the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 25 Sep 2026
3D surface displacements from digital image correlation on terrain models
Abstract. We present a methodology to retrieve 3D surface displacement based on Digital Image Correlation (DIC) applied
to multitemporal terrain models. Our approach has been developed to overcome the DIC limitation in the vertical component
of the displacement field when horizontal shifts are larger than the grid sampling. To validate the performance, we applied
the approach to two terrain models acquired over the Brienz/Brinzauls landslide, where surface displacements affect the entire
slope with heterogeneous amplitudes and directions. The comparison with in-situ measurements shows that DIC can accurately
retrieve horizontal and vertical displacements, providing a clear representation of the spatial extent of the mass movement, as
well as an accurate distinction of the internal landslide compartments. Our results are in good agreement with those obtained
using a state-of-the-art point correlation method, but require less preprocessing and computational effort. Thus, the proposed
DIC strategy can be considered as a valid alternative for measuring 3D surface displacements in scenarios where multitemporal
terrain models are available.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Earth Observation.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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Status: open (until 20 Nov 2026)
- CC1: 'Comment on egusphere-2026-5055', George Brencher, 16 Oct 2026 reply
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RC1: 'Comment on egusphere-2026-5055', Anonymous Referee #1, 22 Oct 2026
reply
This study by Oestreicher and co-authors presents an algorithm to estimate the 3D displacement of slow-moving objects from two DEMs acquired at different time steps. The authors use a Lagrangian point of view to estimate the velocity between two gridded DEMs. The horizontal velocity is classically estimated by correlation of shaded DEMs. The novelty comes from the use of a techniques called “shift-back” that associates pre and post pixels by blocks instead of by points as in the more classical “point-wise” method, to derive the vertical motion. By analyzing synthetic tests simulating homogeneous movements, authors find an improvement of 6% of the results compared to the point-wise method. The application of the techniques to the prior movements before the Brienz rockslide using drone acquisitions at 0.1m spacing shows similar results than with 3D motion estimates from Point-Clouds analysis, and good agreement with in situ GNSS measurements. This study tackles an interesting topic. Indeed, most of the time, comparisons of 3D displacement from satellite/drones/aerial DEMs are calculated with the Eulerian formalism and evaluated with in situ GNSS data through Lagrangian formalism. Pointing out this bias is important, even if a complete analysis of the literature on this topic is lacking here.
This study is well written, with clear figures well chosen and very useful annexes to understand the tests realised. However, I also found this study lacks a complete state of the art on the Lagrangian estimates of the velocity between two DEMs, and a better contextualisation of the proposed method, that would help the reader to identify the novelty of the study. Overall, the shift-back method is not precisely-enough exposed. I am also wondering about the validity of the evaluation of the method. Indeed, the method is compared either to other Lagrangian estimates from synthetic gridded DEMs with homogeneous displacements using a “point-wise” method or from correlations on point-clouds of real data (so more heterogeneous). This questions the results of the method to heterogeneous case studies, compared to more classical “point-wise” techniques. The question of the heterogeneity also leads me to wonder whether the method could be applied to other DEMs than drone data, less resolved, where the heterogeneity of the displacement fields would not necessarily meet the criteria of homogeneity at the scale of the “shift-back” windows. For all these reasons I think this manuscript needs substantial revisions.
Major comments:
(1) There is a large number of studies using Lagrangian point of view to estimate the velocities between two time-separated gridded DEMs. Most of them use DIC on shaded (or slopes, or convexity) DEMs to evaluated the horizontal shift, followed by the “point-wise” techniques to estimate the vertical motion. Among these studies, Zhou et al. (2015), Delorme et al., (2020), Hanagan et al., (2026), Fey et al (2015) are referred in the text. This list is not complete and no analysis of the methods/results used in these studies is realised. A better synthesis of the existing bibliography should be realised in the introduction to better contextualise the novelty of the proposed method. I provide here some additional references. I also see George Brencher is providing more references in his open comments.
Aati, S., Milliner, C., & Avouac, J. P. (2022). A new approach for 2-D and 3-D precise measurements of ground deformation from optimized registration and correlation of optical images and ICA-based filtering of image geometry artifacts. Remote Sensing of Environment, 277, 113038.
Q. Yang et al., "High-Precision 3-D Deformation Information Extraction of Mine Surfaces Using UAV LiDAR Technology," in IEEE Transactions on Geoscience and Remote Sensing, vol. 63, pp. 1-16, 2025, Art no. 4403316, doi: 10.1109/TGRS.2025.3535558.
Daehne, A. and Corsini, A. (2013), Kinematics of active earthflows revealed by digital image correlation and DEM subtraction techniques applied to multi-temporal LiDAR data. Earth Surf. Process. Landforms, 38: 640-654. https://doi.org/10.1002/esp.3351
Berg, N., Hori, T. & Take, W.A. Calculation of 3D displacement and time to failure of an earth dam using DIC analysis of hillshade images derived from high temporal resolution point cloud data. Landslides 17, 499–515 (2020). https://doi.org/10.1007/s10346-019-01284-7
(2) It is not clear by how much and why the proposed shift-back method is better than the point-wise method? First, the difference between the shift-back and the point-wise approaches is not clear to me, as the point-wise approach is obtained by evaluating the horizontal shift between points using DIC that works on windows of finite size, as it is for the shift-back methods. Furthermore, both methods need similar interpolations of the DEMs, since horizontal shifts are evaluated similarly, and lead to decimal values of a pixel. Could you be more specific on the main differences between these two methods?
