Regional-scale Earth surface process analyses require cost-effective, large-area coverage, high-resolution digital elevation models (DEMs). Stereogrammetry, employing optical data from two or more overlapping images, emerges as a viable method for generating 3D topography in areas with sparse vegetation cover.
Introduction
Digital elevation models (DEMs) are crucial for analyzing the geomorphic processes shaping landscapes. Investigating such processes in regions characterized by both active tectonics and climate sensitivity provides valuable insights into associated hazards. This work focuses on the arid intermontane Calchaquí valley of the Eastern Cordillera of the NW Argentinian Andes, a region undergoing active deformation and highly sensitive to climatic forces. The area witnesses significant discharge events during the South American Monsoon season, resulting in heavy rainfall and flooding. Its predominantly dry, sparsely vegetated land is vulnerable to extreme discharge events. Hence, topographic analyses of this area are of relevance.
While freely available DEMs often lack the resolution to reveal intricate topographic details, high-resolution lidar-derived DEMs are costly and practical only for small-scale evaluations. For regional-scale assessments, stereogrammetry provides a cost-effective, high-resolution option for generating digital topography (Shean et al., 2019). Stereogrammetry generates three-dimensional (3D) models of objects or landscapes with the help of two or more overlapping pairs of photographs taken from different viewpoints.
This study uses the SPOT 6 (Satellite pour l’Observation de la Terre) images to generate a high-resolution (3m) DEM. The DEM is created with the help of the NASA Ames Stereo Pipeline, a collection of freely available and open-source automated tools for geodesy and stereogrammetry (Beyer et al., 2018). This DEM serves for studying actively deforming structures in an intra-continental setting in NW Argentinian Andes. Additionally, multiple DEMs generated using different algorithms and parameters have been compared to analyze their accuracy.
This internship was supervised by Prof. Dr. Bodo Bookhagen.
Study Region
The fault-bounded intermontane Calchaquí valley lies in the southeastern part of the Eastern Cordillera of the NW Argentinian Andes. The area is part of the Andean foreland and falls in the Salta Province, near the city of Cachi. The ongoing Andean orogenic deformation has led to the formation of inverted structures in the Andean foreland of NW Argentina (Strecker et al., 2012). This has resulted in thick-skinned deformation and recent seismicity. The reactivation of lower Paleozoic and Cretaceous basement structures has formed basement-cored mountain ranges with partially connected depocenters (Carrera et al., 2006).
The DEM created in this work is of an anticlinal feature in the Calchaquí valley, presumably formed over a blind thrust fault, due to the reactivation of the basement structure. The DEM serves as a basis for studying how these structures form and evolve by looking into the behavior of river networks and the deformation of fluvial terraces. This can also be used for hazard studies such as debris flows and landslides.
Data
- Panchromatic tri-stereo SPOT 6 satellite imagery at a resolution of 1.5m of a growing anticline in the Calchaquí valley
- Copernicus 30m DEM
Methods
The work is divided into two sections. The first section discusses the basic steps involved in DEM generation using the Ames Stereo Pipeline (ASP). In the second, comparative analyses on DEMs created using different algorithms and parameters have been performed.
Part 1: DEM Generation
A high-resolution DEM can be generated using ASP by analyzing stereo images taken from different viewpoints. These images captured from slightly different angles help to create depth perception and reconstruct the spatial structure of the observed terrain. ASP provides a range of stereo-matching algorithms and predefined parameters designed for creating a DEM. Some of the tools that ASP offers for DEM generation are described below.
Bundle Adjustment
Error in satellite position and orientation can affect the accuracy of a DEM created using ASP. These errors can be corrected using a pre-processing step called bundle adjustment. Bundle adjustment helps minimize the error between the estimated pixel locations of 3D objects and their actual positions in the captured images - ensuring consistency among observations of a single ground feature across multiple images.
Stereo Correlation
Correlation is the most important process within ASP. Stereo correlation matches the neighborhood of each pixel in the left image to a similar neighborhood in the right image. It works on a pair of overlapping stereo images from corresponding cameras and creates a point cloud that can be converted to a DEM.
