Terrain-Aware Digital Shadow

• Terrain-aware digital shadow is a geometry-conditioned representation that models visibility, occlusion, and operational constraints using the underlying terrain structure.
• It spans applications from SAR radar shadow detection to autonomous robotics, digital twins, and satellite photogrammetry, enabling precise terrain queries and navigational insights.
• Implementations use diverse methods such as DEMs, continuous neural terrain functions, and active-sensing techniques to optimize real-time terrain mapping and cost estimation.

Terrain-aware digital shadow denotes a class of geometry-conditioned digital representations in which terrain, relief, or scene structure is used to infer visibility, occlusion, traversability, or operational constraints of a physical environment. The term is used in several closely related ways across the literature. In synthetic aperture radar, it refers to a DEM-based model that predicts where terrain blocks the radar line of sight and therefore produces shadow in a geo-referenced SAR image (Prasath et al., 2013). In autonomous robotics, it can denote a spatially aligned prediction layer or terrain-reflective world model used for path planning, cost prediction, and navigation in unvisited space (Fortin et al., 2024). In environmental digital twins for sUAS, it is defined as a unidirectional mapping from the physical world to the digital representation that supports real-time terrain queries, proactive monitoring of terrain conditions, and runtime planning and situational awareness (Bernal et al., 22 Aug 2025). In continuous terrain modeling, it appears as a differentiable neural terrain function that supports off-grid queries, derivatives, topology, and compression (Feng et al., 2024, Feng et al., 21 May 2026). Taken together, these formulations suggest a common core: a terrain-aware digital shadow is not merely a visual shadow mask, but a digital artifact whose behavior is explicitly conditioned on terrain or scene geometry.

1. Conceptual scope and relation to digital twins

The literature does not use a single universal definition. In the sUAS digital-twin setting, the Terrain-Aware Digital Shadow is specifically the terrain component of a broader Environmental Digital Twin, and the distinction between shadow and twin is explicit: the shadow is a unidirectional mapping from the physical world to the digital representation, whereas the broader twin includes bidirectional synchronization between real and virtual sUAS (Bernal et al., 22 Aug 2025). In outdoor mapping, Terra is presented as a terrain-aware digital shadow because it provides a compact, queryable representation that preserves geometry, semantics, topology, and terrain structure, and is then reused for object retrieval, region monitoring, and terrain-aware navigation (Samuelson et al., 23 Sep 2025). In off-road autonomy, UAV-assisted self-supervised terrain awareness is described as an aerial “observer” that builds a terrain-aware digital shadow of the ground for a UGV by pairing terrain-aligned aerial images with proprioceptive ground-truth costs (Fortin et al., 2024).

These usages differ in immediate purpose, but they share several structural properties. First, the representation is spatially grounded in terrain or scene geometry rather than inferred only from appearance. Second, it is operational rather than merely descriptive: it is queried to support detection, planning, geolocation, navigation, or reconstruction. Third, it often separates physical-state acquisition from downstream task use. This is explicit in Terra’s three-phase design—task-agnostic metric-semantic mapping, terrain-aware 3D scene graph construction, and task-driven querying and navigation—and in the sUAS Environmental Digital Twin workflow, where terrain data are fused first and then validated across unit, integration, and system tests (Samuelson et al., 23 Sep 2025, Bernal et al., 22 Aug 2025).

2. Terrain as an occlusion and visibility field

A foundational formulation appears in radar shadow detection. Given a geo-referenced SAR image and a corresponding DEM, the DEM is rotated into radar geometry so that each row matches a radar line of sight in slant range, and shadow extraction is then reduced to a sequence of 1D row-wise projection problems (Prasath et al., 2013). For a line of sight, the projection line is

$l(x)=a(x)\cdot x+H,$

where $H$ is the sensor height, $x$ is pixel position along the line of sight, and $a(x)$ is the local slope value. Shadow is determined by the intersection of this radar line with the terrain profile from the rotated DEM, and the resulting mask is generated row by row and superimposed on the DEM or SAR representation. The reported behavior is explicitly geometric: shadow length depends on incidence angle, sensor height, terrain slope or elevation, and depression angle; low depression angles and high-relief terrain produce larger shadowed regions; and shadows closer to nadir are not detected at all (Prasath et al., 2013).

