In industries handling high volumes of bulk materials—such as energy, mining, logistics, and civil infrastructure—monitoring stockpiles is a critical task. It supports supply chain visibility, regulatory compliance, financial forecasting, and strategic decision-making. Historically, this task relied on ground surveys or UAV-based photogrammetry—methods that do not scale easily across many sites or continents.
A scientific paper co-authored by Prof. Gabriele Facciolo, Scientific Consultant at Digital Sense and professor at ENS Paris-Saclay, presents a new approach: using Shape-from-Shading (SfS) on daily satellite imagery to estimate stockpile volumes. The method requires only monoscopic images from PlanetScope satellites—not expensive stereo imagery or drones. The solution is mathematically rigorous, computationally lightweight, and suitable for wide-scale deployment.
This article summarizes that work -published in the ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences- and explains its relevance for enterprise-scale monitoring systems.
What is stockpile monitoring?
Stockpile monitoring refers to the process of measuring the volume and changes in shape of piles of materials stored in open-air environments such as coal, minerals, aggregates, or industrial waste.
Traditionally, stockpile volumes were measured manually with topographic surveying equipment. These methods, though accurate, are time-consuming, costly, and often pose risks to workers on-site.
In the last two decades, technological innovation has introduced a wide range of remote sensing tools for stockpile monitoring. These include UAVs (drones) equipped with LiDAR or cameras for stereo-photogrammetry, aerial imagery, and high-resolution satellite data.
While UAVs provide high precision, they are not optimal for continuous global monitoring due to their limited operational range and the need for human intervention.
In contrast, satellite imagery offers a compelling alternative: global coverage, low operational costs, and high revisit frequency. While high-resolution satellite stereo imagery is cost-prohibitive for continuous monitoring and limited by acquisition constraints, lower-resolution images have long been considered insufficient for precise volumetric estimations. The study we review here presents a compelling argument to the contrary.
Why does it matter?
This process is vital in numerous sectors:
- Mining companies monitor ore, aggregate, and overburden volumes.
- Energy producers track coal or biomass inventories at storage depots or power plants.
- Logistics hubs and ports need to manage bulk goods such as grain or fertilizer.
Stockpile volumes are not just a measure of physical material—they represent financial assets, logistical risk, and strategic decisions. The ability to monitor these volumes continuously, automatically, and globally has far-reaching implications:
- Energy sector transitions: Coal stockpiles in European ports declined notably during the EU’s energy transition from coal to gas between 2018 and 2020. Such observations directly support macroeconomic and environmental policymaking.
- Market intelligence and price forecasting: Commodity stock level estimates can be used to anticipate supply fluctuations and price changes.
- Logistics optimization: With frequent updates, organizations can respond more effectively to changes in supply chains, weather impacts, or demand spikes.
- Compliance and transparency: Regulators, investors, and stakeholders benefit from third-party verifiable volume measurements that do not rely on self-reported data.
Yet most organizations cannot deploy drones at every location, every day. A scalable, automated, space-based solution fills this gap.
The new method proposed in the study leverages low-resolution but high-frequency PlanetScope imagery (3m resolution, daily revisit) and a shape-from-shading (SfS) technique to reconstruct 3D information from single images. This approach enables high-frequency, low-cost, unsupervised, and wide-area monitoring of stockpiles without the cost of high-res stereo imagery, UAV deployment or manual techniques.
Shape-from-Shading: A mathematically grounded alternative
At the heart of this method lies a mathematical technique called Shape-from-Shading (SfS). This method estimates the 3D shape of surfaces from a single 2D image, based on how light and shading appear. The figure below illustrates how the information of shading allows us to estimate the 3D structure from a single image.
The key insight of the paper is that stockpiles—being highly convex, relatively homogeneous, and without steep slopes—are ideal candidates for this kind of simplified reconstruction.
While stereo methods require multiple views of a scene, SfS can work with a single image, making it particularly suitable for high-frequency, low-cost satellite imagery where stereo pairs are not always available.
PlanetScope satellites provide daily global coverage with a ground sample distance (GSD) of approximately 3 meters, but not in a stereoscopic configuration. However, a single image is sufficient for shape estimation via shading information.
Core principles of SfS applied in this method
- Assumes a Lambertian surface (diffuse reflectance). That is, the surface reflects light evenly, which is approximately true for granular materials like coal, sand, or ore.
- Requires knowledge of the light source direction. The sun’s azimuth and elevation are included in satellite image metadata.
- Estimates surface normals from the sun direction and the brightness gradients.
- Solves a system of partial differential equations (PDEs), with adequate boundary conditions that capture the specificity of this problem.
By assuming low terrain slopes (most stockpiles have angles of repose below 45°), which implies that there are no cast shadows, the paper simplifies the nonlinear model into a linear approximation improving stability of the reconstruction.
📷 Figure 1: Shape-from-Shading vs Stereo
In the figure above, the SfS model (d) provides a comparable shape estimate to stereo (c), despite being derived from a single low-res image.
Methodology and implementation
The authors apply their method to two real-world coal stockpile sites, using time-series of PlanetScope images over seven months.
Key steps:
- Images are first filtered to exclude cloudy or blurry scenes.
- A preprocessing pipeline aligns images using phase correlation and performs radiometric normalization.
