Digital terrain models (DTMs), as representations of the earth’s surface, are an indispensable source of information in the geosciences. Structure-from-motion (SfM), especially in combination with multi-view-stereo (MVS) algorithms that substantially increase point cloud densities (thus correctly termed SfM-MVS [1
]), has become an increasingly popular technology (overviews by [1
]). Many studies have a methodological nature, focusing on the new technology and its possibilities, whilst others applied SfM-MVS, e.g., to geomorphological [3
] and glaciological [5
] problems. Usually, small areas (102
m²) are considered and terrestrial or low-altitude image platforms such as UAVs, blimps and kites are used. Bakker et al. (2016) [3
] have investigated whether SfM-MVS can be applied to plane-based aerial images. This is more challenging due to fewer images, a minor change in viewing angle (usually nadir), and a smaller image overlap. Bakker et al. (2016) [3
] showed that SfM-MVS-derived DTMs have similar qualities as DTMs derived with conventional photogrammetry, even when using archival imagery acquired decades ago. The accuracies of the relatively small area of interest (AOI), a braided riverbed, were comparable, and changes in the order of decimetres could be detected.
In glaciology, DTMs are widely used to observe ongoing processes and monitor changes [7
]. Differences between DTMs from different dates (years to decades apart) provide valuable information on local or glacier-wide surface elevation changes, e.g., the geodetic mass balance (e.g., [8
]). The application of SfM-MVS on historical, archival aerial imagery to detect mountain glacier changes has not yet been systematically investigated. In alpine areas, topography is highly challenging because of the steep slopes and the large elevation gradient. Generally, glaciers cover larger areas (in the order of square kilometres), making it harder to derive high accuracies in steep topography (e.g., [10
]), because of the reduced area of potentially stable terrain and the smaller possibility for good distribution of ground control points (GCPs), which are essential for generating a high-quality DTM. Additionally, extracting information from homogeneous (snow or ice-covered) surfaces is challenging due to low image texture. Archival aerial imagery is a valuable source of information, notably for long-term changes in glacier volume. Imagery is potentially available for many parts of the world from dates of more than 50 and sometimes even more than 100 years back in time. SfM-MVS could make the analysis of such data attractive because of the smaller effort of time and expert knowledge required, and the larger point cloud that potentially results in higher ground resolution.
The major goal of this study was to investigate whether it is possible to retrieve DTMs from aerial images using widely-used commercial SfM-MVS software, and whether these DTMs are of sufficient quality to analyse changes in glacier elevation. Therefore, we compared the resulting DTMs with those produced with conventional photogrammetry using the same input data, and assessed their quality with statistics from the bundle adjustment process and the performance over stable terrain using an independent reference DTM. Thereby, we could highlight the strengths and weaknesses of the two technologies for glaciological purposes. The final question addressed is whether it will be possible to reconstruct long-term glacier elevation changes or even geodetic mass balances with just a few commands by executing automated processes if the corresponding glacier outlines are available.
4.1. Bundle Adjustment
In total, 23 out of 27 possible DTMs could be generated with a satisfying level of quality, i.e., an RMS error that is lower than the glacier signal for each period and a ground resolution that enables the analysis of change patterns (Table 2
). After an iteration of quality checks and reprocessing, this quality could be achieved for every date and software, where a matching of images over the glacier tongue was possible. Using the RMSE, we found no significant difference between different software. However, DTMs from glacier monitoring flights with lower flying altitudes show smaller internal errors (RMSEavg
= 1.10 m) than those from the general mapping flights (RMSEavg
= 2.03 m). The ground resolution of the DTM reflects the finally calculated point density and also the quality of the filtered point cloud. ERDAS-IP yields a lower average resolution (5.67 m) than PhotoScan (3.33 m) and Pix4Dmapper (2.67 m). A similar number of GCPs were used per software, but more were required for ERDAS-IP with increasing number of input images. The number of automatically detected tie points, however, is two orders of magnitude higher for PhotoScan and Pix4Dmapper.
For the year 1946 only PhotoScan was able to achieve sufficient tie point correspondence for successful image matching. With ERDAS-IP we were not successful in establishing a geometric model for aerotriangulation because of a lack of camera parameters, image delineation indications and a relatively low image quality. It is a clear advantage that SfM-MVS methods do not rely on this information.
