PDSS-Net: Physics-Aware Shadow Synthesis

• The paper introduces a physics-aware synthesis network that applies a linear illumination degradation model to generate coarse shadow images from shadow-free inputs.
• It employs a hybrid method combining physics-guided de-exposure with a CycleGAN-based generator enhanced by Spatial-Decay Coordinate Attention to simulate smooth umbra-to-penumbra transitions.
• The approach produces a high-quality synthetic dataset (AeroDS-Syn) using real shadow statistics, addressing data scarcity for effective shadow removal training in aerospace imagery.

Searching arXiv for PDSS-Net and closely related shadow-physics papers. Physics-aware Degradation Shadow Synthesis Network (PDSS-Net) is the shadow-synthesis component introduced within the two-stage AeroDeshadow framework for high-resolution aerospace imagery (ASI). Its function is to generate synthetic shadowed images from shadow-free ASI in a manner that explicitly models illumination decay and spatial attenuation, thereby constructing the paired dataset AeroDS-Syn with soft boundary transitions for subsequent deshadowing training (Lu et al., 17 Apr 2026). In this formulation, PDSS-Net is not the final restoration model; it is the front-end synthesis stage that addresses two difficulties identified for ASI: the severe lack of strictly paired training data and the inadequacy of homogeneous shadow assumptions in scenes containing a dark umbra plus a broad penumbra transition zone.

1. Problem setting and position within AeroDeshadow

PDSS-Net is motivated by the observation that deep shadow-removal methods developed for natural images do not transfer directly to ASI because strictly paired shadow/shadow-free data are largely unavailable and because aerospace shadows often exhibit continuous illumination variation rather than a single binary dark region (Lu et al., 17 Apr 2026). The AeroDeshadow framework therefore separates the problem into two stages. In Stage 1, PDSS-Net synthesizes physically plausible shadows from shadow-free images and pseudo-shadow masks. In Stage 2, the Penumbra-aware Cascaded DeShadowing Network (PCDS-Net) is trained on those synthetic pairs and applied to real-world ASI.

Within this pipeline, PDSS-Net is the mechanism that “bridges the synthetic-to-real domain gap” by producing triplets of shadow-free image, synthesized shadow image, and shadow mask. The inputs to PDSS-Net are a shadow-free aerospace image $I_{free}$, a pseudo-shadow mask $I_{psm}^{hard}$, and, during training and prior extraction, real shadowed images $I_{rs}$ with corresponding masks. Its refined output is a generated shadow image

$I_{gs} = G(I_{ds}, I_{psm}),$

where $I_{ds}$ is an initial physics-guided de-exposure result.

The significance of this design is architectural as well as statistical. PDSS-Net does not ask the generator to invent realistic shadows from scratch. Instead, it first imposes a physically motivated degradation model and only then applies learned refinement. This suggests a hybrid forward model in which coarse shadow support and attenuation are constrained explicitly, while boundary realism and non-linear transition behavior are handled by the generator.

2. Physical degradation model and extraction of shadow priors

The physical core of PDSS-Net is a linear illumination degradation model derived from the photometric assumption that surface irradiance is mainly composed of direct sunlight and diffuse skylight, and that cast shadows arise when direct illumination is partially or fully occluded (Lu et al., 17 Apr 2026). For a real shadowed image $I$, the shadow pixels and nearby lit pixels are assumed to satisfy

$I_{s} = w \cdot I_{l} + b,$

where $I_s$ denotes shadow pixel values, $I_l$ denotes adjacent lit-region pixel values, $w \in \mathbb{R}^3$ is a channel-wise illumination scaling factor, and $I_{psm}^{hard}$0 is a channel-wise environment light shift bias.

PDSS-Net does not learn these parameters from arbitrary latent codes. Instead, it builds a library of $I_{psm}^{hard}$1 pairs from real shadowed ASI. Given a real shadowed image and its binary shadow mask $I_{psm}^{hard}$2, the method uses morphological erosion and dilation to isolate a shadow core region $I_{psm}^{hard}$3 and an adjacent lit region $I_{psm}^{hard}$4, excluding boundary-mixed pixels. The physical degradation parameters are then estimated as

$I_{psm}^{hard}$5

where $I_{psm}^{hard}$6 are the standard deviation and mean vectors of the shadow-core region and $I_{psm}^{hard}$7 are the corresponding statistics for the adjacent lit region.

This prior-extraction procedure is central to the method’s “physics-aware” designation. The degradation parameters are sampled from real shadow statistics rather than fitted purely by adversarial pressure. A plausible implication is that the generator is constrained to operate near observed ASI shadow distributions before any learned image translation occurs.

