PDSA-DBUNet: dual-branch U-Net for abdominal medical image segmentation driven by polynomial dynamic sparse attention

1 Introduction

Medical image segmentation is a fundamental task in computer-aided diagnosis and treatment planning (Azad et al., 2024). It aims to delineate anatomical structures or lesions from medical images and provides essential support for lesion localization, quantitative organ analysis, image-guided surgery, radiotherapy, and clinical decision-making. Among various segmentation scenarios, abdominal computed tomography (CT) image segmentation is particularly important because it involves multiple organs and lesions with diverse anatomical characteristics (Blankemeier et al., 2026). Accurate segmentation of abdominal organs and tumors can assist clinicians in evaluating organ morphology, identifying abnormal regions, and formulating reliable treatment strategies (Gan et al., 2026).

Despite its clinical importance, abdominal CT segmentation remains challenging. Abdominal organs and tumors often show large variations in shape, size, appearance, and spatial location across patients and slices. Low gray-level contrast makes anatomical boundaries difficult to distinguish, while small tumor regions are easily affected by complex background tissues, leading to false positives or missed segmentation. In addition, downsampling operations in deep networks may weaken fine-grained boundary details. Therefore, an effective abdominal segmentation model should capture both local boundary information and global anatomical context while maintaining computational efficiency.

Convolutional neural networks (CNNs) have achieved remarkable progress in medical image segmentation (Purwono et al., 2022). U-Net and its variants are widely adopted because their encoder–decoder structure and skip connections can preserve spatial details and recover high-resolution segmentation maps (Ronneberger et al., 2015). However, convolution operations are inherently local and have limited ability to model long-range dependencies. Transformer-based architectures can capture global interactions through self-attention, but dense token modeling introduces high computational cost and may insufficiently preserve fine boundary and texture information. Recent CNN–Transformer hybrid methods improve local–global representation learning, but still face challenges in redundant token computation, boundary preservation, and adaptive feature fusion.

To address these issues, this paper proposes a Polynomial Dynamic Sparse Attention-driven Dual-Branch U-Net, termed PDSA-DBUNet, for abdominal medical image segmentation. The proposed network adopts a parallel CNN–Transformer architecture to jointly preserve local spatial details and model global contextual dependencies. In the Transformer branch, a dynamic sparse visual token generation module adaptively aggregates dense image tokens into a compact set of discriminative sparse tokens, thereby suppressing redundant background responses and emphasizing organ regions and blurred boundaries. The Polynomial Mixer is incorporated into the dynamic sparse token modeling process. It performs efficient global contextual interaction over the compact sparse token set without constructing a dense pairwise attention matrix. In addition, a dual-scale parallel attention fusion module enhances the interaction between CNN-derived local details and Transformer-derived global semantics. The main contributions of this paper are summarized as follows:

• We propose PDSA-DBUNet, a dual-branch U-Net architecture for abdominal medical image segmentation. It integrates CNN-based local detail extraction and Transformer-based global context modeling in a parallel framework.
• We design a Polynomial Dynamic Sparse Attention (PDSA) module that combines input-adaptive sparse token aggregation with a Polynomial Mixer. The former aggregates informative anatomical features into a compact sparse-token set and suppresses redundant background responses, while the latter enables efficient global feature interaction without dense pairwise self-attention.
• We construct a Dual-Scale Parallel Attention Fusion (DSPAF) module to strengthen the interaction between local CNN features and global Transformer features, enabling more effective integration of boundary details and contextual semantics.
• Extensive experiments on the LiTS and KiTS19 datasets demonstrate that PDSA-DBUNet achieves superior segmentation performance and a favorable accuracy–efficiency balance compared with representative CNN-based, Transformer-based, and hybrid segmentation methods.

2 Related work

2.1 CNN-based medical image segmentation methods

With the development of deep learning, CNN-based methods have become dominant in medical image segmentation. Before the widespread adoption of deep learning (Lei et al., 2023a), medical and biological images were commonly analyzed using mathematically grounded approaches, including threshold-based segmentation, histogram- and RGB-based filtering, and structural similarity assessment (Ždímalová et al., 2022). Compared with these traditional methods, CNNs can automatically learn hierarchical representations for dense prediction. Long et al. (2015) proposed the fully convolutional network (FCN), which extended classification networks to pixel-wise segmentation through convolutional encoding, deconvolutional upsampling, and skip connections. However, FCN has limited ability to recover fine boundaries. Ronneberger et al. (2015) proposed U-Net, which adopts a symmetric encoder-decoder structure and skip connections to preserve spatial details. Although U-Net has become a representative baseline in biomedical image segmentation, its standard convolution operations still restrict long-range dependency modeling.

To improve feature extraction and fusion, many U-Net variants have been proposed. ResUNet (He et al., 2016) introduces residual connections to alleviate gradient degradation, while DenseUNet (Cai et al., 2020) uses dense connections to enhance feature reuse. UAMSNet (Ju et al., 2025) introduces hybrid receptive field extraction and multi-organ boundary-enhanced attention to address blurred boundaries and shape variations in abdominal CT images. Multi-scale convolution, dilated convolution, dynamic convolution, and deformable convolution further enlarge receptive fields and improve adaptability to irregular organs and lesions. For feature fusion, U-Net++ (Zhou et al., 2019) redesigns skip pathways through nested dense connections, and U-Net3+ (Huang et al., 2020) aggregates multi-level features through full-scale skip connections. Attention-based variants, such as SA U-Net (Guo et al., 2021), further enhance target localization and long-range feature interaction.

Overall, CNN-based methods are effective in extracting local textures, edges, and spatial details, but their local receptive fields limit global anatomical modeling. This limitation may lead to inaccurate segmentation when abdominal organs and tumors show large shape variations, blurred boundaries, and complex backgrounds.

2.2 Transformer-based medical image segmentation methods

To overcome the limited global modeling ability of CNNs, Transformer-based architectures have been introduced into medical image segmentation. By computing correlations among image tokens, self-attention can capture long-range dependencies and model global semantic relationships beyond local convolution. Existing Transformer-based segmentation methods mainly improve medical image segmentation from two aspects: hierarchical attention modeling and efficient multi-scale contextual representation.

