Shadow-Aware 3D Gaussian Splatting (SA-3DGS)

• SA-3DGS is a shadow-aware variant of 3D Gaussian splatting that explicitly models geometry-consistent cast shadows and disentangles illumination from appearance in multi-temporal satellite imagery.
• It leverages per-Gaussian albedo and near-surface reflection features, a shared skylight model, and efficient ray marching to compute solar visibility and render accurate, soft shadows.
• The method incorporates a physics-based remote-sensing rendering equation with a shadow consistency constraint, enabling precise novel view synthesis even under sparse-view and varying lighting conditions.

SA-3DGS, in the sense used by "ShadowGS: Shadow-Aware 3D Gaussian Splatting for Satellite Imagery," denotes a shadow-aware extension of 3D Gaussian Splatting for multi-temporal satellite imagery that explicitly models geometry-consistent cast shadows, disentangles illumination from appearance, and preserves fast rasterization-based rendering (Luo et al., 4 Jan 2026). The method is motivated by the fact that multi-temporal satellite images of the same area are acquired at different dates, with varying solar elevation and azimuth, atmospheric conditions, and sensor or view geometry; shadows therefore move, stretch, and change intensity across time, so naive fusion confounds geometry and appearance and degrades reconstruction and synthesis (Luo et al., 4 Jan 2026). ShadowGS addresses this with per-Gaussian albedo and near-surface reflection features, a globally shared skylight model, efficient ray marching for geometry-aware solar visibility, a remote-sensing rendering equation, a shadow consistency constraint, and a shadow map prior for sparse-view settings (Luo et al., 4 Jan 2026).

1. Terminology and scope

In the cited literature, the abbreviation "SA-3DGS" is not unique. In "ShadowGS: Shadow-Aware 3D Gaussian Splatting for Satellite Imagery," the term refers specifically to ShadowGS (Luo et al., 4 Jan 2026). Other papers use the same or closely related abbreviation for distinct methods, including Scale-Adaptive Gaussian Splatting (Song et al., 2024), Semantic-Aware Gaussian Splatting (Xiong et al., 2024), a Self-Adaptive Compression method for 3DGS (Zhang et al., 5 Aug 2025), and a sparse-aware flat-minima optimization framework for 3DGS (Seo et al., 1 Jul 2026).

Expansion	Paper	Focus
Shadow-Aware 3D Gaussian Splatting	"ShadowGS: Shadow-Aware 3D Gaussian Splatting for Satellite Imagery" (Luo et al., 4 Jan 2026)	Multi-temporal satellite imagery, shadow disentanglement, geometry-consistent shadows
Scale-Adaptive Gaussian Splatting	"SA-GS: Scale-Adaptive Gaussian Splatting for Training-Free Anti-Aliasing" (Song et al., 2024)	Test-time anti-aliasing
Semantic-Aware Gaussian Splatting	"SA-GS: Semantic-Aware Gaussian Splatting for Large Scene Reconstruction with Geometry Constrain" (Xiong et al., 2024)	Semantic guidance and geometry regularization
Self-Adaptive Compression	"SA-3DGS: A Self-Adaptive Compression Method for 3D Gaussian Splatting" (Zhang et al., 5 Aug 2025)	Pruning, codebooks, repair
Sparse-aware 3DGS via flat minima	"Improving Sparse-View 3DGS Generalization via Flat Minima Optimization" (Seo et al., 1 Jul 2026)	Sparse-view generalization

This ambiguity is consequential because the ShadowGS formulation is tied to remote-sensing physics rather than to anti-aliasing, semantic regularization, compression, or sparse-view flat-minima optimization. A plausible implication is that acronym-based citation or implementation lookup can be error-prone unless the paper title or arXiv identifier is specified explicitly.

