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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

AHN-2 is the second part of the Actueel Hoogtebestand Nederland project, which concerns the acquisition of high-resolution altimetry data over the entire Netherlands using airborne laser scanning. The accuracy assessment of laser altimetry data usually relies on comparing corresponding tie elements, often points or lines, in the overlapping strips. This paper proposes a new approach to strip adjustment and accuracy assessment of AHN-2 data by using planar features. In the proposed approach a transformation is estimated between two overlapping strips by minimizing the distances between points in one strip and their corresponding planes in the other. The planes and the corresponding points are extracted in an automated segmentation process. The point-to-plane distances are used as observables in an estimation model, whereby the parameters of a transformation between the two strips and their associated quality measures are estimated. We demonstrate the performance of the method for the accuracy assessment of the AHN-2 dataset over Zeeland province of The Netherlands. The results show vertical offsets of up to 4 cm between the overlapping strips, and horizontal offsets ranging from 2 cm to 34 cm.

Airborne Laser Scanning is an active optical range measurement technique that is used for acquiring accurate height data of the ground surface. The advantages of airborne laser scanning include high measurement accuracy, fast acquisition capability, and large spatial coverage. The Netherlands is the first country that was entirely covered by airborne laser altimetry measurements through the Actueel Hoogtebestand Nederland (AHN) project [

The airborne laser scanning measurements are acquired in multiple flight strips, and are independently georeferenced using data from on-board navigation sensors,

The error budget of airborne laser scanning has been a subject of extensive research [

An alternative approach to assessing the relative accuracy of laser altimetry data is the comparison of corresponding features in overlapping strips. Vosselman [

This paper proposes a new approach to strip adjustment and accuracy assessment of airborne laser scanner data by using planar features. The choice of planar features is particularly appropriate for the accuracy assessment of AHN-2 data over the Netherlands, because buildings with gable roof planes are present almost in all parts of the country, and also the high point density of the AHN-2 data is a determining factor in the increased reliability of the extracted planes. The basis of the proposed approach is that by evaluating the adjustment between the corresponding planes in two overlapping strips an estimation of the systematic and random errors in the data can be obtained. In the strip adjustment, a transformation is estimated between the strips by minimizing the distances between points in one strip and their corresponding planes in the other. The advantage of such an estimation model is twofold. First, incorporating a large number of reliable point-to-plane distance observations in a least-squares estimation model improves the precision of the estimated transformation parameters. Second, if two strips cannot be adjusted by only a 3D offset, an affine transformation can be estimated from which possible rotations between the strips can be derived. In addition, the estimation model is linear, which makes it independent of an initial approximation of the transformation parameters.

The paper proceeds with an overview of laser altimetry over the Netherlands and the status of the AHN-2 project in Section 2. Section 3 describes the proposed approach to strip adjustment, including the segmentation method for extracting planar segments, the robust plane fitting and the mathematical model for the estimation of strip adjustment parameters. The results of the accuracy assessment of the AHN-2 data over Zeeland province are presented in Section 4. The paper concludes with some remarks in Section 5.

The Actual Height model of the Netherlands (AHN) part 2 is a joint program between the ministry of water management (Rijkswaterstaat) and the 26 water boards conducted in the period from 2007 to 2012. Water boards are the oldest legislative bodies in the Netherlands responsible for monitoring dykes and managing water quantity and quality. The importance of a country-wide height model for these organisations is evident, as the Netherlands is a delta partly below the sea level. During the first phase of the AHN project between 1997 and 2003 the entire Netherlands was laser scanned to make a height model with an altimetric accuracy of 16 cm and a point density varying from 1 point per 16 m^{2} to 1 point per 32 m^{2}. For the AHN-2 the requirements were tightened to achieve a higher accuracy and an increased point density.

While the AHN-2 is coordinated by the Waterschapshuis (the executive body of the Dutch water boards in the area of information and communication technology) the acquisition and quality control of the data are done by private companies. The first acquisition was done by Fugro over Zeeland province in the winter of 2007 using the FLI-MAP 400 laser scanner system mounted on a helicopter [

The planned specifications of the AHN-2 data include an average density of 10 points per m^{2} with 5 cm systematic error in height and 5 cm standard deviation. With such point density an object of 2 m by 2 m size can be correctly identified with a maximum planimetric error of 50 cm. The quality control procedures have been drafted by the Waterschapshuis, and executed by the companies NEO and Geodelta. The quality control consists of more than 40 procedures, including the point density check, the filtering of vegetation, the point distribution and the quality of the strip adjustment.

