4.2.1 Image triangulation
In a first step, the scanned analogue aerial images had to be oriented to recover the exterior parame- ters of the camera. This was done with Leica Photogrammetry Suite (LPS; Wang et al., 2004). For each investigated year an image block was set up, containing three aerial images for 2001 and 1988 and containing four aerial images for 1956. Camera calibration protocols on the interior orientation were available for all aerial images from swisstopo.
Table 2. The σ0 of the exterior orientation of the three image blocks calculated in LPS and root mean square error
(RMSE) of the control points. XYZ: Ground coordinates und xy: stereo intersection accuracy of the GCPs in image coordinates.
DTM σ0 (Pixel) Control point RMSE (X in
m, x in pixel) 2001 0.48 X: 1.3, Y: 0.6, Z: 1.5 x: 0.21, y: 0.57 1988 0.60 X: 1.9, Y: 1.3, Z: 2.5 x: 0.15, y: 0.66 1956 0.99 X: 1.6, Y: 1.5, Z: 1.7 x: 0.62, y: 0.34
Fischer et al.: Monitoring topographic changes in high-mountain faces
Tie points were measured manually to obtain the relative orientation of the image block. Because of the extremely steep terrain and associated strong distortions in the aerial images, automatic tie point extraction could barely be applied. The absolute orientation of the image blocks requires ma- nually measured ground control points (GCP). Because of the lack of survey points on the Monte Rosa east face, the coordinates of the GCPs were extracted from a topographic map (swisstopo, sheet no. 1348, edition 2003, 1:25,000) and the DHM25, a digital elevation model with 25 m grid spacing (DHM25 Level 2, swisstopo). Existing buildings such as alpine huts and pronounced un- movable surface features were taken as GCPs. LPS uses a one-step bundle adjustment for tie points and GCPs. The bundle adjustment yielded at a global accuracy of σ0 = 0.48, 0.6 and 0.99 pixel for
the different image blocks (Table 2). This corresponds to about 10-20 cm in object space, consider- ing an averaged image scale. The variation of the σ0 value from 0.48 to 0.99 pixel for 2001 to 1956
respectively, can be explained by the better image quality for the more recent aerial images. The global accuracy of the exterior orientation is very high for all image blocks, with values of 10-20 cm in object space.
The root mean square error (RMSE) value of the control points describes the accuracy of the GCPs and ranges from 0.6 to 2.5 m in planimetry and height (Table 2, XYZ values). This deviation was caused mainly by the imprecise GCP coordinates and the inaccuracy of manual point measure- ments. However, the stereo intersection accuracy of the GCPs in image coordinates resulted in half of a pixel (Table 2, xy values), which showed the high quality of the orientation considering the height and steepness of the rock wall.
4.2.2 DTM generation
DTM generation from the oriented aerial images was subsequently done in SAT-PP (Satellite im- age Precision Processing, ETH Zurich). The main component of this software package is an en- hanced multiple image matching algorithm for the extraction of image correspondences and the generation of 3D data. The approach uses a coarse-to-fine hierarchical solution with an effective combination of several image matching algorithms and automatic quality control (Zhang, 2005; Wolff and Gruen, 2007). The exterior orientation parameters recovered in LPS were imported into SAT-PP. Once the pre-processing of the original images (noise reduction, edge enhancement, pro- duction of image pyramids) was completed, it was possible to begin the extraction and matching of feature points, grid points and edges. This image matching produced a large number of points for the subsequent DTM generation and attained pixel level accuracy. Least squares matching methods were used to achieve more precise matches for all the matched features and for the identification of some false matches. Detailed mathematical descriptions of the SAT-PP software package are given in Gruen et al. (2005), Zhang (2005), Zhang and Gruen (2006).
In preparation for the automatic point extraction and matching process of the aerial images in SAT- PP, seed points had to be measured manually in each stereo pair of the image blocks. Here, a factor of ten-times more points than is usually necessary had to be measured manually in flat and ice-free areas because of the complex and steep topography as well as the widespread ice coverage. Some large vertical errors occurred due to incorrect automatic matching, mainly in steep and shadowy areas, and at damaged or polluted points or areas on the diapositives of the aerial images. Im- provements in these areas were obtained via enhanced manual measurements of seed points as well as vertical lines. Point density resulting from the matching process with several points/m2 on aver- age was as high as, or even higher than, the LiDAR point clouds. Taking into account the ground resolution of the aerial images (0.06-0.28 m, Table 1), the final DTM grids were generated at a ground resolution of 2 m.
4.2.3 Co-registration of DTMs
A direct comparison of multi-temporal DTMs requires the definition of a common reference sys- tem to avoid errors due to shifts in the individual DTMs. Due to inaccuracies of the GCPs used in planimetry and height of 0.6 to 2.5 m and a minimal number of GCPs within the face, the photo- grammetrically derived DTMs showed offsets between each other of several meters. To reduce such differences, all DTMs had to be transformed into a common reference system. Therefore, the LiDAR DTM acquired in 2007 has been taken as reference surface for all other processed DTMs. Automatic co-registration of the DTMs on the reference DTM was conducted with LS3D (Least Squares 3D Matching; Akca and Gruen, 2007). The LS3D method estimates the transformation parameters of one DTM to a reference one, using the Generalized Gauss-Markoff model, minimiz- ing the sum of squares of the Euclidean distances between the surfaces (Gruen and Akca, 2005). This method is a one-step solution for the matching and georeferencing of multiple 3D surfaces that are globally matched and simultaneously georeferenced. In a first step, called registration, each DTM was transformed onto the 2007 LiDAR-DTM. Only unchanged surfaces were transformed on the corresponding surfaces of the reference DTM, errors and also areas with topographic changes were excluded. These unchanged surfaces were manually selected in known stable bedrock (five zones with a size of at least 1000 m2), equally distributed over the whole face. The transformation of individual DTMs to the reference DTM allowed, in addition, assessment of their relative accura- cy. In a second step, the difference between the entire areas of the transformed DTMs was calcu- lated. For this DTM comparison, errors as well topographic changes were included in the calcula- tions (in the following termed ‘comparison’). These comparisons quantitatively revealed topo- graphic changes that occurred within the investigated periods.
5. Results