- Region of Interest (ROI) Delineation: Stockpile zones are manually identified once per site.
- A linearized version of the SfS model is solved iteratively to compute a Digital Elevation Model (DEM) of the stockpiles. This solution is computed by assuming Dirichlet boundary conditions on the boundary of the ROI at a constant altitude. This permits computing a unique solution to the PDE.
- Occlusions caused by cranes or other infrastructure are handled by integrating mixed boundary conditions (Dirichlet and Neumann) to avoid artifacts leading to false depressions or elevations in the reconstruction.
- The reconstructed elevations are scaled using reference stereo reconstructions (where available) to estimate absolute stockpile volumes.
📷 Figure 4: Time-Series Image Corregistration and Radiometric Normalization
Handling occlusions and real-world noise
Cranes and other infrastructure can occlude the ROI resulting in deviations from the assumed reflectance model. This leads to artifacts leading to incorrect volume estimations unless handled (see figure below).
To deal with these problems the method proposes a solution consisting in:
- Bright occluding objects are first detected via intensity thresholding.
- Areas with occluding objects are then removed from the domain of the PDE solution and Neumann conditions are imposed on their boundaries, while everything else remains Dirichlet.
This effectively ignores the bright pixels and allows for discontinuities of the solution on these points. The figure shows how properly defined boundary conditions lead to more accurate 3D reconstructions.
📷 Figure 3: Boundary Condition Effects
Experimental results:
The methodology was tested on two real-world coal storage sites, each observed using PlanetScope imagery over a 7-month period. After filtering, approximately 100 images per site were used to generate time-series volume estimates.
- Site 1: 2.58 × 1.58 km (larger area, well-defined stockpiles).
- Site 2: 1.17 × 0.46 km (smaller area, more challenging shapes).
The results were validated using stereo reconstructions from SkySat imagery on a subset of dates. While stereo DEMs provided the reference maximum elevation (approx. 15 meters), the SfS-derived volumes exhibited remarkable consistency and temporal coherence with the stereo volumes. For operational purposes, the SfS results proved accurate enough to detect meaningful volume changes.
Results indicate that the SfS-based approach captures the shape and evolution of large stockpiles reliably. While smaller stockpiles (e.g., <10m in diameter) present challenges due to resolution constraints, larger formations are well resolved.
📈 Figure 6: Volume Estimates Over Time
This graph demonstrates how SfS provides continuous monitoring, capturing stockpile variations even when stereo images are unavailable.
Here's what makes the solution stand out:
- Accuracy: Compared with stereo-based digital elevation models (DEMs), the SfS-derived volumes are consistently within a practical margin of error. While SfS cannot reach the precision of stereo methods, its consistency and frequency offer an unmatched operational advantage.
- Resilience to image noise: Cloudy or blurry images are filtered automatically. Radiometric corrections and image alignment are applied using state-of-the-art algorithms, including phase correlation and relative radiometric normalization.
Even with its lower resolution, the SfS method produced realistic volume estimations, particularly useful in detecting directional trends, identifying anomalies, or triggering alerts in a monitoring system.
Implications for enterprise deployment
This methodology offers compelling benefits for decision-makers:
- Global Scalability: Apply the same model across 10, 100, or 1,000 sites without sending teams on-site.
- Low operational burden: No on-site work or UAVs needed. No custom scheduling with high-res satellite providers.
- Temporal coverage: Daily updates enable time-series analysis and early anomaly detection.
- Cost-efficiency: Leverages existing low-cost imagery. No UAV deployment. No expensive stereo image licensing. Just a smart algorithm applied to affordable imagery.
- Automation readiness: The entire process can be embedded in a remote sensing platform or cloud-based analytics pipeline, suitable for integration into digital twins or supply chain dashboards.
Given the increasing need for real-time, scalable intelligence in supply chains and ESG monitoring, this solution offers an optimal trade-off between precision, cost, and scalability.
The approach is well-aligned with strategic goals around digital transformation, AI adoption, and environmental monitoring.
Digital Sense: From research to deployment
At Digital Sense, we specialize in turning advanced research like this into robust engineering systems. Our work stands at the intersection of scientific excellence and engineering execution.
Our differentiators:
- A team with PhDs, masters and experienced engineers with decades of research and over 300 peer-reviewed publications.
- A proven track record with top-tier partners like Satellogic, CNES, Orsted, CESBIO, and more.
- End-to-end project capabilities—from model development to real-time deployment on cloud-native infrastructure.
- Deep integration of scientific rigor and production scalability.
Whether you’re building an internal monitoring system, seeking a research partner for custom solutions, or looking to add intelligence to your spatial data, Digital Sense can deliver.
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References
📄 This article is based on the scientific publication [1]:
[1] d’Autume, M., Perry, A., Morel, J.-M., Meinhardt-Llopis, E., & Facciolo, G. (2020). Stockpile Monitoring Using Linear Shape-from-Shading on PlanetScope Imagery. ISPRS Annals, V-2-2020, 427–434. DOI
[2] Matsushita, Y. (2021). Shape from Shading. In: Ikeuchi, K. (eds) Computer Vision. Springer, Cham. https://doi.org/10.1007/978-3-030-63416-2_829
