PCDS-Net: Penumbra-Aware Shadow Removal

• The paper introduces PCDS-Net, a penumbra-aware de-shadowing network that employs dual encoders and cascaded decoding to restore shadowed aerospace images.
• It leverages morphological decomposition to create precise umbra and penumbra masks, enabling zone-specific restoration and minimizing correction artifacts.
• Experiments demonstrate improved quantitative metrics (PSNR, SSIM, RMSE, BRISQUE) over baseline methods, confirming the efficacy of adaptive fusion and region-aware loss.

Penumbra-aware Cascaded DeShadowing Network (PCDS-Net) is the restoration stage of AeroDeshadow, a unified two-stage framework for aerospace imagery (ASI). It takes a shadowed image $I_s$ and a shadow mask $I_m$, explicitly decouples umbra and penumbra, and restores these regions progressively in a cascaded manner. The network is motivated by two difficulties emphasized for ASI: strictly paired training data are severely lacking, and homogeneous shadow assumptions fail to handle the broad penumbra transition zones inherent in aerospace scenes. Within AeroDeshadow, PCDS-Net is trained only on the synthetic paired dataset AeroDS-Syn and is reported to generalize to real-world ASI without requiring paired real annotations (Lu et al., 17 Apr 2026).

1. Conceptual basis and problem formulation

PCDS-Net is defined around a region-sensitive view of shadow removal rather than a homogeneous correction model. In the AeroDeshadow formulation, shadows in ASI are described as having large and soft transition zones because of long-range illumination, occluder geometry, and atmospheric scattering. The stated failure modes of uniform correction under a binary mask are over-correction in deep umbra, under-correction or halos in penumbra, and color inconsistency with non-shadowed background. PCDS-Net is designed to counter these effects by recovering high-frequency textures in the umbra while ensuring smooth, physically plausible transitions in penumbra (Lu et al., 17 Apr 2026).

The input-output mapping is explicitly stated. The network receives a shadow image $I_s$ and its mask $I_m$, and produces a restored shadow-free image $I_{sr}$. Penumbra awareness is introduced by deriving two region masks from $I_m$ via morphological operations: an umbra mask $I_{um}$, defined as an eroded version of $I_m$, and a penumbra mask $I_{pm}$, defined as a dilated-minus-eroded boundary transition region. The paper therefore treats penumbra not as an incidental artifact of restoration, but as a distinct restoration regime embedded in the architecture and the loss design.

This regional decomposition places PCDS-Net in a lineage of shadow-removal methods that separate core shadow from transition effects. An earlier decomposition-based framework used SP-Net for umbra correction, M-Net for matte-based penumbra modeling, and I-Net for detail refinement, again distinguishing full shadow from smooth boundary attenuation (Le et al., 2020). PCDS-Net differs in implementing this separation through dual encoders, adaptive fusion, and cascaded decoding rather than a shadow-parameter-plus-matte decomposition.

2. Position within the AeroDeshadow framework

AeroDeshadow is organized as a two-stage pipeline. Stage 1 is PDSS-Net, the Physics-aware Degradation Shadow Synthesis Network; Stage 2 is PCDS-Net. PDSS-Net addresses the data problem by synthesizing paired ASI data with realistic umbra and penumbra, while PCDS-Net addresses the model problem by restoring shadowed inputs using a penumbra-aware architecture (Lu et al., 17 Apr 2026).

The synthetic training set for PCDS-Net is AeroDS-Syn, described as triplets $(I_{\text{free}}, I_{\text{gs}}, I_m)$, where $I_m$0 is the synthesized shadow image. The synthesis stage is physically guided. Between a shadow pixel $I_m$1 and its neighboring lit pixel $I_m$2, PDSS-Net uses

$I_m$3

with $I_m$4. The parameters are extracted from real shadowed images using core shadow and adjacent lit regions: $I_m$5 A soft pseudo mask is constructed by

$I_m$6

and the initial synthesized shadow image is

$I_m$7

These details matter because PCDS-Net does not operate in isolation. It learns from a synthetic distribution whose penumbra is explicitly modeled as soft and spatially decayed. The paper states that no explicit domain adaptation is used; generalization is attributed to physics-consistent synthetic data together with the penumbra-aware architecture and the boundary-aware physical smoothness loss. This suggests that PCDS-Net should be interpreted not only as a restoration network, but as one half of a coupled synthesis–inversion system.