The same visibility logic appears in lidar scan matching, but as a beam-aligned preprocessing problem rather than an image-formation problem. Shadowing arises because a nearby occluder blocks returns from farther surfaces, and the visible edge of the shadow shifts as the sensor moves, producing systematic bias in voxel-based scan matching. The proposed mitigation is spherical gridding: points are transformed into spherical coordinates $(r,\alpha,\beta)$, grouped into angular wedges, and adaptive radial boundaries are estimated from radial jumps using a threshold $T$ and minimum cluster size $N$ (McDermott et al., 2022). This converts shadow handling into a 2D angular segmentation problem aligned with the lidar beam geometry. Unlike ground-plane removal, the method applies to arbitrary terrains, including shadows on urban walls and in hilly terrain, while retaining key ground points needed to estimate $z$, pitch, and roll. In the reported simulations, the spherical-grid method brought predicted and actual uncertainty much closer together and converged in all trials on both roadway and off-road scenes (McDermott et al., 2022).

A related but broader extension appears in Air-to-Ground channel modeling. There, 3D building geometry is projected into 2D ground shadow regions to determine LOS and NLOS regions for an aerial base station. For each rooftop vertex, the shadow projection is

$$\mathbf{s}_{n,v_n} = h^{\text{ABS}} \cdot \frac{\left(\mathbf{x}_{v_n}^b - \mathbf{x}^{\text{ABS}}\right)}{h^{\text{ABS}} - h_n^b} + \mathbf{x}^{\text{ABS}},$$

and the total shadowed region is the union of all building shadows (Vinogradov et al., 19 Nov 2025). The resulting LOS map is then intersected with user routes, and deterministic path loss is combined with spatially correlated shadow fading to form a spatially consistent radio map. A plausible implication is that terrain-aware digital shadowing generalizes naturally from terrain elevation to any environment geometry that induces stable, physically meaningful visibility boundaries.

3. Terrain substrates: DEMs, DTMs, and continuous neural terrain functions

Many terrain-aware digital shadows depend on a terrain substrate that is itself produced or learned from sensing data. One such substrate is an automatically generated Digital Terrain Model from LiDAR point clouds. The input point cloud is represented as

$P_i = (x_i, y_i, z_i, r_i, g_i, b_i),$

and the pipeline consists of preprocessing, heightmap generation, and terrain modeling (Easson et al., 2019). Preprocessing includes rasterization, statistical outlier removal, extraction of lowest and highest returns, and initialization of texture and material structures. Heightmap generation models terrain as

$H$0

where $H$1 is the ground surface and $H$2 captures non-ground anomalies such as buildings, shrubs, biomass, overhangs, and man-made structures. Ground/non-ground separation uses lowest and highest returns, terrain is fit with a low-degree polynomial via SVD, holes are filled by inpainting, and the result is converted into a terrain mesh with diffuse and normal maps for Unreal Engine 4 with LoD support (Easson et al., 2019). In this formulation, the terrain-aware digital shadow is not yet the shadowing logic itself; it is the renderable, ground-only terrain substrate on which such logic can operate.

A more analysis-oriented substrate is the continuous terrain function introduced by ImplicitTerrain. The terrain is represented as

$H$3

with surface

$H$4

and is learned using a Surface-plus-Geometry cascaded INR with sinusoidal activations (Feng et al., 2024). Because the representation is differentiable, it exposes $H$5, $H$6, and higher derivatives directly through automatic differentiation. This enables Morse-theoretic terrain analysis, including critical points, separatrix lines, Morse Incidence Graphs, persistence-based simplification, and derivative-driven topographical features such as slope, aspect, and mean curvature. Reported reconstruction quality on Swiss terrain tiles includes $H$7 PSNR around 59.75–64.85 dB, SPG PSNR up to 67.08 dB, and a model size of 1.51 MB versus a 7.6 MB raster input (Feng et al., 2024).

ImplicitTerrainV2 moves this representation toward a practical neural terrain data format. It retains the continuous function

$H$8

but adds a Wavelet Complexity Field for spatially adaptive frequency masking, complexity-aware adaptive sampling, derivative-aware supervision via gradient matching, and post-training quantization plus entropy coding (Feng et al., 21 May 2026). The gradient-matching loss supervises both height and slope, and the reported shape-stage ablation reduces GradMAE from 0.097 for a SIREN baseline to 0.024 with gradient matching and to 0.015 with frequency embedding plus gradient matching. On 50 Swiss terrain tiles, V2 reaches 66.25 dB end-to-end PSNR, improves over the prior work by 5.70 dB, uses 3.2× fewer parameters, trains in 55 s per tile on a single GPU, and compresses to 1.23 bpp with a 0.28 dB PSNR drop (Feng et al., 21 May 2026). This suggests a terrain-aware digital shadow can be stored not only as a raster or mesh, but as a compact, differentiable neural object.