One line of research focuses on hierarchical or directional attention mechanisms to enhance global context modeling. Swin-Unet (Cao et al., 2022) adopts a pure Transformer-based U-shaped architecture and uses window attention with shifted-window attention to construct hierarchical representations. This design reduces the computational cost of standard self-attention and improves global context modeling. MedT (Valanarasu et al., 2021) introduces gated axial attention to capture long-range dependencies along different spatial axes with lower attention complexity. MissFormer (Huang et al., 2022) further improves Transformer-based medical image segmentation by enhancing hierarchical representation learning and long-range contextual interaction. These methods show that Transformers can improve semantic modeling for medical images. However, their performance still depends heavily on token interactions and stacked attention layers, and the lack of CNN-based local inductive bias may weaken fine boundary, texture, and small-lesion representation.

Another line of research improves Transformer segmentation through multi-scale representation, volumetric context modeling, efficient token interaction, or frequency-domain enhancement. Swin UNETR (Hatamizadeh et al., 2022) introduces Swin Transformer blocks into a U-shaped encoder–decoder framework to capture contextual dependencies in medical images. nnFormer (Zhou et al., 2023) strengthens volumetric medical image segmentation through Transformer-based inter-slice semantic modeling. SegFormer3D (Perera et al., 2024) explores an efficient Transformer design to reduce the computational burden of dense token modeling. A multi-scale convolutional attention frequency-enhanced Transformer network was further proposed to strengthen feature representation from both spatial and frequency perspectives (Yan et al., 2025). These methods improve the ability of Transformers to describe complex anatomical structures and multi-scale variations. Nevertheless, dense token modeling still introduces high memory and computational costs, especially for high-resolution CT images. Additional attention branches or enhancement modules may also increase structural complexity.

Several efficient Transformer architectures have been proposed to reduce the computational cost associated with dense token interactions. Perceiver (Jaegle et al., 2021) employs asymmetric cross-attention to map high-dimensional inputs into a fixed-size latent bottleneck, thereby reducing the dependence of computational cost on the original input size. Lite Transformer (Wu et al., 2020) introduces Long-Short Range Attention, combining convolution-based local modeling with self-attention-based long-range dependency learning to improve computational efficiency. DynamicViT (Rao et al., 2021) further reduces computation by progressively pruning less informative visual tokens according to input-dependent importance scores. These methods improve efficiency through latent-space compression, hybrid local–global modeling, or dynamic token pruning. However, they were mainly designed for general-purpose perception, sequence modeling, or image classification rather than dense prediction in medical image segmentation. In particular, they do not provide a unified mechanism that both preserves the spatial correspondence between compact token representations and the original dense feature map and restores these representations to the dense spatial domain for subsequent pixel-level prediction.

Overall, Transformer-based methods have shown strong potential in global semantic modeling for medical image segmentation. However, dense token interactions still introduce redundant background information and high computational cost, while pure or mainly Transformer-based structures may insufficiently preserve fine-grained boundary details. These limitations motivate the design of an efficient Transformer branch with dynamic sparse visual token generation and a Polynomial Mixer to reduce token redundancy while preserving global contextual modeling.

2.3 CNN–transformer hybrid medical image segmentation methods

CNNs and Transformers provide complementary feature representations for medical image segmentation (Lei et al., 2023b). CNNs are effective in extracting local textures, edges, and spatial details because of their local inductive bias, whereas Transformers are more suitable for modeling global context and long-range dependencies through token interactions. Therefore, CNN–Transformer hybrid architectures have become an important research direction in medical image segmentation. According to the way CNNs and Transformers are combined, existing methods can be broadly divided into two categories: serial or stacked CNN–Transformer structures and parallel CNN–Transformer structures (Sun, 2025).

In serial or stacked CNN–Transformer structures, convolutional features are usually extracted first and then fed into Transformer blocks for global context modeling. TransUNet (Chen et al., 2021) is a representative method of this category. It uses CNNs to extract local image features and introduces a Transformer encoder to model long-range semantic dependencies. BoTNet (Srinivas et al., 2021) embeds self-attention into convolutional bottleneck blocks, enhancing global representation while retaining a CNN backbone. Recent hybrid methods, such as HTC-Net (Tang et al., 2024), further combine convolutional representation learning with Transformer-based global modeling to improve segmentation performance. These methods improve the global modeling ability of conventional CNNs. However, serial or stacked designs usually rely on dense token modeling after convolutional feature extraction. During this process, shallow boundary and texture information may be weakened, while the Transformer branch still introduces considerable computational cost.

Parallel CNN–Transformer structures aim to learn local and global representations simultaneously. TEC-Net (Sun et al., 2023) adopts parallel CNN and Transformer branches to enhance the interaction between local detail extraction and global context modeling. CTCSANet (Ding et al., 2026) improves hybrid feature fusion through cross-stage feature integration and adaptive channel-spatial attention. BRAU-Net++ (Lan et al., 2026) and TransUMobileNet (Cai et al., 2025) further explore U-shaped hybrid architectures and attention-based feature fusion for medical image segmentation. Compared with serial structures, parallel designs can better preserve local details while modeling global dependencies. However, most existing parallel methods still process dense Transformer tokens or rely on complex attention modules. In addition, simple fusion strategies, such as addition, concatenation, or single-scale attention, may be insufficient to adaptively integrate CNN-derived boundary details and Transformer-derived semantic context.

Overall, existing CNN–Transformer hybrid methods have achieved promising results, but three limitations remain for abdominal organ and tumor segmentation. First, serial or stacked structures may weaken shallow boundary information during tokenization or deep feature transformation. Second, dense token modeling in Transformer branches introduces redundant background information and increases computational cost. Third, existing fusion strategies may not fully exploit the complementarity between local details and global semantics, especially for blurred boundaries and small tumor regions. To address these limitations, this study proposes PDSA-DBUNet. The proposed network adopts a parallel CNN–Transformer architecture to preserve local detail extraction and global context modeling simultaneously. A dynamic sparse visual token generation mechanism and a Polynomial Mixer are introduced to reduce redundant token computation and improve efficient global interaction. In addition, a dual-scale parallel attention fusion module is constructed to strengthen adaptive interaction between CNN-derived local features and Transformer-derived global semantic features.