The method also softens the manually annotated pseudo-shadow mask before synthesis: $I_{psm}^{hard}$8 This produces an edge-preserving soft mask that serves as an initial approximation to penumbra. The coarse shadowed image is then generated by physics-guided de-exposure: $I_{psm}^{hard}$9

This blending rule keeps $I_{rs}$0 outside the pseudo-shadow region, applies the physically estimated degradation $I_{rs}$1 inside it, and interpolates continuously across the softened boundary. The mechanism implies that umbra-like regions correspond to high values in $I_{rs}$2, while penumbra-like transition zones emerge where the soft mask varies smoothly between $I_{rs}$3 and $I_{rs}$4.

3. Network architecture and the Spatial-Decay Coordinate Attention module

PDSS-Net contains three core components: the Shadow Illumination Decay Estimator, the Physics-guided Initial Synthesis Module, and a Refinement Generative Network with Spatial-Decay Coordinate Attention (SDCA) (Lu et al., 17 Apr 2026). The first component is the non-parametric prior library of $I_{rs}$5 extracted from real shadowed imagery. The second component produces the coarse de-exposure image $I_{rs}$6. The third component refines that image into the final synthesized shadow domain.

The refinement stage adopts a CycleGAN-based framework for unpaired image translation. Its generator is a U-Net style encoder-decoder with skip connections, and SDCA is inserted at the skip connections. The generator takes $I_{rs}$7 and $I_{rs}$8 as input and outputs the refined shadow image $I_{rs}$9.

SDCA is the module specifically designed to represent the transition from umbra to penumbra. For an input feature map

$I_{gs} = G(I_{ds}, I_{psm}),$0

the module applies directional attention as

$I_{gs} = G(I_{ds}, I_{psm}),$1

where $I_{gs} = G(I_{ds}, I_{psm}),$2 and $I_{gs} = G(I_{ds}, I_{psm}),$3 are horizontal and vertical attention maps. The coordinate pooling stage is

$I_{gs} = G(I_{ds}, I_{psm}),$4

followed by

$I_{gs} = G(I_{ds}, I_{psm}),$5

The local perception branch is

$I_{gs} = G(I_{ds}, I_{psm}),$6

with

$I_{gs} = G(I_{ds}, I_{psm}),$7

This branch is intended to preserve local structure, especially umbra edge sharpness. The decay simulation branch is

$I_{gs} = G(I_{ds}, I_{psm}),$8

where the paper states that a depthwise $I_{gs} = G(I_{ds}, I_{psm}),$9 strip convolution is applied along the spatial dimension to simulate the gradual distance-decay effect of the penumbra transition. The two branches are fused as

$I_{ds}$0

After splitting the fused tensor, the attention maps are predicted by

$I_{ds}$1

The architectural interpretation is explicit in the paper: the local branch preserves sharp local structure, while the decay branch simulates non-linear spatial attenuation. PDSS-Net therefore does not explicitly predict separate umbra and penumbra masks; instead, it synthesizes them implicitly through the combination of soft-mask initialization and SDCA-guided refinement.

4. Synthesis pipeline and construction of AeroDS-Syn

PDSS-Net constructs AeroDS-Syn by combining real shadow statistics, pseudo-shadow geometry, and unpaired adversarial refinement (Lu et al., 17 Apr 2026). The source material consists of 2,260 real shadowed images, 2,260 unpaired shadow-free images, and 2,260 manually annotated pseudo-shadow masks. The original imagery has spatial resolution $I_{ds}$2, is initially cropped to $I_{ds}$3, and is then normalized to $I_{ds}$4 using Real-ESRGAN for annotation and training consistency.

The synthesis procedure follows a fixed sequence. First, a library of real-scene $I_{ds}$5 parameters is extracted from real shadowed imagery. Second, a clean image $I_{ds}$6 and a manually annotated hard pseudo-mask $I_{ds}$7 are selected. Third, the hard mask is softened with the guided filter: $I_{ds}$8 Fourth, a sampled $I_{ds}$9 pair is used to generate the coarse shadowed image $I$0 through the de-exposure equation above. Fifth, the CycleGAN-style generator refines $I$1 into

$I$2

Finally, the triplet

$I$3

is stored as a supervised sample in AeroDS-Syn.

AeroDS-Syn contains 2,260 triplets total, with 2,000 training and 260 testing samples. The real-scene generalization benchmark AeroDS-Real contains 260 real shadowed samples with manually annotated masks and no paired shadow-free references. The resulting dataset is best described as semi-automatically constructed synthetic paired data: the source images are real, the pseudo-shadow masks are manually annotated, and the shadows are synthesized by PDSS-Net under real-scene physical priors and real shadow-domain adversarial supervision.

This dataset-construction role is inseparable from the network’s purpose. PDSS-Net is not merely an image editor; it is a data-generation mechanism designed so that PCDS-Net can later learn from physically plausible examples containing realistic umbra darkness, broad penumbra transitions, and non-uniform spatial attenuation.