4. Robotics, mapping, and runtime decision support

In off-road robotics, terrain-aware digital shadows are explicitly action-relevant. UAV-assisted self-supervised terrain awareness pairs a half-ton Clearpath Warthog with a DJI Mavic 3E hovering about 10 m above the robot and trains a ResNet-18 plus 3-layer fully connected regressor to predict one terrain metric at a time from terrain-aligned image patches (Fortin et al., 2024). The targets are vibration $H$9, bumpiness $x$0, and power consumption $x$1, all derived from proprioception and smoothed with a discretized Gaussian filter. The dataset contains 2.8 km of off-road data, 13,484 ground-based images, 12,935 aerial images, and 7,536 unique terrain patches collected in quarry, forest trails, high vegetation, rough gravel, and mossy areas (Fortin et al., 2024). UAV imagery improves terrain-property prediction by 21.37% on the whole dataset and 37.35% in high vegetation, and the scouting demonstration uses drone imagery and RTK localization to build local terrain-property maps, run Dijkstra’s shortest-path algorithm, and execute an optimized UGV path in an unseen area (Fortin et al., 2024). Here the digital shadow is a predictive terrain-cost field over unvisited space.

Terra generalizes this operational use into a hierarchical terrain-aware 3D scene graph. It begins with a sparse metric-semantic map from LiDAR, IMU, and RGB imagery using LIO-SAM for geometry and CLIP-based semantic embeddings associated to LiDAR points via image masks (Samuelson et al., 23 Sep 2025). Terrain masks are produced by a fine-tuned YOLO-v11n-seg model for sidewalk, grass, and asphalt, while FastSAM provides open-set class-agnostic masks for non-terrain content. Terrain-aware place nodes are then constructed from a separate 2D generalized Voronoi diagram for each terrain type, with inter-terrain links added to ensure connectivity. Region nodes are built by clustering place-node embeddings either agglomeratively or spectrally, with a four-level hierarchy split at 50, 100, 200, and 400 m (Samuelson et al., 23 Sep 2025). The resulting graph supports open-set object retrieval, region monitoring, and A* navigation in which terrain preferences are encoded directly in edge weights. Reported evaluation shows mIoU 0.786, F-mIoU 0.451, and F1 0.854 for terrain segmentation by YOLO-v11n-seg, while the broader 3DSG remains memory efficient and outperforms Clio in region classification (Samuelson et al., 23 Sep 2025).

The sUAS Environmental Digital Twin literature uses terrain-aware digital shadow in a more explicitly validated runtime sense. The terrain model is built by fusing USGS elevation, NHDPlusHR hydrography, transportation datasets, and NLCD land-cover data retrieved with HyRiver, then indexed with STRTree and supplemented with satellite imagery segmented by a pretrained and fine-tuned DeepLabv3 model trained on LandCover AI (Bernal et al., 22 Aug 2025). Each grid cell stores corner coordinates, centroid, elevation, land-cover classification, and associated discrete features. The TDS is then used for path planning, obstacle avoidance, altitude-above-ground maintenance, and geolocation by ray–terrain intersection. Validation follows a 3-Dimensions process spanning granularity of tests, simulation-to-real-world progression, and analysis from simple to edge conditions. Reported field findings include average lat/lon geolocation error of about 1.5 m, maximum error about 4.2 m, elevation error below 1 m, and person-geolocation errors of more than 10 m in some cases when altitude or GPS uncertainty is poor (Bernal et al., 22 Aug 2025). The emphasis is not only on terrain representation, but on trustworthiness under compound uncertainty.

5. Optical, satellite, and generative shadow reasoning

In optical satellite photogrammetry, terrain-aware digital shadowing becomes an illumination-aware reconstruction problem. Shadow Neural Radiance Fields extends NeRF by separating density, albedo, solar visibility, and diffuse sky illumination (Derksen et al., 2021). Standard NeRF is written as

$x$2

whereas S-NeRF introduces a local solar visibility field $x$3 and a sky-color field $x$4, leading to

$x$5

Training remains self-supervised through image reconstruction, but is reinforced by Solar Correction, which traces rays from the sun’s direction and constrains learned solar visibility to agree with geometric transmittance (Derksen et al., 2021). On WorldView-3 urban scenes around Jacksonville, S-NeRF reduces altitude mean absolute error in shaded areas relative to NeRF—for example from 5.607 to 3.342 m in area 004, from 7.627 to 4.799 m in area 068, and from 8.035 to 4.499 m in area 214—and supports shadow detection, albedo synthesis, transient-object filtering, and DEM-like altitude rendering (Derksen et al., 2021). The key conceptual move is explicit modeling of shadows as informative evidence about geometry rather than nuisance variability.

