GDCUnet: Deformable U-Net for Vessel Segmentation

• GDCUnet innovatively integrates SAFDConvolution to learn globally deformable offset fields, achieving superior segmentation of intricate, self-similar retinal vasculature.
• The model blends a U-Net inspired encoder–decoder topology with global self-attention, enhancing sensitivity to thin and tortuous vessel structures.
• Empirical evaluations on the CHASEDB1 dataset demonstrate improved IoU and Dice scores, though the added global attention increases computational demands.

GDCUnet (Globally Deformable Convolution U-Net) is a deep learning model for fundus vessel segmentation that integrates a novel deformable convolutional module, SAFDConvolution. This module, based on spatial attention and feedforward networks, employs globally learned sub-pixel displacement fields to warp feature maps, enabling the network to capture long-range structural patterns and address the complexity of globally self-similar vascular features in retinal imagery. The architecture and empirical findings demonstrate that GDCUnet achieves state-of-the-art performance while maintaining flexible applicability for tasks involving self-similar and intricate geometric motifs (Zhu et al., 24 Jul 2025).

1. Architecture and Network Design

GDCUnet adopts a U-Net-inspired encoder–decoder topology, optimized for binary mask prediction in retinal vessel segmentation. The encoder successively downsamples spatial resolution, extracting hierarchical semantic features, while the decoder upsamples to reconstruct full-resolution segmentations. Crucially, GDCUnet diverges from typical U-Net by replacing parts of the standard convolutional blocks in intermediate encoder and decoder stages with SAFDConvolution blocks, which enhance sensitivity to thin, tortuous, and self-similar vessel structures. Skip connections employ tensor addition (rather than concatenation), providing a model-lightweight approach.

Structural progression:

Stage	Operation	Spatial size	Channels
Input	RGB image	$H_s \times W_s$	3
Enc-1	conv/SAFDConv block	$H_s \times W_s$	16
Pool-1	max-pool	$H_s/2 \times W_s/2$	16
Enc-2	block	$H_s/2 \times W_s/2$	32
Pool-2	max-pool	$H_s/4 \times W_s/4$	32
Enc-3	block	$H_s/4 \times W_s/4$	64
Pool-3	max-pool	$H_s/8 \times W_s/8$	64
Enc-4	block	$H_s/8 \times W_s/8$	128
Bottleneck	deeper feature proc.	$H_s/16 \times W_s/16$	256

The decoder is symmetric, with bilinear interpolation for upsampling and addition-based skip fusions.

2. SAFDConvolution: Deformable Module with Globally Learned Relative Offsets

SAFDConvolution is the core architectural innovation, distinguishing itself from conventional deformable convolutions in both offset learning and application:

• Offset Learning: Rather than predicting kernel-point-specific offsets with local convolutions, it formulates the offset field as a globally learned, continuous sub-pixel displacement field ($\Delta \mathbf{p} : \mathbb{Z}^2 \to \mathbb{R}^2$), shared across channels. This field is generated via a pipeline comprising multi-head self-attention (global context modeling) and feedforward networks applied to the entire spatial feature grid.
• Feature Map Warping: The spatial feature map is first warped according to the learned field and subsequently convolved using a fixed kernel, effectively achieving a deformation of the convolutional sampling grid through a relative displacement.
• Modularity: The offset-prediction stage is decoupled from kernel size, and the displacement field is shared across channels, leading to parameter efficiency. This facilitates plug-and-play compatibility with any conventional convolution kernel.
• Expressiveness: The approach supports globally self-similar shape modeling, vital for anatomical and structural patterns such as retinal vasculature.

3. Implementation Protocol and Hyperparameters

GDCUnet is optimized and evaluated using the CHASEDB1 fundus dataset (train-test split: 0.86 : 0.14). The model leverages Adam optimizer (β₁ = 0.0, β₂ = 0.99) with cosine annealing, batch size 4, input and output resolutions fixed at 256×256, 4000 training epochs on NVIDIA Tesla V100 GPUs. SAFDConvolution’s parameters (e.g., kernel size $H_s \times W_s$0, dilation $H_s \times W_s$1, expansion $H_s \times W_s$2, attention heads $H_s \times W_s$3, and hidden dimension) are tuned via ablations, with Setting 5 ($H_s \times W_s$4, $H_s \times W_s$5, $H_s \times W_s$6, $H_s \times W_s$7, hidden 64) yielding the best empirical performance. The loss combines binary cross-entropy and Dice loss equally.

SAFDConvolution typical settings:

Setting	$H_s \times W_s$8	$H_s \times W_s$9	$H_s/2 \times W_s/2$0	$H_s/2 \times W_s/2$1	Hidden dim
5	5	1	2	4	64

4. Empirical Performance and Ablation Findings

Comprehensive benchmarking against mainstream baselines (U-Net, UNet++, Attention U-Net, UCTransNet, DConnNet, etc.) demonstrates that GDCUnet (Setting 5) achieves peak performance: IoU 0.6304, Dice 0.7733, HD 15.36, Recall 0.7596, Specificity 0.9853, Precision 0.7875, with 1.40M parameters. It shows marked improvements in segmenting thin and low-contrast vessel branches and exhibits superior edge delineation.

Ablation results confirm the superiority of SAFDConvolution:

Conv Variant	IoU	Dice
Conventional	0.5833	0.7368
Deformable V3	0.6130	0.7601
SAFDConvolution	0.6304	0.7733

SAFDConvolution offers up to 0.0471 IoU and 0.0365 Dice gain over standard convolution and 0.0174/0.0132 gain over the best deformable baseline.

Feature map visualizations and t-SNE analyses further reveal that SAFDConvolution induces higher domain invariance, tighter clustering, and less domain shift, signifying stronger generalization.

5. Operational Considerations and Limitations

The inclusion of multi-head self-attention leads to increased computational overhead due to global matrix multiplications, characteristic of Transformer-like components. This may present limitations in deployment on resource-constrained hardware, prompting the need for future research into sparse attention mechanisms and efficiency optimizations.

6. Broader Applicability and Prospects

The SAFDConvolution module’s flexibility, context-awareness, and local adaptability render it applicable to a broad class of machine vision problems characterized by globally self-similar or tubular structures. Suggested application domains include network or road extraction, leaf venation analysis, crack detection, and anatomical segmentation involving repeated geometric motifs. Prospective research directions include optimizing for hardware efficiency, extending self-similar deformation modeling to further tasks, and quantifying the tradeoff between expressiveness and complexity.

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GDCUnet exemplifies a principled integration of global context-aware deformation within the U-Net paradigm, delivering leading segmentation performance on challenging retinal vessel datasets and providing a reconfigurable foundation for broader deployment in structured vision tasks where self-similar spatial features predominate (Zhu et al., 24 Jul 2025).