Debris-Flow Erosion Volume Estimation Using a Single High-Resolution Optical Satellite Image
Abstract
1. Introduction
- An NPC constraint is introduced using a random permutation operator to handle heterogeneous albedo distributions.
- The adaptability of the SFS-based depth super-resolution is extended, using publicly available global DEM as the initial reference, enabling terrain estimation under more complex surface conditions.
- High-resolution GF-6 optical satellite data are used for debris-flow erosion volume estimation, and results are quantitatively compared with airborne LiDAR-derived erosion volumes.
2. Methodology
2.1. Background of SRSFS
2.1.1. Imaging Model
2.1.2. Piecewise Constant Albedo
2.2. NPC SRSFS
Algorithm 1 Update of the non-local piecewise smooth constrained albedo. |
Input: Image , parameters , where is the iteration tolerance, is the dimensionality of the image, step factors |
1. Initialize: |
%%main loops |
2. while do |
%Dual ascent in |
3. |
4. |
5. |
6. |
%Primal descent in |
7. |
8. |
%Auxiliary variables update step |
9. |
10. |
end while |
Output: albedo |
Algorithm 2 NPC SRSFS. |
Input: Image , low-resolution , parameters weight of the augmented Lagrangian |
1. Initialize: |
%%main steps of ADMM |
2. while do |
%Albedo update |
3. Update using the primal-dual method as |
%Lighting update |
4. Estimate using pseudo-inverse as |
%Auxiliary variable update |
5. Update using L-BFGS as |
%Depth update |
6. Refine by the conjugate gradient method as |
%Extrapolation step |
7. Perform extrapolation as |
end while |
Output: estimated |
2.3. Debris-Flow Erosion Volume Estimation
Algorithm 3 Debris-flow erosion volume estimation. |
Input: Post-disaster image, Pre-disaster image (optional), GDEM |
Main steps: |
%Post-disaster image processing |
1. Generate the debris-flow area mask |
2. Estimate the post-disaster DSM using NPC SRSFS |
%Pre-disaster image processing (optional) |
3. Estimate the pre-disaster DSM using NPC SRSFS (or simply interpolate from GDEM) |
%DSM differencing |
4. Compute the difference between post-disaster and pre-disaster DSMs |
%Volume calculation |
5. Calculate debris-flow erosion volume within the left area |
Output: estimated debris-flow erosion volume |
3. Experiments and Discussion
3.1. Research Area and Datasets
3.2. Experimental Results
3.3. Parameter Analysis
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
Appendix A.1. Orthographic Camera Model
Appendix A.2. Update of Albedo with NPC
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Method | Calculation Approach | Erosion Volume (m3) | Relative Error (%) |
---|---|---|---|
SRSFS | Post-event DSM–GDEM | 52.07 × 103 | −47.78 |
Post-event DSM–Pre-event DSM | 59.38 × 103 | −40.45 | |
NPC SRSFS | Post-event DSM–GDEM | 106.41 × 103 | +6.72 |
Post-event DSM–Pre-event DSM | 109.25 × 103 | +9.57 | |
Aerial LiDAR | Post-event DSM–Pre-event DSM | 99.71 × 103 |
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Zhang, P.; Wang, S.; Zhou, G.; Zheng, Y.; Li, K.; Ji, L. Debris-Flow Erosion Volume Estimation Using a Single High-Resolution Optical Satellite Image. Remote Sens. 2025, 17, 2413. https://doi.org/10.3390/rs17142413
Zhang P, Wang S, Zhou G, Zheng Y, Li K, Ji L. Debris-Flow Erosion Volume Estimation Using a Single High-Resolution Optical Satellite Image. Remote Sensing. 2025; 17(14):2413. https://doi.org/10.3390/rs17142413
Chicago/Turabian StyleZhang, Peng, Shang Wang, Guangyao Zhou, Yueze Zheng, Kexin Li, and Luyan Ji. 2025. "Debris-Flow Erosion Volume Estimation Using a Single High-Resolution Optical Satellite Image" Remote Sensing 17, no. 14: 2413. https://doi.org/10.3390/rs17142413
APA StyleZhang, P., Wang, S., Zhou, G., Zheng, Y., Li, K., & Ji, L. (2025). Debris-Flow Erosion Volume Estimation Using a Single High-Resolution Optical Satellite Image. Remote Sensing, 17(14), 2413. https://doi.org/10.3390/rs17142413