Automatic Pancreas Segmentation in CT Images Using EfficientNetV2 and Multi-Branch Structure

1  Introduction

Pancreatic cancer is recognized as one of the deadliest tumors and is projected to become the second leading cause of cancer-related mortality in the United States [1]. Early screening and diagnosis are crucial for improving the survival rate of patients with pancreatic cancer [2]. Computed tomography (CT) is the first-line imaging modality for diagnosing suspected pancreatic cancer [3]. However, manual delimitation of the pancreas in abdominal CT images is not only skill-demanding and time-consuming but also prone to subjective inconsistency. Therefore, there is an urgent need for a method that can quickly and accurately segment the pancreas, alleviating radiologists’ workload and aiding physicians in early screening of pancreatic inflammation or lesions, as well as in surgical planning.

Traditional pancreatic image segmentation techniques achieved low dice coefficients (<75%) [4], such as region growing [5], threshold-based [6] and atlas-based methods [7]. They rely on human interaction, have limited ability for self-learning, and are susceptible to noise interference. Unlike conventional methods, certain approaches based on deep convolutional neural networks (CNN) have shown remarkable effectiveness in medical image segmentation, especially in the field of liver [8], lung [9], and brain [10] segmentation. However, the majority of these methods are tailored for organs with regular shapes and large areas; the pancreas’s tiny size, significant variability, and confusing environment render it ineffective. As shown in Fig. 1, accurate pancreas segmentation is an extremely challenging task due to the following facts: (1)pancreas occupies a quite small portion in the CT images, making it difficult to detect or capture; (2)pancreas exhibits significant individual differences in shape and location, making its structure complex and variable; (3)pancreas appears blurred margin due to the low contrast with surrounding tissues.

Figure 1: CT slices from three cases. The pancreatic region is highlighted in red from three case

Some researchers directly apply 3D fully convolutional networks to locate and segment the pancreas from volumetric data [11,12]. Mo et al. [13] introduced a iterative 3D feature enhancement network to enhance multi-level integrated features and single features at different levels, suppressing non-target information and improving the fine details of the pancreas. Due to the GPU limitations, an entire CT scan needs to be cropped to sub-volumes and the input size is fixed at 64×64×24, which makes the network confused because of the restricted receptive field. Meanwhile, it is difficult to deploy on real-time devices, as a CT scan requires approximately 2 min for reasoning. To alleviate this issue, the 2D U-Net [14,15] and its modifications are used to struggle with the complex scenarios of small and irregularly shaped pancreas. Such as increasing the number of consecutive convolutions, adding residual connections, and employing parallel convolutions with different kernel size [16–18]. However, the detail loss caused by pooling operations, limited multi-level feature extraction capabilities, and insufficient context capture continue to hinder improvements in the accuracy of pancreatic segmentation. Attention Gate (AG) is proposed to work on the skip connections of U-Net [19]. The network can focus on the most relevant aspects by using the attention mechanism, rather than allowing all information to feed into the decoder. But when this attention module performs weighted selection on shallow features based on raw deep features, it does not consider multiple scales target information. Introducing weighted guided losses at different phases of the decoder helps the network produce more accurate feature maps, thereby improving the restoration of target details [20]. However, the weight adjustment is challenging, making the model training and optimization process more complicated.

Focusing on smaller input regions around the target can lead to higher segmentation accuracy. Therefore, a few techniques involve resampling pancreatic CT slices during data preprocessing, such as directly resizing to smaller dimensions of 224×224 [21], or cropping to a smaller region referring to the approximate scopes of pancreatic annotations, like 208×224 [15,17], 208×208 [22], and 192×256 [16]. The former operation of resizing may cause the loss of some valuable details, while the latter dynamic cropping requires tracking the relative positional information. Unlike the fixed reduction of network input, Liu et al. [23] segmented liver, kidney, and spleen using the proposed vision geometry group u-shaped net (VGGU-Net), and dynamically constructed the pancreatic candidate boxes by calculating the contour center points of the three organs. However, this method requires a lot of preparation work before segmenting the pancreas, leading to a considerable increase in both the processing overhead and the workload for the segmentation model. To get higher accuracy, certain coarse-to-fine [24–27] approaches first provide a coarse localization of target regions, and then refine the candidate areas in subsequent stages. Hu et al. [25] utilized the DenseASPP [28] network to learn pancreatic location and probability maps, generating coarse-scaled segmentation results. They then applied a geodesic distance-based saliency transformation to predict the final segmentation. The method has an inference time of 77.3 s per case and a computational load exceeding 37k giga floating-point operations (GFLOPs), which decreases inference time but still incurs high resource consumption. Two different networks are used to extract a pancreatic candidate region and make dense predictions within that area [26]. This not only leads to the repeated extraction of similar low-level features but also increases the network parameters and computational burden.