3 Network architecture of PDSA-DBUNet

This paper proposes a dual-branch network, named PDSA-DBUNet, for abdominal medical image segmentation. The overall architecture is shown in Figure 1. Unlike conventional methods that rely only on CNNs or Transformers for feature extraction, PDSA-DBUNet adopts a parallel CNN–Transformer encoder. This design enables the network to model local spatial details and global contextual information at the same time.

The proposed network consists of three main components: a dual-branch encoder, two core feature interaction modules, and a decoder. The dual-branch encoder includes a CNN branch and a PDSA Transformer branch, which are responsible for local detail extraction and global context modeling, respectively. The CNN branch extracts multi-scale convolutional features to preserve textures, edges, and boundary structures, whereas the PDSA Transformer branch generates sparse global representations to capture long-range anatomical dependencies with reduced token redundancy. The two branches are connected through the DSPAF module, which adaptively integrates CNN-derived local details and PDSA-derived global semantics. Finally, the decoder progressively restores the spatial resolution and produces the pixel-wise segmentation map.

Abdominal organ and tumor segmentation is challenging because anatomical structures often exhibit large variations in shape, size, and location, while low tissue contrast and complex backgrounds make small lesions difficult to distinguish. CNNs are effective for boundary localization but are limited in modeling long-range dependencies. In contrast, Transformers provide global semantic modeling but may introduce redundant background tokens and high computational costs when applied to high-resolution CT images. To address these limitations, PDSA-DBUNet preserves local detail representation through the CNN branch and introduces Polynomial Dynamic Sparse Attention into the Transformer branch. This design reduces redundant token computation, improves global feature interaction through polynomial mixing, and enhances the representation of organ boundaries, small tumor regions, and complex anatomical structures.

Let the input medical image be denoted as I ∈ R C × H × W, where C is the number of input channels, and H and W denote the height and width, respectively. The input image is first fed into the CNN encoder branch to extract multi-scale local features. Let F 0 = I, and the encoding process can be written as F i = E i ( F i − 1 ), where E i ( ⋅ ) denotes the i-th CNN encoding stage. F i denotes the convolutional feature map at the corresponding scale. Shallow features contain rich edge, texture, and local structural information, while deep features contain stronger semantic information. To enable global context modeling, the encoder feature F i is also used as the input to the PDSA Transformer branch. Given the feature map F i ∈ R C i × H i × W i, where C i, H i, and W i denote the channel number, height, and width at the i-th scale, respectively, it is flattened into a two-dimensional token sequence in Equation 1:

X i ∈ R N i × C i , N i = H i W i . (1)

Then, a Linear projection maps the tokens into the Transformer embedding space in Equation 2:where W e ∈ R C i × D and b e ∈ R D are learnable parameters. Z i ∈ R N i × D denotes the initial token embedding, and D is the embedding dimension. During encoding, the CNN branch and the PDSA Transformer branch work in parallel. The CNN branch extracts multi-scale local features to preserve spatial details and support boundary recovery, whereas the PDSA Transformer branch generates sparse global features to capture long-range contextual information. At each selected scale, the sparse Transformer features are restored to the corresponding spatial positions. They are then fused with CNN features through the DSPAF module. The fused features are sent to the decoder. The decoder progressively upsamples the features to the input resolution. Finally, the segmentation map is generated by a linear projection layer in Equation 3:where F d denotes the final decoded feature, and Y denotes the pixel-wise segmentation result.

Z i = X i W e + b e . (2)

Y = Conv 1 × 1 F d . (3)

The CNN branch consists of five hierarchical residual encoding stages with output channel dimensions of 64, 128, 256, 512, and 1024. Given an input image I ∈ R C × H × W, Stage 1 operates at the original spatial resolution, while MaxPool2d with a 2 × 2 kernel and a stride of 2 is applied before Stages 2–5, producing feature resolutions of H × W, H / 2 × W / 2, H / 4 × W / 4, H / 8 × W / 8, and H / 16 × W / 16, respectively. Each stage contains a residual block composed of two convolutional layers, each followed by BatchNorm2d and ReLU, together with a 1 × 1 convolutional shortcut for channel projection. The shallow stages mainly capture textures, edges, and fine anatomical boundaries, whereas the deeper stages extract higher-level semantic features. The outputs of all five stages are aligned with the corresponding PDSA Transformer features and fused through DSPAF modules to integrate local structural details with global contextual information.

3.1 Polynomial dynamic sparse attention module

In standard Transformers, self-attention is usually computed over all image tokens. However, abdominal CT images contain large background regions. Organ boundaries, tumor regions, and small targets occupy only limited areas. Directly computing pairwise relationships among all dense tokens causes high computational and memory costs. It also introduces irrelevant background tokens into global modeling. This may weaken the attention to key anatomical regions.

To address this issue, we design a Polynomial Dynamic Sparse Attention module, termed PDSA. As shown in Figure 2, PDSA first generates a compact sparse-token set from dense image features through input-adaptive weighted aggregation. The generated sparse tokens are subsequently processed by the Polynomial Mixer for efficient global contextual interaction. By combining sparse-token aggregation with polynomial feature mixing, PDSA reduces redundant computation and enhances the discriminative representation of organs and lesions.

3.1.1 Dynamic sparse visual token generation

Given the input token embedding Z i ∈ R N i × D, where N i denotes the number of original dense tokens and D denotes the embedding dimension, a learnable projection is first used to generate the spatial importance weights in Equation 4:where W a ∈ R S × D, Z i T ∈ R D × N i, and A i ∈ R S × N i. The Softmax operation is applied along the dense-token dimension. The proposed formulation performs global learnable projection over the dense token sequence and does not involve a neighborhood-radius parameter.