deSEO addresses a different EO problem: paired supervision for satellite shadow removal. It derives training pairs from the S-EO shadow detection dataset by selecting the least-shadowed acquisition for a crop as a weak reference and pairing it with shadowed counterparts that satisfy temporal, seasonal, footprint-overlap, view-geometry, and no-data constraints (Beltrame et al., 5 May 2026). The pairing pipeline includes Jacobian-based orientation normalization, LoFTR-RANSAC registration, and a per-pixel validity mask that restricts learning to reliably aligned regions despite residual off-nadir parallax. The deshadowing model is DSM-aware, uses a U-Net generator with optional self-attention and DSM concatenation, a PatchGAN discriminator modulated by a soft shadow attention mask, and reconstruction, perceptual, color, HSV, adversarial, and stabilizing losses on valid pixels only (Beltrame et al., 5 May 2026). The ablation study is especially diagnostic: removing DSM reduces PSNR to about 9, SSIM to about 0.18, and raises RMSE to around 90, indicating that DSM is the dominant geometric cue (Beltrame et al., 5 May 2026).

Physics-grounded shadow generation from monocular geometry priors pushes the same principle into image synthesis. A dense point map $x$6 is estimated from the image using MoGe-2, a dominant light direction $x$7 is predicted, and a coarse shadow support is computed from a geometric alignment test. For an object point $x$8, receiver point $x$9, displacement $a(x)$0, forward projection $a(x)$1, and perpendicular component $a(x)$2, a receiver pixel is shadowed if

$a(x)$3

with $a(x)$4 (Hu et al., 5 Dec 2025). This coarse, physically grounded estimate is then refined by a coarse-to-fine mask predictor and a diffusion framework with frozen denoising U-Net and intensity encoder. On DESOBAV2, the method reports BOS-free GRMSE 13.201, LRMSE 45.657, GSSIM 0.916, GBER 0.109, and mean angular light-direction error 5.701° overall (Hu et al., 5 Dec 2025). The model remains explicitly limited by the single dominant light assumption and by dependence on monocular geometry quality.

6. Rendering, active sensing, and recurring limitations

Terrain-aware digital shadowing is also a rendering and active-sensing problem. For curved planetary terrain, soft shadows are computed by treating shadowing as a global minimization problem along a shadow ray. The terrain renderer defines a shadow fraction from the ratio of ray height above terrain to traveled distance, but minimizes the numerator $a(x)$5 globally rather than the ratio itself (Jung et al., 2020). The search is solved with dynamic programming over a maximum mipmap hierarchy, with practical runtime treated as effectively constant when only a small number of mip levels is needed. The reported engine runs in real time, with mean frame time 5.4 ms at 185 Hz in a default configuration, versus 18.2 ms for uniform stepping, and up to 237% speedup while handling lunar umbrae exceeding 30 km and penumbrae exceeding 5 km (Jung et al., 2020). This is a terrain-aware digital shadow in the strict sense of physically computing cast shadows over curved terrain at planetary scale.

A complementary active-sensing formulation appears in smartphone structured light for rover terrain sensing. A smartphone projects a regular grid onto the ground, observes the deformed grid with its front camera, extracts grid intersections with band-limited filtering, LoG enhancement, skeletonization, and intersection detection, and reconstructs local terrain unevenness by triangulating matched grid nodes (Nobuaki, 29 Nov 2025). Because standard 1D-DTW does not preserve global lattice topology, the paper proposes topology-constrained 2D-DTW: pairwise 1D-DTW distances are computed between grid columns, a distance matrix is formed, and a globally consistent monotonic path is found by dynamic programming,

$a(x)$6

yielding column-wise alignment that preserves the grid needed for triangulation (Nobuaki, 29 Nov 2025). In this setting, the “shadow” is not an ambient cast shadow but a structured projection shadow whose deformation encodes local height variation, slope, and small bumps.

Across the literature, recurring limitations are explicit and often modality-specific. SAR shadow extraction cannot detect shadows near nadir, and its behavior depends strongly on incidence angle, sensor height, and terrain relief (Prasath et al., 2013). Automatic DTM generation assumes a smooth low-order terrain model that may fail on very rugged landforms (Easson et al., 2019). S-NeRF assumes Lambertian reflectance and spatially uniform sky illumination in shadowed regions, and is trained separately for each scene (Derksen et al., 2021). Lidar shadow mitigation requires scene-dependent thresholds $a(x)$7 and $a(x)$8 and does not address moving objects or other non-shadow disturbances (McDermott et al., 2022). Physics-grounded monocular shadow generation assumes a single dominant light direction and can fail when object geometry is incomplete (Hu et al., 5 Dec 2025). These limitations indicate that terrain-aware digital shadowing is not a single mature technique, but a family of geometry-aware representations whose fidelity depends on the interaction between terrain model, sensing geometry, illumination model, and downstream task.