2. Problem setting, inputs, and reconstruction pipeline

ShadowGS is formulated for multi-temporal satellite images with known RPC camera models, acquisition timestamps, and solar angles (Luo et al., 4 Jan 2026). It handles RGB imagery on DFC2019 and pansharpened multispectral imagery on IARPA2016; the ground sampling distance is 0.3 m/pixel (Luo et al., 4 Jan 2026). The method refines RPCs via bundle adjustment to obtain poses and a sparse point cloud for Gaussian initialization, then approximates the refined RPCs with a local pinhole camera in the local tangent plane; the average reprojection error for RPC fitting is less than 0.5 px (Luo et al., 4 Jan 2026). Orthorectified DEMs are not required, and DSMs are used for evaluation only (Luo et al., 4 Jan 2026).

The multi-temporal registration stage co-registers images via BA and SfM using the refined RPCs (Luo et al., 4 Jan 2026). For each timestamp $t$, the solar direction $\mathbf{s}_t$ is taken from metadata and used to compute ray-marched solar visibility (Luo et al., 4 Jan 2026). The training and inference flow is: initialize 3D Gaussians from SfM points; render via 3DGS rasterization; compute solar visibility by ray marching; apply the remote-sensing rendering equation to compose color from albedo and illumination; optimize photometric, geometry, and shadow-related losses; then render novel views under arbitrary sun directions using the disentangled model at inference (Luo et al., 4 Jan 2026).

This pipeline is designed for scenes in which the same geometry is observed under different illumination regimes. The central methodological claim is that shadow behavior should be treated as a structured, geometry-linked phenomenon rather than as unmodeled appearance noise (Luo et al., 4 Jan 2026).

3. Gaussian representation, projection, and geometric quantities

Each 3D Gaussian is parameterized by center $\mu \in \mathbb{R}^3$, scale $s \in \mathbb{R}^3$, rotation quaternion $q \in \mathbb{R}^4$, opacity $o$, and appearance features represented with spherical harmonics (Luo et al., 4 Jan 2026). Its covariance is

$\Sigma = R S S^{\top} R^{\top},$

where $R$ is the rotation from $q$ and $S$ is a diagonal scaling matrix derived from $\mathbf{s}_t$0 (Luo et al., 4 Jan 2026). The Gaussian itself is

$\mathbf{s}_t$1

Projection uses EWA splatting, with projected 2D covariance

$\mathbf{s}_t$2

where $\mathbf{s}_t$3 maps world-to-camera coordinates and $\mathbf{s}_t$4 is the Jacobian of the projection (Luo et al., 4 Jan 2026). Rendering follows standard front-to-back alpha compositing,

$\mathbf{s}_t$5

with $\mathbf{s}_t$6 the color of the $\mathbf{s}_t$7-th splat (Luo et al., 4 Jan 2026).

ShadowGS also derives depth and normal quantities from ray–Gaussian intersections. For a pixel $\mathbf{s}_t$8, the intersection of the camera ray with a 3D Gaussian induces a 1D Gaussian along the ray, and the peak defines the ray–Gaussian intersection depth contribution $\mathbf{s}_t$9 (Luo et al., 4 Jan 2026). Depth and normals are alpha-blended, and the method applies a depth–normal consistency loss,

$\mu \in \mathbb{R}^3$0

where $\mu \in \mathbb{R}^3$1 is the normal estimated from the rendered depth map via finite differences (Luo et al., 4 Jan 2026). This regularization couples geometric smoothness with the splatted representation and supports more stable shadow reasoning.

4. Physics-based remote-sensing rendering and disentanglement

A central component of ShadowGS is the remote-sensing rendering equation. The sun direction is computed from metadata as

$\mu \in \mathbb{R}^3$2

where $\mu \in \mathbb{R}^3$3 is elevation above the horizon and $\mu \in \mathbb{R}^3$4 is azimuth from the $\mu \in \mathbb{R}^3$5-axis (Luo et al., 4 Jan 2026).