A i = Softmax W a Z i T , (4)

The spatial importance weights are first used to generate a preliminary sparse representation. For the s-th sparse token, the weighted aggregation is defined as in Equation 5:where t ̄ s ∈ R D denotes the preliminary sparse token obtained from the dense token sequence. Each sparse token is obtained by weighted aggregation of key regions from the original image tokens. Therefore, it preserves discriminative information related to organ regions, tumor regions, and blurred boundaries. Compared with dense token processing, this operation significantly reduces the number of tokens for subsequent global modeling.

t ̄ s = ∑ n = 1 N i A s , n Z i , n , (5)

To improve the adaptability of sparse tokens to different image regions, element-wise feature modulation is further introduced. Let q s ( Z i ) denote the spatial response map generated from the input features for the s-th sparse token. Let γ ( ⋅ ) denote a normalization function that constrains the weights to [0, 1]. Let ρ ( ⋅ ) denote the GELU activation function. For the s-th sparse token, a learnable linear mapping is applied to the n-th dense token in Equations 6, 7:

q s Z i , n = w s q T Z i , n + b s q . (6)

The response is normalized using the Sigmoid function:

m s , n = Sigmoid q s Z i , n . (7)

The normalized scalar response is broadcast along the feature dimension, and the s-th sparse token is obtained as (see Equation 8):

t s = GELU ∑ n = 1 N i A s , n m s , n Z i , n . (8)

Here, w s q ∈ R D, b s q ∈ R, A s , n ∈ R, and t s ∈ R D. Through the dynamic sparse token generation process, the PDSA module adaptively selects key visual regions according to the input image content. It reduces redundant background tokens and enhances the attention to abdominal organ boundaries and small tumor regions.

After sparse token generation, the spatial relationship between sparse tokens and dense image positions is retained by A i. This relationship is used to project the sparse Transformer features back to the original dense spatial positions. Given the output sparse tokens T i L ∈ R S × D after L PDSA blocks, the dense token sequence is restored as in Equation 9:where A i T ∈ R N i × S, T i L ∈ R S × D, and Z ̃ i ∈ R N i × D. The restored token sequence is then reshaped into a spatial feature map in Equation 10:

Z ̃ i = A i T T i L , (9)

F i t = Reshape Z ̃ i ∈ R D × H i × W i . (10)

This restoration step allows the sparse global features generated by the PDSA Transformer branch to be fused with CNN features at the same spatial resolution.

3.1.2 Polynomial global feature mixing

After obtaining the sparse token set T i, the PDSA module uses a Polynomial Mixer for global contextual modeling. Conventional multi-head self-attention explicitly computes pairwise interactions among all tokens. Its computational complexity grows quadratically with the number of tokens. In contrast, the Polynomial Mixer aggregates token information into a shared global state. It then uses a gating mechanism to select relevant context for each token. This avoids explicit construction of the attention matrix.

Given the sparse token sequence T i ∈ R S × D, it is first mapped into an internal feature space in Equation 11:where W p ∈ R D × D p is a learnable projection matrix. D p denotes the internal dimension of the Polynomial Mixer, and ϕ ( ⋅ ) denotes the GELU activation function. Therefore, U i ∈ R S × D p. Then, a polynomial mapping is used to aggregate all sparse tokens into a shared global state (see Equations 12, 13): where α p ∈ R 1 × D pis a learnable polynomial coefficient, and 1 S ∈ R S × 1is an all-ones vector. The matrix α ̃ p denotes the coefficientα pbroadcast along the sparse-token dimension. Moreover,U i ⊙ p ∈ R S × D p denotes the element-wise p-th power of U i. Therefore, the Hadamard product is dimensionally well defined, and h i represents the global state shared by all sparse tokens. To allow each token to adaptively retrieve relevant information from the shared global state, a gating weight is computed as in Equation 14:where W g ∈ R D p × D p is a learnable projection matrix, and σ ( ⋅ ) denotes the Sigmoid function. Therefore, G i ∈ R S × D p. The output of the Polynomial Mixer is formulated as in Equation 15:where W o ∈ R D p × D is the output projection matrix. Here, h i is broadcasted along the token dimension and interacts with the gating weight G i through element-wise multiplication. In this way, each sparse token can adaptively select relevant global contextual information from the shared state. To improve training stability and nonlinear representation, residual connections and a feed-forward network are used in the PDSA block. The l-th PDSA block is formulated as in Equations 16, 17: where FFN ( ⋅ ) denotes the feed-forward network. Through this design, the PDSA module integrates dynamic sparse token generation and polynomial global mixing. It reduces redundant computation caused by dense background tokens and achieves efficient global contextual interaction. Therefore, this module enhances the representation of organ regions, tumor regions, and blurred boundaries with lower computational cost.

U i = ϕ T i W p , (11)

α ̃ p = 1 S α p ∈ R S × D p , (12)

h i = 1 S T ∑ p = 1 K α ̃ p ⊙ U i ⊙ p ∈ R 1 × D p , (13)

G i = σ U i W g , (14)

PoM T i = G i ⊙ Broadcast h i W o , (15)

T ̂ i l = T i l − 1 + PoM T i l − 1 , (16)

T i l = T ̂ i l + FFN T ̂ i l , (17)

3.1.3 Complexity analysis

The efficiency of the PDSA module comes from two aspects. First, dynamic sparse token generation reduces the number of tokens from N i to S, where S ≪ N i. Second, polynomial global feature mixing avoids explicit pairwise token interactions.

For standard multi-head self-attention on dense tokens, the computational complexity is approximately O ( N i 2 D ), and the memory cost of the attention matrix is O ( N i 2 ). These costs increase rapidly as N i increases, which is common in high-resolution medical images.

In the proposed PDSA module, sparse token generation requires a linear projection and weighted aggregation. Its computational cost is approximately O ( S N i D ). After sparse token generation, the Polynomial Mixer operates on only S sparse tokens. Let D p denote the internal dimension of the Polynomial Mixer, and let K denote the polynomial degree. The main cost of polynomial feature mixing is O ( S D D p + K S D p ). Thus, the overall complexity of the PDSA module can be written as O ( S N i D + S D D p + K S D p ). Since S is much smaller than N i, the proposed module avoids the quadratic computational cost of dense self-attention. It also avoids storing a dense N i × N i attention matrix. Therefore, the Transformer branch becomes more efficient while retaining global contextual modeling ability.

3.2 Dual-scale parallel attention fusion module

The CNN branch and the PDSA Transformer branch provide complementary feature representations. The CNN branch preserves local textures, edges, and spatial details, which are essential for boundary recovery. In contrast, the PDSA Transformer branch captures long-range dependencies and global semantic information, which helps model anatomical relationships among organs and lesions.