5. Objective functions, implementation, and empirical behavior

PDSS-Net is trained with a CycleGAN-style objective augmented by task-specific constraints (Lu et al., 17 Apr 2026). Its total loss is

$I$4

with

$I$5

The adversarial loss is LSGAN-style: $I$6 The cycle consistency term is

$I$7

where $I$8 is the inverse generator. The background consistency loss,

$I$9

enforces invariance outside the shadow region. The identity loss,

$I_{s} = w \cdot I_{l} + b,$0

penalizes unnecessary changes when a real shadow image is already in the target domain.

The reported implementation uses PyTorch, NVIDIA RTX 3090 Ti, Adam, initial learning rate $I_{s} = w \cdot I_{l} + b,$1, linear decay, batch size 2, 100 training epochs, and input size $I_{s} = w \cdot I_{l} + b,$2. The paper explicitly notes that it does not mention perceptual, mask-supervision, attenuation-map, edge, or explicit smoothness losses for PDSS-Net beyond the four losses above.

The synthesis evaluation uses MeanSLR / SLR Range and $I_{s} = w \cdot I_{l} + b,$3. On AeroDS-Syn test data, the real reference has MeanSLR $I_{s} = w \cdot I_{l} + b,$4, SLR Range $I_{s} = w \cdot I_{l} + b,$5, and $I_{s} = w \cdot I_{l} + b,$6. PDSS-Net reports MeanSLR $I_{s} = w \cdot I_{l} + b,$7, SLR Range $I_{s} = w \cdot I_{l} + b,$8, and $I_{s} = w \cdot I_{l} + b,$9. The paper compares PDSS-Net against SynShadow, Mask-ShadowGAN, G2R-ShadowNet, UP-ShadowGAN, and RS-GSSR, and states that PDSS-Net best reproduces realistic attenuation, diverse luminance conditions, and smooth penumbra transition.

The ablation evidence is aligned with the method’s design. Removing the De-exposure Processing (DEP) stage yields MeanSLR $I_s$0, SLR Range $I_s$1, and $I_s$2, indicating that the physics-guided initialization materially affects luminance realism. The visual SDCA ablation reports sharp boundary mutations, intensity ringing, and visual discontinuities without SDCA, versus gradual spatial decay and smoother penumbra transitions with SDCA.

6. Relation to adjacent research, interpretation, and limitations

PDSS-Net belongs to a broader line of shadow methods that reject unconstrained 2D image translation in favor of structured degradation modeling, but it is specialized to ASI and to forward synthesis rather than inverse restoration. In natural-image shadow generation, “Physics-Grounded Shadow Generation from Monocular 3D Geometry Priors and Approximate Light Direction” formalizes cast-shadow formation through explicit monocular 3D geometry, a dominant light direction, and a geometry-light-based initial estimate before learned refinement (Hu et al., 5 Dec 2025). In shadow removal, “ShadowDiffusion: When Degradation Prior Meets Diffusion Model for Shadow Removal” factorizes shadows into a mask and a spatially varying attenuation field within a diffusion framework (Guo et al., 2022). “Physics-based Shadow Image Decomposition for Shadow Removal” separates umbra correction, penumbra matte modeling, and detail restoration through SP-Net, M-Net, and I-Net (Le et al., 2020), while “A+D Net: Training a Shadow Detector with Adversarial Shadow Attenuation” constrains shadow attenuation by a simplified physical illumination model during adversarial sample generation (Le et al., 2017). Taken together, these works situate PDSS-Net within a research pattern in which physical priors determine where and how a shadow-like degradation should exist, while the learned network refines appearance.

What distinguishes PDSS-Net within that pattern is its aerospace-specific combination of real-scene degradation statistics, soft pseudo-mask blending, and SDCA-based modeling of spatial decay. The method is explicitly tailored to long-range illumination propagation, atmospheric scattering, broad transition zones, and heterogeneous spectral attenuation in ASI (Lu et al., 17 Apr 2026). Its “physics-aware” content is therefore partly analytical and partly architectural: the channel-wise linear degradation model provides an interpretable initialization, while SDCA injects a directional decay prior that is not derived from a full radiative transfer formulation.

The limitations are equally clear. The conclusion points to future work on extending physical degradation models to more complex atmospheric occlusions such as cloud shadows (Lu et al., 17 Apr 2026). This indicates that the present model is mainly built around cast-shadow degradation with linear attenuation priors plus learned refinement. More generally, the physical core remains a relatively simple channel-wise affine approximation,

$I_s$3

rather than a full optical image-formation model. The network also does not explicitly parameterize separate umbra and penumbra labels, alpha mattes, or geometry-driven occlusion fields. Instead, those effects are synthesized implicitly through the soft pseudo-mask and SDCA refinement.

For that reason, PDSS-Net is best understood not as a general shadow renderer, but as a physics-aware shadow synthesis network whose principal innovation is to convert real ASI shadow statistics into a practical paired-data generator. Its importance within AeroDeshadow lies in establishing a matched forward model for a later inverse problem: PCDS-Net is trained to undo precisely the heterogeneous degradations that PDSS-Net was designed to synthesize (Lu et al., 17 Apr 2026).