Point Cloud Alignment
An existing ground truth, such as a DEM, can be used to rectify imperfectly calibrated camera intrinsic parameters. This significantly reduces distortions in the resulting DEMs which closely align with the ground truth. This work uses Copernicus 30m DEM for point cloud alignment. The resultant transformation matrix can also be used as a part of the bundle adjustment step for robust spatial coherence.
Map-projection
The stereo correlation process can fail if the two images are very different – if the cameras have very different perspectives, the terrain has very steep portions. This results in large disparity values and 3D terrains with noise or missing values. ASP deals with this issue with the implantation of map-projection – the left and the right images can be projected onto a low-resolution smooth terrain without holes. The resultant map-projected images are then used for stereo correlation.
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Workflow Summary
Step 1: The original SPOT 6 stereo images are used during the bundle adjustment (bundle_adjust) step for correcting camera intrinsics.
Step 2: Stereo correlation (parallel_stereo) is performed on the images using the bundle adjustment results obtained in Step 1.
Step 3: The resultant point cloud is converted to a DEM (point2dem).
Step 4: This DEM is aligned (pc_align) to the Copernicus 30m DEM to obtain a transformation matrix.
Step 5: This transformation matrix is further utilized for a second round of bundle adjustment (bundle_adjust) for precise spatial coherence.
Step 6: The original images are then map-projected onto the lower-resolution Copernicus DEM. This step also uses the camera adjustment obtained by previously running bundle_adjust in Step 5.
Step 7: Stereo correlation is performed again using the map-projected images and the camera adjustment results obtained by running bundle_adjust in Step 5.
Step 8: The point cloud is converted to a final DEM (point2dem).
Figure 2: Ames Stereo Pipeline - Workflow Summary
Part 2: DEM Comparison
Various stereo-matching algorithms and other parameters offered by ASP have been used in generating DEMs. Multiple DEMs generated have been compared by two means:
a) Visual Inspection - Smoothness of hillshade, presence of holes, or other artifacts.
b) Intersection Error - as a relative measurement of accuracy
How can intersection error be used as a relative measurement of accuracy?
The rays emanating from matching pixels in the cameras rarely intersect perfectly on the ground because any slight error in the position of the cameras will affect the accuracy of the rays. The actual shortest distance between the rays at this point is an important error metric that measures how self-consistent the two camera models are for this point. The distance between the two emanating rays from matching points in the cameras at their closest point of intersection is the triangulation error or the intersection error (Beyer et al., 2018). Hence, the intersection error can be used as a relative measure of the accuracy of a DEM.
The following parameters have been explored to compare DEM quality:
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Different Stereo-matching Algorithms
ASP offers several stereo-matching algorithms of which the following three have been used:
(i) Block Matching Algorithm (BM): The block matching algorithm divides the target image into fixed-size blocks and finds for each block the corresponding block in the other image that provides the best match (Fuhrt, 2008).
(ii) Semi-Global Matching Algorithm (SGM): The SGM stereovision algorithm enables pixel-wise matching between a pair of stereo images. The results obtained using this algorithm are highly accurate and the speed to generate results is high (Hirschmüller, 2008). The only downside is its characteristic streaks in the final disparity image.
(iii) More-Global Matching Algorithm (MGM): The MGM algorithm is similar to the SGM algorithm with a few extra operations per pixel. It gives higher-quality results by removing the streaking artifacts of SGM. MGM produces qualitatively and quantitatively denser results than SGM with little computation overhead (Facciolo et al., 2015).
Using Map-projected vs Original Images
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Different Image Pairs
SPOT imagery has three image acquisitions over the area of interest within the same orbital pass. The three images are shot with different viewing angles within the same orbit. This enables the generation of 3D models over the area of interest. The three images are named A, B, and C. The second image, B, is acquired by a near-vertical angle. The near-nadir image acquisition enables viewing hidden items and is useful for urban or mountainous areas. The anticline in the present study has some rough patches of very steep terrain for which the second image, B, might be useful. However, the anticline also has areas for which oblique viewing angles work better, and, in that case, image pair AC might be more useful.