As shown in Figure 3, existing network combination strategies usually enhance feature representation by increasing convolutional depth (Isensee et al., 2021), inserting self-attention blocks (Sinha and Dolz, 2021; Picard et al., 2026), or stacking Transformer modules within CNN frameworks (Zhu et al., 2018). Although these designs improve local or global modeling to some extent, they still have limitations. Convolution-dominated structures mainly emphasize local details and may lack sufficient global guidance. Attention-enhanced or stacked Transformer structures can introduce global context, but they may increase computational redundancy and provide limited interaction between shallow boundary details and high-level semantics.

Therefore, directly combining CNN and Transformer features by addition or concatenation is insufficient for abdominal medical image segmentation. Local boundary cues and global anatomical semantics are generated from different feature spaces and may contain inconsistent responses. To address this problem, this paper proposes a Dual-Scale Parallel Attention Fusion module. Instead of using simple feature aggregation, DSPAF performs adaptive feature interaction from both global channel and local spatial scales, enabling more effective fusion between CNN-derived local details and PDSA Transformer-derived global semantics.

The detailed structure of the DSPAF module is shown in Figure 4. The term dual-scale refers to two complementary feature interaction scales. The first is the global channel scale, which uses global average pooling to obtain channel-level semantic responses from the CNN and PDSA Transformer branches. This path is used to model global structure and semantic dependency. The second is the local spatial scale, which uses convolutional interaction to enhance local boundaries, textures, and small target regions. These two paths work in parallel, enabling the network to jointly strengthen global semantic selection and local detail recovery. As a result, the proposed fusion module improves pixel-level feature correlation in abdominal medical images and contributes to more accurate segmentation results. Let the CNN feature at the i-th encoding stage be F i c ∈ R C i × H i × W i, and let the spatially restored feature from the PDSA Transformer branch be F i t ∈ R C i × H i × W i. First, channel and spatial alignment are applied to the two branch features in Equation 18:where ϕ c ( ⋅ ) and ϕ t ( ⋅ ) denote feature alignment operations composed of 1 × 1 convolution, normalization, and activation. The aligned features are then fed into two parallel paths.

F ̂ i c = ϕ c F i c , F ̂ i t = ϕ t F i t , (18)

3.2.1 Global channel attention path

The global path first generates channel descriptors for the two branches through global average pooling in Equations 19, 20:

c i = 1 H i W i ∑ h = 1 H i ∑ w = 1 W i F ̂ i , : , h , w c , (19)

t i = 1 H i W i ∑ h = 1 H i ∑ w = 1 W i F ̂ i , : , h , w t . (20)

Here, c i and t i denote the global channel responses of the CNN branch and the Transformer branch, respectively. They are then fed into fully connected layers followed by Sigmoid functions to generate channel attention weights in Equation 21:where W c , W t ∈ R C i × C i and Q i c , Q i t ∈ R C i. They are reshaped to C i × 1 × 1 and broadcast across the spatial dimensions before feature modulation in Equation 22:where ⊙ denotes element-wise multiplication. This process strengthens cross-branch semantic interaction by providing global contextual guidance for the CNN branch and local structural constraints for the Transformer branch.

Q i c = Sigmoid W c c i , Q i t = Sigmoid W t t i , (21)

F i c , g = F ̂ i c ⊙ Broadcast Q i t , F i t , g = F ̂ i t ⊙ Broadcast Q i c . (22)

3.2.2 Local spatial interaction path

The local path is designed to model fine-grained spatial details. It focuses on local boundaries, textures, and small tumor regions. The aligned features from the two branches are concatenated and processed by a 3 × 3 convolution in Equation 23:

F i l = Conv 3 × 3 F ̂ i c ⊙ F ̂ i t , (23)

Element-wise interaction highlights spatial locations jointly activated by the CNN and Transformer branches. The subsequent 3 × 3 convolution captures local neighborhood relationships and refines boundaries, textures, and small anatomical structures. This operation learns local interactions between CNN and Transformer features while recovering spatial details lost during downsampling.

Finally, the global modulation features, local interaction feature, and correlation feature are fused to obtain the output feature at the current scale in Equation 24:

F i f = Conv 3 × 3 Concat F i c , g , F i l , F i t , g + F ̂ i c , (24)

Here, F i f denotes the fused feature generated by the Dual-Scale Parallel Attention Fusion module. The residual term F ̂ i c preserves the original local details and improves training stability.

Through this design, the fusion module performs feature interaction at two levels. The global channel attention path models semantic relationships between the two branches. It guides the network to focus on global organ structures and long-range contextual dependencies. The local spatial interaction path enhances fine-grained representations of boundaries, textures, and small target regions. The fused feature therefore contains both local details from the CNN branch and global semantics from the PDSA Transformer branch. This improves the segmentation of blurred boundaries, small tumor regions, and complex abdominal structures.

3.3 Feature decoder

The decoder takes the fused multi-scale features as input in Equation 25:

F 1 f , F 2 f , F 3 f , F 4 f . (25)

These features are progressively upsampled to recover spatial resolution. At each decoding stage, the upsampled feature is connected with the corresponding encoder feature. This operation compensates for the spatial details lost during downsampling and improves boundary localization.

Let D i ( ⋅ ) denote the i-th decoding stage. The decoding process can be written as in Equation 26:where Up ( ⋅ ) denotes an upsampling operation. The final decoded feature is mapped to the segmentation space by a Linear projection layer in Equation 27:

F d i = D i Concat Up F d i + 1 , F i f , (26)

Y = Conv 1 × 1 F d . (27)

The output Y is the predicted pixel-wise segmentation map. Through the dual-branch structure and the two core modules, PDSA-DBUNet maintains both local detail representation and global contextual modeling. By reducing redundant token computation, the proposed network achieves accurate and efficient abdominal organ and tumor segmentation.

4 Experimental results and analysis

4.1 Datasets and preprocessing

The proposed PDSA-DBUNet was evaluated on the LiTS and KiTS19 datasets. These two datasets were used to assess the segmentation performance on abdominal organs and tumors.