In response to the above problems, prior to training, we design a fixed candidate region based on the pancreas location for cropping, which can preserve the relative positional information while removing part of the background. In the network design, we first utilize the powerful and parameter-efficient neural network EfficientNetV2 [29] as the encoder. This architecture incorporates advanced convolutional modules, such as Fused-MBConv [29], which effectively minimizes information loss during downsampling and preserves important details. EfficientNetV2 is trained using a compound scaling strategy and features a hierarchical progressive structure that enhances the model’s ability to capture global contextual information while extracting multi-level detailed and semantic features. These characteristics facilitate the segmentation of objects of varying sizes and shapes.

Then, we design a residual multi-branch dilated attention (RMDA) module to suppress irrelevant background information and highlight specific pancreatic features. RMDA employs multi-branch dilated convolutions to capture multi-scale pancreatic features from deep semantic representations. This enables the attention mechanism to more effectively guide the network’s focus on critical pancreatic regions across multiple scales, rather than being confined to a single scale. Additionally, RepVGG [30] blocks with a multi-branch structure are introduced into the decoder, where they are responsible for fusing the extracted features and effectively restoring image details. We term our network as ERR-Net (EfficientNetV2-RMDA-RepVGG-Net). The proposed method is experimentally evaluated on two public pancreas datasets and compared with other advanced methods. What’s more, the re-parameterization has been implemented on the trained network, which not only lowers the number of network parameters and FLOPs, but also saves memory overhead and speeds up inference. The primary contributions of our work can be summed up as follows:

1. A novel network based on EfficientNetV2 and multi-branch structure, ERR-Net, is proposed for pancreatic segmentation.

2. We adopt EfficientNetV2 as the encoder and modify it to extract and preserve pancreatic features of varying sizes and shapes, improving the capabilities of extracting complex features and representation learning, as well as the computational efficiency.

3. A multi-branch structure RMDA is designed to act on skip connections, suppressing irrelevant background noise and highlighting useful pancreatic features. Meanwhile, RepVGG blocks are introduced in the decoder to fuse features from both deep and shallow layers, effectively restoring detailed information about the pancreas. Furthermore, by utilizing re-parameterization, the entire model has made improvement in lightweight, with fewer parameters, less computation, and faster inference speed.

The remainder of this paper is organized as follows. Section 2 briefly reviews the related work. Section 3 describes our approach and Section 4 presents the experimental results. Section 5 contains a brief discussion. Finally, Section 6 draws conclusions.

2  Related Work

Pancreas segmentation is part of the medical image analysis field and serves as the foundation for further pancreas-related diagnosis [31]. With further research, various techniques have been presented to perform abdominal pancreas segmentation. Traditional pancreas segmentation methods, such as atlas [32], region growth [5] and simple linear iterative clustering [33], are reliant on manual extraction of features or human involvement during the segmentation procedure. Due to the disadvantages of low accuracy, time-consuming, and missing automation, they have been replaced by the quickly evolving deep learning. Especially, significant improvements have been brought to pancreas segmentation by CNN-based techniques because of CNN’s strong model capabilities to fit various data distributions. Specifically, the pancreatic segmentation models can be separated into one-stage and two-stage models based on the various stages of the model.

Gibson et al. [34] presented the DenseVNet segmentation network, which enabled high-resolution activation maps through feature reuse and memory-efficient dropout. Attention Gate [19] was integrated into 3D U-Net to suppress unrelated regions while highlighting significant features during the segmenting pancreas. Fang et al. [12] developed a globally guided progressive fusion network in which the encoder utilized 3D convolution to extract the features, while the decoder employed 2D convolution to conserve memory consumption. Although 3D convolutions can learn the three-dimensional spatial relationships of the pancreas, they face challenges related to substantial computational expenses and GPU memory consumption. Due to the tiny size of the pancreas itself, some convolution operations are computationally wasted. Zheng et al. [35] proposed using shadowed sets to identify the uncertain regions of the result of pancreas segmentation and calculate the weight for them. During training, the weight was employed to induce the network to focus more on the uncertain areas of the pancreas. Huang et al. [36] designed a lightweight network for pancreatic segmentation by merging U-Net and MobileNet-V2 [37]. Before training, they cropped the image according to the centroid and fed it into the segmentation network. Although the model has a relatively low parameter count of 6.3 million, its segmentation accuracy remains insufficient. Liu et al. [23] utilized 2D VGGU-Net to obtain the position of the liver, kidney, and spleen, calculating the contour center points of the three abdominal organs in each CT slice. They are used to dynamically construct candidate boxes for the pancreas and crop redundant backgrounds. However, the inaccurately cropped regions will affect the model’s segmentation performance, and this approach requires a lot of preparation work before segmenting the pancreas.