Then, the shift-back method should be affected by discontinuities effects that are not illustrated here because the synthetic tests are all homogeneously shifted. Advantages of the method should be better evaluated with other synthetic tests and comparisons with the point-wise method should be undertaken on the real case-study of Brienz rather on the simple homogeneous case-study, in order to discuss the pros and cons of the two methods. This would lead to conclusions on the brought of the proposed method for more realistic heterogeneous case studies and feed a discussion on the heterogeneity impact on the results.
(3) Following this discussion on the application of the method to heterogeneous velocity fields, I am wondering what would be the results of the methods on DEMs obtained by satellite images, less resolved than drones, but very frequently used for geomorphic applications. Indeed, the proposed method has been shown to perform best for windows of 64 pixels, leading to homogeneity of the displacement fields over 6.4 meters for the drones data. For very-high-resolution images of Pleiades (1m-2m gridded DEMs), this would impose homogeneity of the ground displacement field at the scale of 64 to 128 m, and for ASTER-DEMs (30m), homogeneity should be at scales of 1800m. The tests realized in Annex A can be useful for that purpose, but it is also not clear if, for instance, a downscaled DEMs from drone at 1m is similar to a Pléiades DEM at 1m resolution. A discussion on that aspect fed by tests on real data would be interesting for the Earth-Observation community.
Specific comments:
It is not clear to me which sampling frequency is used to shift back the DEMs? Authors mention in parts 3.1.2 that the translation is applied “as a rigid shift per correlation window” (Line 185). However it is also mentioned (Line 168) that “The stride between the moving windows was set to 75 % overlap between adjacent windows”. In case the values of the horizontal shift is not the same between two overlapping windows, I don’t get what would be the rigid shifts on the common pixels of the two overlapping windows? Certainly a conceptual scheme is lacking to clearly explain the techniques.
L193: It is mentioned that the point-wise method uses interpolation of the DEMs, suggesting a major difference with the shift-back procedure. I don’t understand this point. Indeed, since the horizontal shifts from image correlation leads to decimal values of a pixel size, there might be also interpolations of the shifted back DEM.
Figure A1: Do you have an idea why the PCC and DIC approaches are more similar in the vertical direction than in the horizontal (dispersion of the DIC-PCC curves is lower in the vertical)?
Citation: https://doi.org/10.5194/egusphere-2026-5055-RC1
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There are several research papers from the glaciology community that have used DEM hillshades to measure horizontal surface velocity (e.g., Kraaijenbrink et al. 2016; Rounce et al. 2018). In many ways, using DEMs or hillshades to estimate glacier surface velocity is advantageous, as DEM products are unaffected by changes in surface albedo (e.g. surface snow cover) and illumination, unlike optical images. Recent studies have combined horizontal surface velocity with vertical elevation change measurements, taking into account local surface slope to estimate Lagrangian surface elevation change over glacier surfaces using complementary approaches (e.g., Bhushan et al. 2024; Van Tricht et al. 2021). Brencher et al. (2026) used the 3D change maps from stereo DEMs to validate horizontal and vertical displacement maps obtained using Satellite InSAR time series over Imja Lake moraine dam in Nepal.
It would be worthwhile to include these papers in the discussion section of the current manuscript, and to discuss their similarities to and differences from the workflow proposed in the manuscript.
- George Brencher and Shashank Bhushan
References
Bhushan, Shashank, David Shean, Jyun-Yi Michelle Hu, Grégoire Guillet, and David Robert Rounce. 2024. “Deriving Seasonal and Annual Surface Mass Balance for Debris-Covered Glaciers from Flow-Corrected Satellite Stereo DEM Time Series.” Journal of Glaciology, September 25, 1–21. https://doi.org/10.1017/jog.2024.57.
Brencher, George, Scott T. Henderson, and David E. Shean. 2026. “Quantifying Degradation of the Imja Lake Moraine Dam with Fused InSAR and SAR Feature Tracking Time Series.” The Cryosphere 20 (1): 67–86. https://doi.org/10.5194/tc-20-67-2026.
Kraaijenbrink, Philip, Sander W. Meijer, Joseph M. Shea, Francesca Pellicciotti, Steven M. De Jong, and Walter W. Immerzeel. 2016. “Seasonal Surface Velocities of a Himalayan Glacier Derived by Automated Correlation of Unmanned Aerial Vehicle Imagery.” Annals of Glaciology 57 (71): 103–13. https://doi.org/10.3189/2016AoG71A072.
Rounce, David R., Owen King, Michael McCarthy, David E. Shean, and Franco Salerno. 2018. “Quantifying Debris Thickness of Debris-Covered Glaciers in the Everest Region of Nepal Through Inversion of a Subdebris Melt Model.” Journal of Geophysical Research: Earth Surface 123 (5): 1094–115. https://doi.org/10.1029/2017JF004395.
Van Tricht, Lander, Philippe Huybrechts, Jonas Van Breedam, Alexander Vanhulle, Kristof Van Oost, and Harry Zekollari. 2021. “Estimating Surface Mass Balance Patterns from Unoccupied Aerial Vehicle Measurements in the Ablation Area of the Morteratsch–Pers Glacier Complex (Switzerland).” The Cryosphere 15 (9): 4445–64. https://doi.org/10.5194/tc-15-4445-2021.