For the LiTS dataset, 131 contrast-enhanced abdominal CT cases were used. Following the predefined experimental protocol, 100 cases were used for training, and the remaining 31 cases were used for testing. The training set contained 44,719^−ΔΔCT slices, and the testing set contained 15,429^−ΔΔCT slices. The segmentation targets included the liver and liver tumors. During preprocessing, the CT intensity values were clipped to the Hounsfield unit range of [ − 200,250 ] and then normalized to [0, 1]. All 2D slices were resized to 512 × 512 before being fed into the network. During training, random horizontal flipping, random vertical flipping, and Gaussian noise perturbation were adopted for data augmentation.

The KiTS19 dataset was used to evaluate kidney and kidney tumor segmentation. It contains 210 abdominal CT volumes with corresponding manual annotations. Each case includes the original CT scan and the ground-truth mask in NIFTI format. In this study, the dataset was split at the case level into 168 training cases, 21 validation cases, and 21 testing cases. The segmentation targets included the kidney and kidney tumor. The same preprocessing strategy was applied to the KiTS19 dataset. The CT intensity values were clipped to [ − 200,250 ], normalized to [0, 1], and resized to 512 × 512. The same data augmentation operations were used during training.

4.2 Experimental setup

All experiments were implemented using PyTorch 1.7.0. The training and testing procedures were conducted on two NVIDIA GeForce RTX 3090 Ti GPUs with 24 GB memory. The CPU was an Intel Core i9-9900X processor with 10 cores and a base frequency of 3.5 GHz.

The Adam optimizer was used to optimize the network parameters. The initial learning rate was set to 1 × 1 0 − 4. The batch size was set to 8, and the model was trained for 100 epochs. Cross-entropy loss was adopted as the training objective.

For comparative experiments, PDSA-DBUNet was compared with several representative segmentation methods, including U-Net (Ronneberger et al., 2015), UAMSNet (Ju et al., 2025), BoTNet (Srinivas et al., 2021), TransUNet (Chen et al., 2021), CTCSANet (Ding et al., 2026), Swin-Unet (Cao et al., 2022), nnU-Net (Isensee et al., 2021), and Swin UNETR (Hatamizadeh et al., 2022). These methods cover CNN-based, Transformer-based, and CNN–Transformer hybrid segmentation architectures. To ensure a fair comparison, all methods were trained and evaluated under the same experimental settings.

4.3 Evaluation metrics

Five evaluation metrics were used for quantitative comparison, including Dice (Dice, 1945), VOE (Heimann et al., 2009), RVD (Heimann et al., 2009), ASSD (Taha and Hanbury, 2015), and MSSD (Taha and Hanbury, 2015). Dice was used to measure the overlap between the predicted segmentation and the ground-truth mask. VOE and RVD were used to evaluate volumetric segmentation errors. ASSD and MSSD were used to measure boundary deviations between the predicted mask and the ground-truth mask. Lower values of VOE, RVD, ASSD, and MSSD indicate better segmentation performance.

The Dice coefficient is defined as in Equation 28:where P denotes the predicted segmentation result, and G denotes the ground-truth mask. VOE is defined as in Equation 29:

D i c e P , G = 2 | P ∩ G | | P | + | G | , (28)

V O E P , G = 1 − | P ∩ G | | P ∪ G | . (29)

RVD is defined as in Equation 30:

R V D P , G = | P | − | G | | G | . (30)

ASSD measures the average symmetric surface distance between the predicted boundary and the ground-truth boundary. MSSD measures the maximum symmetric surface distance between the two boundaries.

4.4 Comparative results on the LiTS dataset

Tables 1 and 2 report the quantitative results on the LiTS test set for liver and liver tumor segmentation, respectively. Liver segmentation evaluates the ability of each method to delineate a large abdominal organ with complex anatomical boundaries, whereas liver tumor segmentation further assesses model robustness in detecting small, irregular, and low-contrast lesions. As shown in Table 1, PDSA-DBUNet achieves the highest Dice score of 96.79% for liver segmentation. Compared with Swin UNETR and nnU-Net, which obtain Dice scores of 95.13% and 94.02%, respectively, the proposed method improves the Dice score by 1.66 and 2.77 percentage points. Compared with the conventional U-Net baseline, the improvement reaches 2.80 percentage points. These results demonstrate the stronger region-overlap performance of the proposed dual-branch architecture.

TABLE 1. Quantitative comparison of liver segmentation on the LiTS test set.

TABLE 2. Quantitative comparison of liver tumor segmentation on the LiTS test set.

For volumetric consistency, PDSA-DBUNet achieves the lowest RVD of 1.06%, slightly outperforming nnU-Net, which obtains the second-best RVD of 1.08%. This result indicates that the predicted liver volume is highly consistent with the ground-truth annotation. For the remaining metrics, TransUNet achieves the lowest VOE of 4.03%, BoTNet obtains the lowest ASSD of 1.23 mm, and UAMSNet achieves the lowest MSSD of 30.20 mm. PDSA-DBUNet obtains a VOE of 4.28%, an ASSD of 1.48 mm, and an MSSD of 30.60 mm, remaining competitive in both regional and boundary-related evaluation. Overall, the proposed method achieves a favorable balance among region overlap, volumetric consistency, and boundary accuracy.

These metrics reflect different aspects of segmentation performance. Dice and RVD mainly evaluate region overlap and volumetric consistency, whereas ASSD and MSSD focus on boundary errors, with MSSD being more sensitive to extreme local deviations. PDSA-DBUNet achieves the highest Dice score and the lowest RVD, indicating better overall region and volume estimation. Because no explicit boundary loss is used, slight contour deviations may remain in low-contrast regions, affecting ASSD and MSSD. The qualitative results in Figure 5 also show that the proposed method produces more complete liver regions while maintaining competitive boundary performance.

Table 2 presents the quantitative results for liver tumor segmentation. This task is particularly challenging because tumors are often small, heterogeneous, irregularly shaped, and difficult to distinguish from adjacent liver tissues. PDSA-DBUNet achieves the highest Dice score of 86.13%. It outperforms Swin UNETR and nnU-Net, which obtain Dice scores of 84.91% and 84.87%, by 1.22 and 1.26 percentage points, respectively. Compared with the conventional U-Net baseline, the Dice score is improved by 3.97 percentage points. These results demonstrate the stronger capability of PDSA-DBUNet to identify challenging liver tumor regions.