As the pancreas and pancreatic tumors make up a minor fraction of the original input data, a significant pixel imbalance occurs. Therefore, the two-stage framework has been proposed by some researchers. Yu et al. [38] proposed a multi-stage saliency segmentation method, which recurrently uses the segmentation mask of the current stage to refine the cropping and segmentation results in the subsequent stage. Chen et al. [39] presented the feature propagation and fusion network (FPF-Net) for extracting features. It employed two similar networks for detecting and segmenting the pancreas, which increased the number of network parameters and complexity. A deep U-Net is used by Qiu et al. [40] to locate the pancreas and crop CT images during the coarse-stage. And they designed the residual transformer [41] UNet (RTUNet) to extract multi-scale characteristics from a global perspective that captures large position changes of the pancreas. However, this model requires a long training time of 48 h and is highly dependent on the segmentation outcomes from the coarse-stage network. Zheng et al. [42] introduced an extension-contraction transformation network (ECTN) within a two-stage cascaded framework to achieve accurate pancreatic segmentation. However, they come with a significant increase in parameter count, growing geometrically compared to 2D networks, which presents challenges in terms of computational efficiency.

3  Methods

This section consists of two main components: data pre-processing and network architecture design. Take note that our proposed approach is grounded in 2D manipulations. Therefore, all CT volumes are divided into 2D slices and the axial slices are used to train our models.

3.1 Data Pre-Processing

Before training the model, the data pre-processing is carried out on the pancreas dataset to obtain candidate regions of the pancreas, minimize the impact of noise, and enhance the presentation of the pancreas. The process of data pre-processing is presented in Fig. 2a. It is mostly composed of the following steps:

Figure 2: (a) The diagram depicting the pipeline of data pre-processing; (b) The image display of the pre-processing result. Note: The red rectangular box contains the region of the pancreas. After pre-processing, the pancreatic region appears more distinct, and certain background information has been removed

(1) The statistical analysis is conducted on the quantity of slices in pancreas CT scans. In the NIH dataset, there are 7059 slices with pancreatic masks in the axial view, and the count of slices with pancreatic labels varies between 46 and 145 for each case. To ease the problem of low contrast between pancreas and the adjacent abdominal organs, according to some research works [23,43], the CT values are truncated to [−100, 240] Hounsfield Unit (HU). From Fig. 2b, it is evident that the clarity of the pancreatic area has been notably improved. The CT values are normalized to the range of [0, 1] when converting them to pixel values.

(2) The candidate regions selected in this method are based on the positions of the pancreas. In NIH dataset, the pancreas position ranges from 167 to 405 in the x-axis and from 143 to 360 in the y-axis. To facilitate the calculation of the segmentation network, the candidate region coordinates are extended as [158:414, 124:380], ensuring cropping the CT images to a uniform size of 256×256. This operation effectively mitigates the impact of noise and irrelevant background during model training.

(3) Some data augmentation techniques are adopted to enhance the robustness of models and alleviate the over-fitting during network training, including Random Scaling, Horizontal Flip, Gaussian Blur, and Random Rotation. These techniques are chosen to introduce variability in object size, orientation, and image quality, simulating the natural variations typically observed in medical images. While advanced augmentation methods like Mixup and CutMix, which generate synthetic samples through interpolation, were considered, they were not included in this study.

3.2 ERR-Net Network Architecture

ERR-Net adopts a symmetrical encoder-decoder architecture and skip connections. As shown in Fig. 3, the adjusted EfficientNetV2 is employed as the encoder to extract the complicated multi-level features of the pancreas. The encoder has five outputs, namely five kind feature maps of original size, 1/2, 1/4, 1/8, and 1/16. 1/16 size of the feature maps serve as the input of the decoder, while the remaining four feature maps are preserved to fused with the features of the decoding end.

Figure 3: The network architecture of ERR-Net. S represents the size of stride in Fused-MBConv/MBConv. H×W×C denotes the size of feature maps

We design an RMDA module and insert it into the four skip connections. In this module, multi-scale semantic information from deeper layers is guided to pay attention to the target region. Then, the feature maps from the shallow layers will be re-weighted to suppress irrelevant features and highlight pancreatic features.

During the process of decoding, the sizes of the feature maps are doubled using upsampling and progressively recovering to the original image resolution. Four enhanced encoding features are concatenated with the upsampled feature representations, and RepVGG blocks are introduced to fuse deep semantic features and shallow detail information, improving detail recovery in segmentation. Lastly, through a 1×1 convolution of the output layer, the final feature layers are mapped into a specific number of categories for pixel category prediction, yielding the segmentation results.