The method disentangles four components (Luo et al., 4 Jan 2026):

• Albedo $\mu \in \mathbb{R}^3$6 or $\mu \in \mathbb{R}^3$7, parameterized by per-Gaussian spherical harmonics.
• Near-surface reflection $\mu \in \mathbb{R}^3$8, also parameterized by per-Gaussian spherical harmonics and intended to capture low-order interreflections.
• Skylight $\mu \in \mathbb{R}^3$9, parameterized by a globally shared low-order spherical harmonic model.
• Direct sunlight $s \in \mathbb{R}^3$0 and solar visibility $s \in \mathbb{R}^3$1, where the sun is treated as a directional source and occlusion yields $s \in \mathbb{R}^3$2.

After rasterization, per-pixel albedo and illumination maps are composited (Luo et al., 4 Jan 2026). The direct and indirect terms are then written as

$s \in \mathbb{R}^3$3

$s \in \mathbb{R}^3$4

$s \in \mathbb{R}^3$5

$s \in \mathbb{R}^3$6

The paper also gives a simplified formulation in which the direct term is normalized and $s \in \mathbb{R}^3$7 gates direct versus indirect illumination:

$s \in \mathbb{R}^3$8

No explicit atmospheric scattering terms are modeled; instead, multi-temporal irradiance differences are absorbed by learned spherical harmonic coefficients and, optionally, per-image $s \in \mathbb{R}^3$9 scaling (Luo et al., 4 Jan 2026). The resulting separation is intended to stabilize albedo across timestamps while allowing illumination to vary with sun geometry, thereby reducing geometry–radiance ambiguity (Luo et al., 4 Jan 2026). This suggests that the method treats temporal illumination variation as a first-class latent factor rather than as residual appearance noise.

5. Geometry-consistent cast shadows and solar visibility

ShadowGS computes geometry-consistent cast shadows with efficient ray marching (Luo et al., 4 Jan 2026). Its acceleration structure is a stretched icosahedron BVH over Gaussians, following 3D Gaussian Ray Tracing (Luo et al., 4 Jan 2026). The per-Gaussian bounding volume is scaled with opacity and geometry as

$q \in \mathbb{R}^4$0

with transparency threshold $q \in \mathbb{R}^4$1 ensuring that the BVH covers the effective Gaussian support (Luo et al., 4 Jan 2026).

For each Gaussian center $q \in \mathbb{R}^4$2 and sun ray direction $q \in \mathbb{R}^4$3, the method marches with a fixed step size through the BVH; for each intersected Gaussian $q \in \mathbb{R}^4$4, it computes the 1D intersection peak along the ray,

$q \in \mathbb{R}^4$5

and the response along the ray,

$q \in \mathbb{R}^4$6

Solar visibility for the current Gaussian is then aggregated multiplicatively:

$q \in \mathbb{R}^4$7

where $q \in \mathbb{R}^4$8 is the number of intersections along the ray (Luo et al., 4 Jan 2026). The paper characterizes this as producing soft, geometry-aware cast shadows without aliasing, with integration into splatting through the aggregated $q \in \mathbb{R}^4$9 map (Luo et al., 4 Jan 2026). Shadow masks are rendered per view and per sun direction by rasterizing $o$0 to the image plane and alpha blending it analogously to the other composited maps (Luo et al., 4 Jan 2026).

A key physical observation exploited by ShadowGS is that, for satellite imaging, light rays from the sun and viewing rays are approximately parallel (Luo et al., 4 Jan 2026). When view and sun directions are collinear, cast shadows are self-occluded and should not be visible in the image (Luo et al., 4 Jan 2026). The method enforces this with a shadow consistency constraint: it renders a virtual shadow map $o$1 with view direction aligned to the sun and penalizes deviation from full illumination,

$o$2

Two practical configurations are reported: a fixed camera viewpoint with sun aligned to view, and a setting in which both sun and camera directions are adjusted to be perpendicular to the scene surface (Luo et al., 4 Jan 2026). The stated effect is to encourage splats to align to true surfaces and to increase opacity, improving geometric accuracy and novel-view synthesis (Luo et al., 4 Jan 2026).