The quality control procedures are partly revised and modified every year. In 2008 the quality measures were derived by comparing corresponding elements in strip overlaps, but expressed for the entire coverage area. Since 2009 the quality measures are estimated and expressed per individual strip overlaps. The quality control procedures are not based on a standard methodology, and in fact there is a lack of reliable and commonly accepted methods for the quality control of laser altimetry data in practice.

The airborne laser scanner data are normally acquired strip-wise, with across-track overlap, as shown in

Extracting planar features from laser altimetry data is usually done over urban areas where many buildings with planar roofs are available. There are many methods in the literature for detecting buildings and identifying roof planes in aerial laser data, e.g., [

Planar surfaces that represent gabled roofs and dike slopes are selected from the resulting regions by constraining the regions to a minimum area of 6 m^{2} and a slope between 15 and 70 degrees. The boundaries of the corresponding regions in the two strips are combined and intersected. These intersected regions are buffered inwards with 25 cm (half the raster pixel size) to make sure that the points that are within the intersection area are part of the plane. These points are selected for the estimation of the plane parameters. As the segmentation is performed on gridded data, the selection criteria are not applied on the points directly. Therefore outliers in the selected point cloud might still be present after the segmentation process.

The plane parameters are obtained by applying the Principal Component Analysis (PCA) to the selected points [

The segmentation procedure does not necessarily always provide regions of points that are perfectly coplanar. In practice the regions might contain outliers, e.g., points on the walls, trees or the ground surface. To deal with the outlying points a robust plane fitting has to be applied to the points in both strips. Then only those points that are identified by the robust fitting algorithm as inliers are used to obtain the point-to-plane distances. The robust plane fitting is performed using the RANSAC algorithm [

The output of the previous step is a set of planes in one strip and their corresponding points in the other strip. The parameters of a transformation between the two overlapping strips are estimated by minimizing the distances between points and their corresponding planes. Let the transformation of a set of points _{1}_{2}_{3}^{T} represents a plane with normal _{1}_{2}_{3}^{T} and distance ^{T} denotes the homogenous representation of a point in 3D space. In practice, _{x}_{y}_{z}^{T} is a translation vector and a scale factor is neglected since laser strips are normally assumed to have identical scales. However, to make the estimation model linear, we ignore the orthogonality of R and assume that _{1}^{T}, _{2}^{T}, _{3}^{T} are the three rows of ^{T} is the Euclidian notation of a point in 3D space. For one point on one plane

A special case of the strip adjustment model as described above occurs when we expect the transformation between the strips to be only a translation vector. In such a case, the estimation model given in

It is worth noting that to obtain a solution for the estimation models derived above the design matrices in

The precision of the observables as well as the estimated transformation parameters are derived from the residual vector

The reference variance obtained from the residual vector

The strip adjustment method as described above was employed to assess the accuracy of the pilot AHN-2 dataset acquired by Fugro-Inpark over Zeeland province in 2007. The area consists of a crop land with large farm buildings and several urban areas, of which the city of Flushing is the largest. The data were acquired by the helicopter-mounted FLI-MAP 400 laser scanner from an altitude of 375 meters. The data consists of the forward-, nadir- and backward-looking scan lines. From this dataset, 15 strips were selected, resulting in 13 overlaps, as shown in

To evaluate the performance of the segmentation procedure strip overlap o12 was segmented with different scale parameters. The resulting roof regions were examined and compared with building boundaries from an existing large scale base map and with aerial images of the area. The result is shown in

The point-to-plane distances were derived for each strip overlap from the segmentation results. For every region in one strip plane parameters were computed using the robust plane fitting method. Then, distances between this plane and the inlying points in the corresponding region in the other strip were obtained and entered as observables in the estimation model. Two transformations were estimated for each pair of overlapping strips: a 3D translation only and a full affine transformation.

The mean and standard deviation of the point-to-plane distances before and after the adjustment were computed. Assuming that the data are not contaminated by gross errors (outliers), the mean before the adjustment indicates systematic error in the data. After the adjustment, the mean is expected to be very small, and the standard deviation indicates the random error of the observables and the precision of the estimated parameters.