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Different Sizes of Correlation Kernels and Sub-Pixel Kernels
The correlation kernel size determines the window size in the left and the right image for pixel comparison. Smaller kernel sizes might enhance results for intricate features, but it could also potentially increase the occurrence of false matches or noise. Three different combinations of correlation kernel and sub-pixel kernel sizes were explored.
(i) Correlation kernel: 5x5; Sub-pixel kernel: 11x11
(ii) Correlation kernel: 7x7; Sub-pixel kernel: 15x15
(iii) Correlation kernel: 9x9; Sub-pixel kernel: 21x21
Results
Choice of Stereo-matching Algorithms
Hillshade of the DEMs Overlain by Elevation Values
In Figure 3, the MGM DEM (C) has the least holes, and the BM DEM (A) has the most holes. On a closer inspection (zooming in on the DEMs), it can also be seen that the MGM and the SGM DEMs are smoother when compared to the BM DEM. Overall, the MGM DEM produces the least number of artifacts.
Intersection Errors of the DEMs
The intersection error plot, which is used in this study as a relative measurement of the accuracy of a DEM, also reveals lower overall intersection errors for the SGM and the MGM DEM (which are comparable), and higher intersection error for the BM DEM.
A Zoomed-in Perspective
The most jagged portion of the anticline is selected to look at the performance of the different stereo-matching algorithms in more difficult terrain scenarios.
(i) More artifacts for the BM DEM: The hillshade reveals that the BM DEM has more artifacts than the other two DEMs.
(ii) Higher intersection error for the BM DEM: The intersection error map of the same region reveals denser areas of higher intersection error values for the BM DEM.
(iii) Less good pixel region (more bad pixel region) for the BM DEM: ASP facilitates generating a “good pixel map” which indicates (in gray) pixels that were successfully matched with the correlator, and (in red) those that were not matched. Larger areas of unsuccessfully matched pixels can be seen for the BM algorithm.
Map-projecting the Original Images
Intersection Error of the DEMs
The DEM created using map-projected images has a lower overall intersection error than the one created using original images.
Hillshade and Intersection Error Map of a Zoomed-in Area of the Anticline
The hillshade of the DEM created using map-projected images has fewer artifacts and is relatively smoother.
Choice of Image Pairs
Intersection Error of the DEMs
The intersection error of the DEM created using the oblique image pair, AC, is the highest. However, it appears that for this image pair, there are larger intersection errors in the very jagged portions which might have contributed to the overall higher intersection errors (see below for intersection error maps). The other not-so-jagged portions (which constitute a larger area than a few jagged belts) have lower intersection errors for the DEM created using the oblique image pair (AC).
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Hillshade and Intersection Error Map of Rugged Areas with Steep Slopes
The near-nadir image acquisition for image B enables viewing hidden items and is useful for rugged terrain. The anticline in the present study has some areas with near-vertical slopes for which the DEM created using an oblique image (A or C) and a near-nadir image (B) has a smoother hillshade and lower intersection errors.
Figure 11: The jagged portion of the anticline where the image pair AC with oblique views produces the highest intersection error values. A combination of an oblique view image (A or C) with the near-nadir image (B) produces results with much lower intersection error.
Hillshade and Intersection Error Map of Areas with Gentler Slopes
The areas that do not have very steep slopes are resolved better using oblique images A and C. The hillshade is smoother.
Choice of Correlation Kernel and Sub-pixel Kernel Size
Intersection Error of the DEMs
The subpixel kernel sets the correlation kernel size in units of pixels. The intersection error of the DEM created using a correlation kernel size of 9, and a sub-pixel kernel size of 21 is the lowest.
Hillshade and Intersection Error Map of a Zoomed-in Area of the Anticline
Based on a visual inspection, the DEM created using a kernel size 21x21 is the smoothest.