3. Two-stream encoder, adaptive fusion, and cascaded decoding

The PCDS-Net architecture is a U-shaped cascaded encoder–decoder with a specialized two-stream encoder, attention-based feature fusion, and a cascaded refinement decoder (Lu et al., 17 Apr 2026).

The first stream is the Umbra Feature Encoder (UFE), which focuses on high-frequency texture inside the core shadow. At level $I_m$8, it takes the concatenation $I_m$9, and for deeper levels follows

$I_s$0

The second stream is the Penumbra Feature Encoder (PFE), which focuses on boundary context and illumination continuity. It uses dilated convolutions and takes $I_s$1 at the first level: $I_s$2 The paper notes four scales for both streams.

Fusion occurs through Attention Feature Fusion (AFF) at each scale. Given $I_s$3 and $I_s$4, the initial sum is

$I_s$5

A local branch applies a point-wise convolution-based operator $I_s$6, while a global branch applies global average pooling followed by $I_s$7. The dynamic weight is

$I_s$8

and the fused feature becomes

$I_s$9

This mechanism is described as a learned gate between umbra-centric and penumbra-centric representations.

The decoder then performs coarse-to-fine reconstruction. The deepest fused feature $I_m$0 is processed by a Semantic Aggregation module: $I_m$1 From there, a cascaded multi-scale decoder upsamples, concatenates with same-scale fused encoder features, and refines progressively until a final convolution maps the highest-resolution decoder features to RGB. The stated functional role is clear: high-level semantics are formed at coarse scales, while finer scales recover local detail and boundary transitions.

A common misconception is that penumbra-aware deshadowing must be implemented through a continuous soft-mask predictor. PCDS-Net does not do so. Its penumbra awareness is carried instead by erosion/dilation-derived regions, a dedicated penumbra encoder with dilated convolutions, adaptive fusion, and a boundary-aware physical loss. This contrasts with SoftShadow, which makes the soft mask itself the central predicted representation and jointly tunes SAM with the shadow-removal backbone (Wang et al., 2024).

4. Region-aware optimization and physical smoothness

The total objective for PCDS-Net is

$I_m$2

with $I_m$3 and $I_m$4 (Lu et al., 17 Apr 2026).

The adversarial term uses an LSGAN-style objective: $I_m$5 The reconstruction term combines pixel-wise $I_m$6 loss and perceptual loss: $I_m$7 with $I_m$8 and $I_m$9, where $I_{sr}$0 are VGG-19 feature maps.

The color consistency loss preserves channel ratios and is defined per pixel $I_{sr}$1 as

$I_{sr}$2

This term is particularly relevant to ASI because the paper frames spectral fidelity as important for downstream interpretation tasks.

The most distinctive term is the boundary-aware physical smoothness loss. First, an illumination estimate is computed in Retinex-inspired form: $I_{sr}$3 The loss is then

$I_{sr}$4

The first term enforces illumination smoothness outside penumbra; the second enforces texture and gradient consistency within penumbra. The paper explicitly ties this design to the mitigation of halos and ringing by encouraging the network to place gradient transitions in the penumbra region rather than creating step edges at the shadow boundary.

In the broader literature, penumbra modeling has also been imposed by physical or geometric regularization. SoftShadow uses a penumbra formation constraint on soft-mask gradients, while CFSR uses geometry-conditioned feature aggregation and a frequency split between high-frequency boundary recovery and low-frequency illumination restoration (Wang et al., 2024); (Wang et al., 20 Apr 2026). PCDS-Net occupies a more mask-conditioned, CNN-centric point in this design space.