_{x} and T_{y} are estimated with a precision better than 1 mm. In most of the overlaps, the estimated horizontal offsets are in agreement with those obtained by the line-based method. The discrepancies are in overlaps o6 (T_{x}), o7 (T_{y}) and o9 (both T_{x} and T_{y}), where differences from 10 cm to 20 cm can be observed. In the case of overlap o9, the precision of both T_{x} and T_{y} estimated from the line correspondences is very low, whereas the offsets estimated from the point-to-plane distances using both adjustment models are more precise and very close in magnitude. In fact, both T_{x} and T_{y} estimated from point-to-plane distances are within the range of uncertainty of the offsets estimated by the line-based method. In overlap o6 also the T_{x} values estimated by the plane-based method using both adjustment models are very close and more precise than that estimated by the line-based method. The disagreement in T_{y} corresponding to overlap o7 may be due to the presence of a small rotation between the strips. Note that the mean and standard deviation of the point-to-plane distances after the adjustment with a translation only and those after the full affine transformation have the largest discrepancy in overlap o7 (see

_{z} estimated from the point-to-plane distances for all overlaps. Here the bars representing the precision of the offsets are magnified by a factor of 10. It can be seen that the vertical offsets resulting from the two transformation models are very close. A difference of about 1 cm can be observed in overlap o7, which again might imply the presence of a small rotation between the strips. The precision of the estimated vertical offsets is better than 2 mm.

We have presented a method for the adjustment and accuracy assessment of airborne laser altimetry strips using planar features. The choice of planar features is particularly appropriate for the accuracy assessment of AHN-2 data over the Netherlands, because buildings with gable roof planes are present almost in all parts of the country, and also the high point density of the AHN-2 data is a determining factor in the increased reliability of the extracted planes. The method is based on estimating a transformation between two overlapping strips by minimizing the distances between points in one strip and their corresponding planes in the other. The accuracy assessment of the AHN-2 laser dataset over Zeeland, the Netherlands, was carried out using the proposed plane-based method, and the results were compared with those of a previously-used line-based method. The results show vertical offsets of up to 4 cm between the overlapping strips, and horizontal offsets ranging from 2 cm to 34 cm.

In comparison with the line-based methods, the use of planar features in strip adjustment leads to a more precise estimation of the transformation parameters. The performance of the plane-based methods is, however, dependent on the reliability of the extracted planes. Despite careful selection of the segmentation parameters we found many segments that contained outliers. The robust plane fitting using RANSAC proved very effective in removing these outlying points. In conclusion, for the plane-based strip adjustment method to be used in practice for the quality control of laser altimetry data robust and reliable plane extraction algorithms are of great importance.

The authors would like to thank the AHN steering committee for providing the dataset and ancillary data of Zeeland.

The AHN project.

Overlapping strips. The overlap area between the blue strip and the red strip is represented as the yellow hatched area.

Robust plane fitting to points on a roof segment. Points marked in red are inliers identified by RANSAC.

AHN-2 laser altimetry dataset of Zeeland consisting of 15 strips.

Performance of the segmentation method with different scale parameters.

Roof segments created by using different scale parameters in the segmentation procedure.

Mean of point-to-plane distances before and after the strip adjustment.

Standard deviation of point-to-plane distances before and after the strip adjustment.

Estimated x-offsets and their associated precision (vertical bars) compared to those estimated from line correspondences.

Estimated y-offsets and their associated precision (vertical bars) compared to those estimated from line correspondences.

Vertical offsets and their associated precision (vertical bars) estimated from point-to-plane distances.

Specifications of the 13 strip overlaps.

| |||||
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o1 | s3 | s4 | 21,731,922 | 27,885,585 | 200 |

o2 | s4 | s5 | 23,114,236 | 28,984,667 | 175 |

o3 | s5 | s6 | 28,984,667 | 51,271,482 | 240 |

o4 | s7 | s8 | 24,693,624 | 24,953,061 | 175 |

o5 | s9 | s8 | 24,534,357 | 22,834,121 | 175 |

o6 | s9 | s10 | 35,156,934 | 22,427,804 | 240 |

o7 | s10 | s11 | 10,303,345 | 7,590,510 | 200 |

o8 | s12 | s13 | 24,771,459 | 19,671,036 | 240 |

o9 | s14 | s13 | 3,267,309 | 4,177,717 | 525 |

o10 | s15 | s13 | 22,910,115 | 14,855,334 | 240 |

o11 | s2 | s1 | 4,618,326 | 5,251,392 | 485 |

o12 | s2 | s3 | 4,618,326 | 6,164,108 | 485 |

o13 | s1 | s3 | 65,247,718 | 77,060,363 | 320 |