1 Library

The loop closure error for the target-based registrations is 39.9 mm, for the ICP registrations 110.8 mm and for the keypoint-based registrations 12.5 mm. The fact that the ICP registration leads to the largest loop closure errors shows that this method leads to the worst registration results for the given data set. This is also the reason for the previously observed large differences in the registration parameters. The cause is probably that the overlap of the point clouds, which is necessary for the ICP [67], is too small. The loop closure error of the keypoint-based registration is two thirds smaller than with the target-based method.

With each station or registration, respectively, the uncertainty of the registration chain increases. This is also reflected in the confidence ellipsoids of the stations. After the last registration, the largest semi-major axis confidence ellipsoids (probability level of 68 %) is 11.9 mm for the target-based method. With the keypoint-based method, this maximum uncertainty decreases to 8.6 mm. The direction of the major semi-axis is almost identical to the z-axis and thus the height. In horizontal position, the largest uncertainty also improves from 5.7 mm to 4.3 mm for the keypoint-based method. Figure 10 illustrates the uncertainties in horizontal position by means of confidence ellipses.

Figure 10:

Dataset library: confidence ellipses (probability level of 68 %; magnified 1000 times) for uncertainty in horizontal position when all pairwise registrations are chained.

4.3.2 Castle

For this second data set, the loop closure errors are 11.9 mm for the target-based registrations, 124.9 mm for the ICP registrations and 7.1 mm for the keypoint-based registrations. As in the previous data set, the ICP appears to result in the worst registrations. Considering the uncertainties of the registrations, the major semi-axis of the confidence ellipsoid after chaining all registrations is 8.7 mm for the target-based registrations. It decreases to 6.8 mm for the registrations using keypoints. Again, these values essentially correspond to the uncertainties in height. The maximum uncertainty in horizontal position is reduced from 4.4 mm to 3.6 mm, which is also shown in Figure 11 using confidence ellipsoids.

Figure 11:

Dataset castle: confidence ellipses (probability level of 68 %; magnified 1000 times) for uncertainty in horizontal position when all pairwise registrations are chained.

Conclusively, examination of the traversing of multiple registrations shows clearly smaller loop closure errors and, most importantly, smaller uncertainties with the keypoint-based method presented in this paper. The largest uncertainties at the end of the chains could be reduced by about 25 % compared to the purely target-based method (28 % for dataset Library and 22 % for dataset Castle).