When only few images with little overlap are available, both SfM-MVS software have difficulties with the image matching. For 2001 (eight images) and 08 September 1977, the RMSE of the ERDAS DTM is the smallest, the quality on stable terrain is comparable, and the reconstructed surface area is larger than that from PhotoScan and Pix4Dmapper. For 2005, Pix4Dmapper was not successful in image matching. These experiences confirm the robust performance of conventional photogrammetry for this typical type of application, where a DTM is produced from a limited set of input images.
We found little correlation between the number of input images and the RMSE, but a small positive correlation between the number of GCPs and the RMSE (Figure 3
a,b). This is not surprising, since the number of images and thus the ground area increase with the number of GCPs, and, hence, automatically include a stronger horizontal and vertical distribution and thus higher elevation ranges. The Shannon entropy is a measure of image texture [14
] and only shows a small, non-significant correlation with the RMSE; disregarding one outlier DTM (14 September 1977), the correlation becomes much stronger (R² = 0.55 (p
≤ 0.05); see Figure 3
c,d). Image overlap is also expected to have an effect on DTM quality [3
]. We could see this in our results, where the glacier monitoring flights with an overlap of ~80% yield a mean RMSE of 1.30, while the national mapping flights with an overlap of ~60% yield a mean RMSE of 1.83. The high overlap of the former accommodates the SfM concept, while the mapping flights have an overlap/camera spacing accommodating conventional photogrammetry, with the parallax at the maximum and thus smaller inaccuracies in elevation calculations.
The geometric model is constructed using a combination of several parameters. Different combinations of focal length, image size, and flying height lead to similar results. Unlike for conventional photogrammetry, in the SfM-MVS technique it is possible to apply different image parameters and interior camera orientation settings for every input image in order to achieve the best fitting function. Without providing any input information, we observed that both PhotoScan and the Pix4Dmapper assumed a focal length between 25–30 mm. This is different from the real focal length (commonly 115–150 mm, depending on the camera that was used), but is compensated by different assumptions on image size and flying height.
4.2. DTM Quality over Stable Terrain
Generally, there is high confidence in the models considering the stable terrain statistics (Table 3
). The mean difference values lie between −0.39 m (ERDAS-IP) and 0.3 m (Pix4Dmapper), with an average of −0.04 m. Analogously, the standard deviation is 2.3 m (ERDAS-IP), 2.4 m (PhotoScan), and 1.3 m (Pix4Dmapper), with an average of 2.04 m. The range shows that, even with a higher resolution, the SfM-MVS-produced DTMs contain less noise than the ERDAS DTMs. Standard deviation is typically taken as DTM accuracy, and can in this case also help to select the best DTM per date.
4.3. DTM Intercomparison
A DTM difference was calculated between each DTM and the reference DTM, and the volume change over the glacier between the respective period is compared among the DTM sources. Summing up all periods yields a maximum difference of 15 m or 9.6% between the three software packages (Table 4
). This is mainly caused by two DTMs, which show a clearly different signal than the others from the same date, PhotoScan 1961 and ERDAS 1988, which both have relatively high errors (see Table 3
). Excluding them from the comparison reduces the total difference to 3% of the sum of periods.
Average statistics are one way to compare the DTMs. Another important characteristic is whether the patterns of volume change are similar. This can be compared by analysing the differences between the glacier signal maps from the same period revealed by the DTMs from the different software packages. The general patterns are very similar in every DTM difference image (Figure 4
). When looking at a smaller scale of ±10 m, certain characteristics became obvious: small artefacts of the DEM production, difficulties at lake surfaces and DTM edges (see Figure 5
). A comparison of these DTMs revealed which DTM has problems in which areas. For example, there is a small bulge of several meters in the Photoscan 1983 DTM (see Figure 5
b,c), or a relatively strong effect of >10 m at a proglacial lake surface.
Orthophotos can be produced by rectifying the aerial images. Thus, their geometric quality depends on the underlying DTM. The horizontal accuracy of the orthophotos is on average below 1 m at the GCP locations but can be locally higher, e.g., in areas of steeper terrain. The pixel resolution of the orthophotos depends on the camera resolution and the flying height and is with 0.2–1 m commonly several times higher than that from the DTMs. We have not investigated the radiometric and geometric quality of the orthophotos in detail, but they undoubtedly contain further information that can be exploited.