PDSA-DBUNet also achieves the best results for all four error-based metrics, with a VOE of 23.90%, an RVD of 0.76%, an ASSD of 17.76 mm, and an MSSD of 59.10 mm. Compared with the second-best results, the proposed method reduces VOE by 0.51 percentage points relative to nnU-Net, RVD by 0.27 percentage points relative to both CTCSANet and Swin UNETR, ASSD by 0.36 mm relative to Swin UNETR, and MSSD by 3.05 mm relative to nnU-Net. These consistent improvements indicate that PDSA-DBUNet provides more accurate tumor-region overlap, volumetric estimation, and boundary delineation, particularly for small, irregular, and low-contrast lesions.

Figure 5 presents the qualitative comparison on the LiTS dataset. The first three rows show liver segmentation, whereas the last two rows show liver tumor segmentation. Red, green, and yellow regions denote predictions, ground-truth annotations, and their overlap, respectively.

For liver segmentation, U-Net and UAMSNet exhibit incomplete contours or local boundary leakage. BoTNet and TransUNet improve global region completeness but retain deviations near low-contrast interfaces. CTCSANet generates relatively accurate liver regions, although minor contour mismatches remain. Swin-Unet captures the overall liver shape but still produces local over-segmentation or under-segmentation. nnU-Net produces generally consistent liver regions but retains minor contour deviations in several low-contrast areas. Swin UNETR improves global structural modeling, although slight local under-segmentation or boundary leakage remains. PDSA-DBUNet yields more complete liver masks and larger overlapping regions, indicating improved regional consistency and competitive boundary delineation.

For liver tumor segmentation, the differences are more evident because tumors are generally small, irregular, and low contrast. Several methods produce incomplete masks or scattered false-positive responses. CTCSANet identifies the approximate tumor regions but exhibits local boundary errors. Swin-Unet improves tumor localization, although incomplete overlap remains in challenging cases. nnU-Net identifies the primary tumor regions but shows local under-segmentation, whereas Swin UNETR provides improved lesion localization with residual boundary mismatches. In contrast, PDSA-DBUNet produces more compact tumor masks with fewer false-positive and false-negative regions. This improvement benefits from dynamic sparse token modeling and local-global feature fusion, which enhance lesion representation and spatial localization.

4.5 Comparative results on the KiTS19 dataset

Table 3 presents the quantitative results for kidney and kidney tumor segmentation on the KiTS19 dataset. This task evaluates both paired-organ delineation and the segmentation of irregular tumor regions.

TABLE 3. Quantitative comparison of kidney and kidney tumor segmentation on the KiTS19 dataset.

For kidney segmentation, PDSA-DBUNet achieves the highest Dice score of 94.03%, outperforming Swin UNETR, the second-best method, by 1.80 percentage points. It also exceeds nnU-Net by 2.91 percentage points. The proposed method obtains the lowest ASSD of 1.06 mm, indicating more accurate average boundary alignment. Although TransUNet achieves the lowest MSSD of 19.06 mm, PDSA-DBUNet obtains a competitive value of 20.14 mm while providing clear advantages in Dice and ASSD. Compared with nnU-Net and Swin UNETR, it reduces ASSD by 0.63 mm and 0.57 mm, respectively.

For kidney tumor segmentation, PDSA-DBUNet achieves the best results across all three metrics. It obtains a Dice score of 89.06%, exceeding Swin UNETR and nnU-Net by 1.92 and 3.34 percentage points, respectively. It also achieves the lowest ASSD and MSSD values of 1.91 mm and 17.09 mm. Compared with Swin UNETR, the proposed method reduces ASSD by 0.14 mm and MSSD by 6.97 mm. Compared with nnU-Net, the corresponding reductions are 0.58 mm and 2.65 mm. These results demonstrate that PDSA-DBUNet provides more accurate region localization and boundary delineation for irregular kidney tumors.

Figure 6 presents the qualitative comparison on the KiTS19 dataset. The columns show the input image, ground-truth annotation, and predictions generated by different methods. The first three rows correspond to kidney segmentation, whereas the last row shows kidney tumor segmentation. White regions denote ground-truth masks, and green regions denote predicted masks.

For kidney segmentation, U-Net captures the approximate kidney locations but produces incomplete contours in several cases. UAMSNet improves region continuity, although minor boundary deviations remain. BoTNet generates relatively complete masks but shows local over-segmentation near ambiguous tissue interfaces. TransUNet benefits from global context modeling, yet fine-grained contour details are not fully preserved. CTCSANet provides stable organ localization but retains slight mismatches along blurred boundaries. Swin-Unet captures the overall kidney shape, while small local errors remain around complex contours. nnU-Net produces consistent kidney regions but exhibits limited boundary refinement in several slices. Swin UNETR further improves global structural representation, although slight under-segmentation or boundary leakage can still be observed. In comparison, PDSA-DBUNet generates more complete kidney masks and achieves closer agreement with the ground truth, particularly near low-contrast boundaries.

For kidney tumor segmentation, U-Net and UAMSNet exhibit incomplete lesion coverage or inaccurate boundary localization. BoTNet and TransUNet improve tumor detection but still produce local false-positive or missed regions. CTCSANet and Swin-Unet generate more continuous predictions, although discrepancies remain for irregular tumor contours. nnU-Net identifies the main tumor region but shows local under-segmentation, whereas Swin UNETR provides improved lesion localization with residual boundary mismatches. PDSA-DBUNet produces a more compact and complete tumor mask with fewer false-positive and false-negative regions. These qualitative observations are consistent with the quantitative results in Table 3, where PDSA-DBUNet achieves the highest Dice score and the lowest ASSD and MSSD for kidney tumor segmentation.

4.6 Ablation study

To further verify the effectiveness of the proposed components, ablation experiments were conducted on the LiTS test set. Two key designs were evaluated: the PDSA module and the DSPAF module. The PDSA module was analyzed quantitatively in terms of segmentation accuracy and model complexity, while the DSPAF module was evaluated using attention heat maps to examine its effect on feature localization and response distribution.

4.6.1 Effectiveness of the PDSA module

Table 4 reports the ablation results on the LiTS test set. The baseline U-Net obtains a Dice score of 93.99%. Directly introducing Transformer blocks brings only marginal improvements, with Dice scores of 94.04% and 94.11% for the stacked and parallel variants, respectively. However, these variants substantially increase FLOPs, parameters, and model size, indicating that simple CNN–Transformer combination introduces considerable computational redundancy.