5. Training protocol, ablations, and reported performance

PCDS-Net is implemented in PyTorch, trained on NVIDIA RTX 3090 Ti, optimized with Adam, and initialized with a learning rate of $I_{sr}$5 using a linear decay schedule. The batch size for PCDS-Net is 4 and the training length is 200 epochs. All training and inference inputs are resized or cropped to $I_{sr}$6. The dataset was originally at $I_{sr}$7 and was upsampled via Real-ESRGAN for better annotation and training (Lu et al., 17 Apr 2026).

The reported quantitative results position PCDS-Net as the strongest or one of the strongest methods across the synthetic and real ASI benchmarks used in AeroDeshadow.

Benchmark	Reported PCDS-Net result	Note
AeroDS-Syn Test	PSNR-S 21.91 dB, SSIM-S 0.79, RMSE-S 11.35	best
SRGTA	PSNR-S 22.37, SSIM-S 0.78, RMSE-S 9.41	PSNR-S and RMSE-S best; SSIM-S second best
AeroDS-Real	Entropy 7.40, BRISQUE 12.70	highest entropy; BRISQUE second-best
AISD Test	Entropy 7.17, BRISQUE 11.56	best

The ablation study is central to interpreting the architecture. A baseline with only UFE reports 19.69 dB PSNR and RMSE 13.84 on AeroDS-Syn, with AeroDS-Real BRISQUE 25.02. Using only PFE yields 18.41 dB PSNR and RMSE 16.18. Using UFE + PFE without AFF gives PSNR 20.82 dB, SSIM 0.78, and AeroDS-Real BRISQUE 23.98. The full PCDS-Net reports PSNR 21.91 dB, RMSE 11.35, and AeroDS-Real BRISQUE 12.70. The paper interprets these results as evidence that both umbra and penumbra streams are necessary and that adaptive fusion is crucial to avoid feature interference.

Qualitatively, the reported comparisons emphasize smooth transitions, absence of halo at boundaries, correct color and texture in shadowed structures such as roofs and roads, and continuous transitions from umbra to penumbra to lit regions. The method is also described as maintaining background color fidelity without unnatural cast in complex real scenes.

6. Research context, misconceptions, and limitations

PCDS-Net can be situated among several adjacent directions in shadow removal. Earlier physics-based decomposition methods explicitly separated umbra correction, penumbra matte modeling, and post-refinement, but did so through shadow parameters and matte layers rather than dual-stream feature encoders (Le et al., 2020). Context-transfer methods such as CANet instead relied on contextual patch matching and contextual feature transfer from non-shadow to shadow regions, with a two-stage pipeline operating in CIELab and RGB (Chen et al., 2021). SoftShadow made a different design choice by replacing binary masks with SAM-derived soft masks and a penumbra formation constraint, arguing that binary masks produce artifacts near shadow boundaries (Wang et al., 2024). CFSR, published in the same month as AeroDeshadow, moved toward a physics-constrained multi-modal formulation using depth, normals, DINO, CLIP, HVI color space, and a frequency collaborative reconstruction module (Wang et al., 20 Apr 2026).

This comparison clarifies a recurring misconception. Penumbra awareness is not synonymous with a single representational choice. In PCDS-Net, penumbra awareness is implemented through morphological region decomposition, dedicated boundary-context encoding, adaptive feature fusion, and a region-aware physical loss. In SoftShadow, by contrast, the penumbra is encoded directly as a soft mask. In CFSR, it is handled through geometry-conditioned attention and frequency-decoupled reconstruction. These are different operationalizations of the same modeling problem.

The limitations explicitly mentioned for AeroDeshadow are that the current model focuses on cast shadows on surfaces, while cloud shadows and more complex atmospheric occlusions are not yet explicitly modeled (Lu et al., 17 Apr 2026). The details also indicate a plausible dependence on a reasonably accurate mask $I_{sr}$8 and on the morphological parameters used to derive $I_{sr}$9 and $I_m$0. This suggests that PCDS-Net is best understood as a specialized ASI deshadowing network whose effectiveness depends on both the quality of synthetic penumbra supervision and the quality of the region prior supplied at inference time.