The smallest detectable changes are linked to the combined accuracy of the two DTMs at the start and end of a period and vary according to DTM quality. With the availability of a reference DTM, the standard deviation of values in the stable terrain can be used as an accuracy measure. For a period between two dates, the uncertainty of both DTMs needs to be combined using the square root of the sum of squared standard deviations. Doing this for the example period of 1961–2001 of the ERDAS DTMs, reveals a total uncertainty of
while the elevation change signal over the glacier is 26.8 m. Relevant multi-annual or decadal variations of glacier elevation change (over the full glacier or only parts of it) are typically in the range of meters or more (e.g., [33
]). Thus, the DTMs with such high spatial resolution and high accuracy are a very useful base for investigating the quantity of volume change and its patterns over time (see Figure 6
4.6. Glacier Evolution
Over the time span of 64 years the glacier tongue showed an average elevation change of −67.0 ± 5.3 m (average lowering rate −1.1 ± 0.08 m/year) inside the overlapping area, with a maximum of approximately −137 m close to today’s terminus. The trend is not temporally homogeneous but shows a period of strong negative change from 1946–1961, which is followed by over one decade of an average elevation increase (Figure 7
a). Since 1988 the elevation change has become negative again.
The most striking spatial patterns are locally emphasized elevation changes, which can be linked to the presence of supraglacial debris cover as well as ice cliffs and supraglacial flow channels. To exemplify the different periods and the effect of debris and ice cliffs, we selected three small areas (~0.01 km²) of different surface cover types (clean ice, debris-covered ice, and an area with ice cliffs/flow channels), and followed their evolution over time (Figure 8
). In most periods, the debris-covered area shows the smallest elevation change. The years of positive mass balances in the Alps [34
] in the 1970s and 1980s resulted in an increase in ice mass that was transported downglacier. It reached the cliff area (close to the terminus) later than the areas of the other surface cover types and with smaller intensity.
Apart from 1988, there is no notable difference between DTMs from different software packages and the same date. The standard deviation serves as a measure of DTM accuracy (±0.8–5.5 m; average ±2 m), which is sufficient to detect glacier volume changes for periods from several years to decades, and to investigate patterns of spatial change. The high quality of metric cameras (high radial resolution, small lens distortion, see also [35
]) is certainly a decisive factor in achieving high DTM quality, because it eases the self-calibration of lens distortion during the SfM-MVS process (this has also been pointed out by [3
]). SfM-MVS seems to be weaker with a small number of input images and less image overlap, while this is the strength of conventional photogrammetry. The successful generation of the DTM for 1946 shows the advantage of SfM-MVS to cope with challenging input data even without the use of camera parameters or image properties. Multiple processing of the same images can deliver slightly different results, which has its roots in the random seeding processes of the matching algorithms. Thus, we believe that controlling the model quality during the process is important because adapting GCP selection and placement as well as considering different quality thresholds in the matching process can strongly improve the result.
Restituted lens parameters and camera positions are the product of a number of parameters from image size to flying height. They might not represent the reality (e.g., focal length) but may still lead to high-quality results because of the compensation of one parameter by another. Providing the fixed lens parameters consequently leads to “correct” dependent parameters (e.g., flying height). SfM-MVS has the ability to assume a different camera for each image, so that the combination of parameters yields the best triangulation results. This can also be an advantage for aerial imagery in case of varying image quality. In addition, using PhotoScan and Pix4Dmapper substantially reduces processing time (3–6 times smaller), especially with a larger number of input images.
Despite the mentioned advantages of SfM-MVS, it is important to highlight the similar requirements considering DTM production and quality control. In terms of processing time and DTM quality, it has proven to be efficient to establish a set of base GCPs to be used as input for all DTMs. Just like for conventional photogrammetry, good spatial distribution (horizontally and vertically) of the GCPs is crucial, while quality is more important than quantity in the challenging glacier surroundings. Our experience showed that after a number of 10–15 GCPs the additional benefit to DTM accuracy decreases, even though additional GCPs of high quality will always also increase DTM quality [36
]. For the DTMs in this study, 10–15 GCPs per DTM result in a GCP density per km² (and per ground sampling distance (GSD)) of 0.7–2 GCP/km² (0.2–9.0 × 10−8
GCP/GSD), which coincides well with the results from other studies (e.g., [38
]). Apart from the average GCP density and the total GCP number, the distance to the closest GCP also affects DTM accuracy. Several studies have investigated the effect of a small number of unevenly distributed GCPs on DTM accuracy (e.g., [38
]) and found a substantial decrease of accuracy, but still in a range of ~1–3 m absolute accuracy. Gindraux et al. (2017) [38
] and Tonkin and Midgley (2016) [40
] found a decrease in accuracy of 0.09 and 0.1 m per 100 m distance increase from the next GCP, respectively. In our case, no reference information from the glacier surface was available. However, by combining the base GCPs with GCPs specifically adapted for each date, we achieved an appropriate horizontal and vertical GCP distribution around the glacier margins for all DTMs. Consequently, most pixels on the tongue of Zmuttgletscher are usually within a distance of 100–300 m of a GCP, while some smaller areas reach a maximum distance of 700–800 m. Using a decrease in accuracy of 0.1 m per 100 m distance results in uncertainties of 0.1–0.8 m, which is still smaller than uncertainties estimated from the stable terrain comparison. Due to the appropriate GCP distribution and the similar characteristics of stable terrain and the glacier surface, we also expect the error to be on average in the same range for both areas.