TABLE 4. Ablation results of different configurations on the LiTS test set.

The ablation results show that simply increasing Transformer capacity does not necessarily improve segmentation performance. Compared with U-Net, the Transformer-only, stacked, and parallel configurations introduce substantially higher computational and parameter costs but achieve only limited Dice improvements. This is mainly because conventional self-attention processes the complete dense token sequence, resulting in redundant interactions among homogeneous foreground and irrelevant background regions. In addition, stacked architectures may weaken the complementarity between local CNN features and global Transformer representations.

PDSA addresses these limitations by dynamically aggregating N i dense tokens into S representative sparse tokens, where S ≪ N i. This input-adaptive strategy emphasizes anatomically informative regions, suppresses redundant background responses, and performs global interaction in a compact token space. In the parallel CNN–Transformer structure, PDSA increases the Dice score from 94.11% to 96.14%, while reducing FLOPs from 146.30G to 70.04G and parameters from 496.45M to 40.42M. After further incorporating the DSPAF module, the final PDSA-DBUNet achieves the best Dice score of 96.79%, with 72.87 GFLOPs, 41.62M parameters, and a checkpoint storage size of 129.93 MB. Compared with the parallel CNN–Transformer variant without PDSA, the final model improves Dice by 2.68 percentage points and reduces FLOPs, parameters, and model size by 50.19%, 91.62%, and 80.71%, respectively. These results confirm the effectiveness of PDSA in reducing redundant token computation and DSPAF in enhancing local–global feature fusion, leading to a favorable accuracy–efficiency balance.

Figure 7 further presents a boundary-level visual comparison to evaluate the effectiveness of the PDSA module. The green contour denotes the ground-truth annotation, the red contour represents the prediction generated by the parallel U-Net–Transformer baseline, and the white contour denotes the segmentation result obtained after introducing the PDSA module. The baseline model can roughly localize the target regions, but clear boundary deviations remain around low-contrast tissue interfaces and small lesion regions. This indicates that a simple parallel combination of CNNs and Transformers is still insufficient to suppress background interference and preserve fine boundary details.

After introducing the PDSA module, the predicted contours become closer to the ground-truth annotations, and the boundary deviations are reduced. This improvement may be attributed to the PDSA module, which suppresses redundant background tokens and enhances lesion-related token representations. Meanwhile, the Polynomial Mixer enables global contextual interaction with lower computational cost. Together with the quantitative results in Table 4, these visual results demonstrate that the PDSA module improves segmentation accuracy while effectively reducing model complexity.

4.6.2 Effectiveness of the DSPAF module

Figure 8 presents the attention heat maps generated by different network configurations on liver segmentation samples from the LiTS dataset. The columns correspond to the input image, ground-truth mask, U-Net, Transformer, U-Net with Transformer, and the proposed method with the DSPAF module. Warmer colors indicate stronger network responses, while cooler colors indicate weaker responses.

The Transformer-based model shows broader global responses than U-Net, but its attention maps remain coarse and may activate irrelevant background regions, especially near low-contrast liver boundaries. The parallel U-Net–Transformer structure improves response coverage by combining local convolutional features with global Transformer features. However, without an explicit fusion mechanism, the two branches are not sufficiently coordinated, resulting in residual background interference and incomplete boundary attention. These observations indicate that simply introducing global modeling or parallel feature extraction is insufficient for accurate feature localization.

After introducing the DSPAF module, the proposed network produces more concentrated and anatomically consistent heat maps. The high-response regions are better aligned with the liver masks, while background activations are effectively suppressed. This improvement is mainly attributed to the dual-scale design of DSPAF. The global channel attention path enhances semantic consistency between CNN and PDSA Transformer features, whereas the local spatial interaction path strengthens boundary and texture representation. As a result, DSPAF improves local–global feature interaction and enables more accurate target localization.

Overall, the ablation results confirm the necessity of both proposed modules. The PDSA module improves segmentation accuracy while significantly reducing computational cost. The DSPAF module enhances local–global feature interaction and improves target localization. Together, these two modules enable PDSA-DBUNet to achieve accurate and efficient abdominal medical image segmentation.

5 Discussion

The results on the LiTS and KiTS19 datasets validate the effectiveness of PDSA-DBUNet for abdominal organ and tumor segmentation. The proposed method achieves consistently superior Dice scores across liver, liver tumor, kidney, and kidney tumor segmentation tasks, demonstrating its capability to handle both large anatomical structures and small lesion regions. These gains can be attributed to the complementary dual-branch design. The CNN branch preserves local textures, edges, and boundary details, while the PDSA Transformer branch models long-range anatomical dependencies and global semantic context. Compared with conventional Transformer-based designs, the PDSA module reduces redundant token computation through input-adaptive sparse tokens, and the Polynomial Mixer enables efficient global feature interaction without dense pairwise self-attention. In addition, the DSPAF module further enhances local–global feature interaction by combining global channel attention and local spatial interaction. This design improves semantic consistency between CNN-derived local features and PDSA-derived global features, which is particularly beneficial for blurred boundaries and small tumor regions.

The quantitative and qualitative results provide consistent evidence for the robustness of the proposed network. Higher Dice scores demonstrate improved region overlap, while lower ASSD and MSSD values indicate more accurate boundary localization. Visual comparisons further show that PDSA-DBUNet better preserves organ contours, reduces missed segmentation, and suppresses false-positive responses in complex abdominal CT images. Nevertheless, several limitations remain. First, the current experiments are mainly performed on 2D CT slices, which may not fully exploit inter-slice spatial continuity in volumetric CT data. Second, the evaluation is conducted on two public datasets, and the generalization ability of the model on multi-center clinical data requires further validation. Future work will extend PDSA-DBUNet to three-dimensional or 2.5-dimensional inputs and conduct unified comparisons with nnU-Net 3D, nnFormer, and the original 3D Swin UNETR under the same experimental settings.

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Footnotes

Edited by: Mária Ždímalová, Slovak University of Technology in Bratislava, Slovakia

Reviewed by: Xinhe Chen, National University of Singapore, Singapore

Gan Yunhui, Fudan University, China