6. Sparse-view regularization, outputs, and reported performance

Sparse views cause overfitting and weak constraints in ShadowGS (Luo et al., 4 Jan 2026). To stabilize optimization under limited inputs, the method introduces a shadow prior from FDRNet, described as a self-supervised shadow detector with low false-negative rate on satellite data (Luo et al., 4 Jan 2026). The rendered shadow map $o$3 is supervised against an FDRNet mask $o$4 using BCE,

$o$5

Vegetation is excluded using NDVI for multispectral imagery or DEVI for RGB imagery in order to mitigate false positives in the shadow prior (Luo et al., 4 Jan 2026). The prior is therefore not treated as a universal shadow oracle, but as a constrained regularizer applied where its failure modes are known.

The resulting system renders novel views under arbitrary sun directions using the disentangled representation (Luo et al., 4 Jan 2026). According to the abstract, extensive experiments demonstrate that ShadowGS outperforms current state-of-the-art methods in shadow decoupling accuracy, 3D reconstruction precision, and novel view synthesis quality, with only a few minutes of training (Luo et al., 4 Jan 2026). The same abstract states that the method exhibits robust performance across various settings, including RGB, pansharpened, and sparse-view satellite inputs (Luo et al., 4 Jan 2026).

These claims position ShadowGS as a remote-sensing-specific 3DGS variant whose main contribution is the incorporation of shadow physics into both the forward model and the optimization objective. A plausible implication is that, in satellite reconstruction, accurate shadow handling is not merely a photometric refinement but a geometric prior.

7. Relation to other 3DGS research directions

Within the broader 3DGS literature represented in the data, ShadowGS occupies a distinct niche. "SA-GS: Scale-Adaptive Gaussian Splatting for Training-Free Anti-Aliasing" addresses test-time anti-aliasing by applying a 2D scale-adaptive filter per projected Gaussian and, optionally, exact per-pixel integration or super-sampling (Song et al., 2024). "SA-GS: Semantic-Aware Gaussian Splatting for Large Scene Reconstruction with Geometry Constrain" injects semantic masks from Grounded-SAM or DINO into Gaussian shape control, expected Gaussian counts, and probability density-based point cloud extraction (Xiong et al., 2024). "SA-3DGS: A Self-Adaptive Compression Method for 3D Gaussian Splatting" focuses on pruning, importance-aware codebook compression of spherical harmonics, and codebook repair with a residual MLP (Zhang et al., 5 Aug 2025). "Improving Sparse-View 3DGS Generalization via Flat Minima Optimization" treats Gaussian parameters as trainable weights and regularizes sparse-view learning through anisotropy-aware perturbations and periodic reinitialization (Seo et al., 1 Jul 2026). In a different sensing regime, "SAR-GS: 3D Gaussian Splatting for Synthetic Aperture Radar Target Reconstruction" adapts Gaussian splatting to SAR geometry and attenuation via the SAR Differentiable Gaussian Splatting Rasterizer (Li et al., 25 Jun 2025).

Against that background, ShadowGS is specifically characterized by four coupled elements: per-Gaussian albedo and near-surface reflection features, a globally shared skylight model, efficient ray marching for geometry-aware solar visibility, and physics-based shading that composes direct and indirect illumination (Luo et al., 4 Jan 2026). Its defining emphasis is therefore neither anti-aliasing nor semantic grouping nor compression nor sparse-view flat-minima optimization, but the explicit modeling of geometrically consistent shadows in multi-temporal satellite imagery (Luo et al., 4 Jan 2026).

A common misconception would be to read ShadowGS as a generic illumination-aware extension applicable unchanged to arbitrary 3DGS settings. The paper’s formulation is more specific: it assumes multi-temporal satellite inputs, known RPC camera models, acquisition timestamps, and solar angles, and it exploits the approximately parallel geometry of sun and satellite rays in its shadow consistency constraint (Luo et al., 4 Jan 2026). The method is thus best understood as a remote-sensing-specialized 3DGS formulation rather than as a general-purpose replacement for all SA-3DGS variants.