We found that the lowest DTM resolution without gross artefacts on the glacier surface is lower for PhotoScan and Pix4Dmapper than for ERDAS-IP. This is likely linked to the multi-vision algorithms that result in a much higher point cloud density (e.g., [41
]) which can be an advantage when investigating patterns or smaller features (e.g., moraine breaches, crevasses, thermokarst).
Our results confirm findings by others, such as the ability of SfM-MVS to establish a “dynamic” relation between different parameters required to set up a geometric model [3
], or the necessity of abundant and high-quality GCP input, and a final quality control [3
]. The application of SfM-MVS for glaciological purposes is increasing. The technique has been used for a variety of questions, like the characterization of surface features such as ponds and ice cliffs [5
], the investigation of calving dynamics by extracting surface ice flow from repeat flight campaigns [42
], or the study of supraglacial drainage [6
]. Piermattei et al. (2016) [43
] have also applied it to derive surface elevation changes over an entire glacier, thus determining the mass balance with the geodetic method by using UAV photography. Our study showed that SfM-MVS is well suited to derive geodetic mass balances by also using aerial images because quality and accuracy of the derived DTMs are comparable to modern photogrammetrical DTMs. This shows an opportunity to calculate elevation changes and produce geodetic mass balances for many glaciers, and also to extend existing time series further back. Originally, aerial images were often used for mapping purposes. Using the original images instead of information from the derived maps leads to denser and more precise elevation data, and makes it also possible to produce orthophotos that can be used for other glaciological purposes (e.g., the long-term change of debris-cover on Zmuttgletscher).
By comparing the output of two techniques and three of the currently most popular software packages in the geosciences, we were able to get a good idea of the precision of the resulting DTMs. Not only is the quality within the SfM technique high and, above all, robust, but the differences to the results from conventional photogrammetry are also robust and small. The uncertainty ranges are similar to the ones from the reference DTM, demonstrating that the SfM technology (namely PhotoScan and Pix4Dmapper) is mature enough to be used for scientific (glaciological) purposes under the prerequisites of high GCP quality and sound quality control. SfM-MVS technology might even be preferential to conventional photogrammetry (namely ERDAS-IP), which shows similar quality but lower resolution and longer processing times.
The analysis of the resulting time series of elevation changes over the tongue of Zmuttgletscher reveals an average lowering of approximately 67 m. The change is neither spatially homogeneous nor strongly correlated to absolute elevation, but is rather governed by an interplay of ice dynamics and debris cover, which will be the topic of further investigations.
High-quality DTMs can be achieved by applying SfM-MVS to a small set of aerial images. Their accuracy is comparable to that from DTMs resulting from conventional photogrammetry, but thorough quality control of the results, potentially adapting settings and input data, and reprocessing the data, are inevitable. Therefore, we conclude that the automatic production of geodetic glacier mass balances are still some way ahead. It will, however, become considerably faster for more researchers to produce DTMs over glacial areas that currently lack mass balance data, thus strongly increasing information on decadal glacier changes. We showed this potential with the example of a 64-year time series of elevation changes over the tongue of Zmuttgletscher, revealing rates of change as well as spatial change patterns over several time periods. Additionally, we can imagine a number of other glaciological applications, like methodological investigations of glaciers with an existing glaciological mass balance monitoring programme, or the extraction of information from high-resolution orthophotos. Because of the ease-of-use and the ongoing algorithm improvements, we expect to see more studies applying SfM-MVS to archival aerial imagery, investigating glaciological and other problems in high-mountain areas.