Discussion
Comparison of Intersection Errors
Based on the results, the MGM DEM produces the best quality DEM as opposed to the SGM and the BM DEM. It is worth comparing the intersection errors of these DEMs to the standard MGM DEM. A Q-Q plot, which is a scatterplot created by plotting two sets of quantiles against one another can be used to compare the intersection errors. It can be noted that while the SGM DEM’s intersection error values slightly deviate from the MGM DEM towards higher intersection errors, the BM DEM’s values are significantly deviated.
Elevation Difference between DEMs
Elevation difference values between the MGM DEM and the SGM and the BM DEM respectively can express how closely the DEMs align with the standard MGM DEM. A distribution of these elevation difference values shows a higher standard deviation for the BM DEM as compared to the SGM DEM.
- Mean dh (MGM - SGM): -0.05 +/- 1.12
- Mean dh (MGM - BM): -0.10 +/- 2.15
Disparity Map
The most important process of ASP is stereo correlation. ASP has a collection of algorithms that compute correspondences between pixels in the left image and pixels in the right image. A map showing these correspondences is the disparity map. With the above observations, MGM DEM has been selected as the one producing the most accurate results. It is worth looking into the disparity maps of this algorithm. ASP facilitates dividing the total disparity into vertical and horizontal components. It can be noted that the more rugged features have higher offset magnitudes as compared to the other features of the terrain. This also suggests that the corresponding pixels are most probably incorrectly matched in very steep regions.
Map-projection
Map-projection transforms the original images into a pair of closely aligned images - this leaves only minor perspective differences between the images, which precisely correspond to the features targeted by the stereo correlation process (Beyer et al., 2018). GIF images can elaborate qualitatively on the effect of map-projection on the original images and an improvement in incorrect disparity values between corresponding pixels of the stereo images.
Conclusion
Stereogrammetry holds its importance in generating high-resolution surface models in areas of high relief and sparse vegetation. ASP offers a multitude of parameters for creating and refining a high-resolution DEM. Several parameters have been discussed in this study and it can be concluded that map-projecting the stereo images onto a pre-existing DEM is key to generating accurate DEMs. The disparity between corresponding pixels in original images is not a real perspective difference and can lead to large DEM errors if they are not map-projected before the stereo correlation step. It can also be seen that in difficult terrains, the MGM algorithm can create significantly better results than the other algorithms.
This study highlights the importance of exploring intersection errors across various DEMs to measure their relative accuracy. The DEMs that visually appear smoother and better in quality than others also consistently possess lower intersection error values.
References
Beyer, R. A., Alexandrov, O., and McMichael, S. (2018). The ames stereo pipeline: NASA’s open source software for deriving and processing terrain data. Earth and Space Science, 5(9):537–548.
Carrera, N., Muñoz, J. A., Sàbat, F., Mon, R., & Roca, E. (2006). The role of inversion tectonics in the structure of the Cordillera Oriental (NW Argentinean Andes). Journal of Structural Geology, 28(11), 1921–1932. https://doi.org/10.1016/j.jsg.2006.07.006.
Facciolo, G., de Franchis, C., and Meinhardt, E. (2015). MGM: A Significantly More Global Matching for Stereovision. British Machine Vision Conference.
Furht, B. (2008). Encyclopedia of Multimedia. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-78414-4_132.
Hirschmüller, H. (2008). Stereo processing by semiglobal matching and mutual information. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 30, no. 2, pp. 328-341.
Shean, D. E., Joughin, I. R., Dutrieux, P., Smith, B. E., and Berthier, E. (2019). Ice shelf basal melt rates from a high-resolution digital elevation model (dem) record for Pine Island Glacier, Antarctica. The Cryosphere, 13(10):2633–2656.
Strecker, M. R., Hilley, G. E., Bookhagen, B., & Sobel, E. R. (2012). Structural, geomorphic, and depositional characteristics of contiguous and broken foreland basins: Examples from the eastern flanks of the Central Andes in Bolivia and NW Argentina. Tectonics of Sedimentary Basins, edited, pp. 508–521.
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