3.3 EfficientNetV2

EfficientNetV2, a new family of convolutional neural architectures that represents an improved version of the previous EfficientNet [44] models. Due to non-uniform scaling and training-aware neural architecture search (NAS), EfficientNetV2 has been dramatically boosted with regard to parameter efficiency and training speed. In this paper, we adopt and adjust the pre-trained EfficientNetV2-S as the encoder of our model. The reason for choosing the scale of S is that its training image size is 300 and the evaluation size is 384, which is closest to the image resolution of our training set. Moreover, it has the lightest network configuration and shortest inference time when compared to the other scales. With its powerful feature extraction capability, EfficientNetV2-S can effectively extract details and semantic information of targets, and handle significant alterations in the pancreatic morphology.

EfficientNetV2 extensively utilizes both MBConv [37] and the newly added Fused-MBConv in the early layers, which replaces the depthwise convolution and the expansion convolution of 1×1 in MBConv with a regular 3×3 convolution. The two refined modules minimize the information loss during downsampling. Their structures are shown in Fig. 4. MBConv consists of 1×1 dimension-up convolution, 3×3 depthwise convolution, Squeeze-and-Excitation (SE) attention, 1×1 dimensionality reduction convolution and Dropout layer. Fused-MBConv is composed of regular 3×3 convolution for dimensionality enhancement, SE attention module, 1×1 convolution for dimensionality reduction, and Dropout layer. They both have shortcut connections while the stride is 1 and the input channel of this module is equal to the output channel. BN stands for Batch Normalization (BN), and SiLU is Sigmoid Gated Linear Unit (SiLU) activation function.

Figure 4: The Structural display of MBConv and Fused-MBConv

EfficientNetV2-S is derived from EfficientNetV2 through non-uniform scaling, enhancing the capture of global context information and extracting abundant details and semantic features of the target. The network architecture of EfficientNetV2-S is shown in Table 1, where k represents the kernel size of the convolution, and the numbers behind Fused-MBConv and MBConv represent their expansion ratios. Only layers of stages 0 to 6 in EfficientNetV2-S are employed by ERR-Net. Given the compact size of the pancreas as a segmentation target, the down-sampling frequency of the entire encoder is determined to 4. Therefore, the stride is adjusted to 1 in our model instead of the original value of 2 in the first 3×3 convolution. The stacking process of the Fused-MBConv and MBConv blocks is displayed in the encoder in Fig. 3.

3.4 Residual Multi-Branch Dilated Attention (RMDA)

While skip connections supply detailed information for the decoder, they may fail to draw attention to the crucial details. To suppress irrelevant background information and emphasize specific pancreatic features, we design and insert the RMDA module into skip connections, which performs re-weighted selection on shallow features based on the multi-scale deep semantic information.

Specifically, the network’s receptive field is enlarged by utilizing a multi-branch structure with parallel dilated convolutions, effectively capturing multi-scale information from the feature maps of the deep layers. And the semantic information extracted from deep layers is applied to eliminate irrelevant information, as the correlated information is fused in addition to highlighting crucial pancreatic features. Then, the weights of the low-level features are adjusted by means of calculating the attention coefficient. As shown in Fig. 5, after adopting RMDA, the model focuses more on the target region.

Figure 5: Visualization results of with RMDA

As shown in Fig. 6, the x with size of Cx×Hx×Wx denotes the low-level feature map, g with size of Cg×Hg×Wg represents the high-level feature map, and Hg=Hx/2,Wg=Wx/2. To begin with, a multi-branch structure is leveraged to provide a broader perception range and extract multi-scale information in the high-level feature map g, which contains three parallel dilated convolution with dilation rates of 1, 2, and 4. After that, the correlated features at different scales are fused by means of addition, which not only fuses features from different levels but also fuses features from different receptive fields. The output of multi-branch structure g′ can be expressed as follows:

g′=d13(g)+d23(g)+d43(g)(1)

where drk(⋅) denotes the dilated convolution operation with kernel size of k×k and dilation rate of r, and the channel of output in each dilated convolution is Cx.

Figure 6: Structure of Residual Multi-branch Dilated Attention (RMDA)

Meanwhile, the feature map x is downsampled using a convolutional layer with a kernel size of 2×2 and stride of 2. By adding the two different extracted feature maps, the same region of interest can be enhanced while not ignoring detailed information. Then, the fused feature maps are upsampled to match the dimensions of x, and they go through a Rectified Linear Unit (ReLU) activation function and a 1×1 convolution in turn. Subsequently, the sigmoid function is applied to the feature maps to obtain the attention map α, and α is defined as shown in Eq. (2):

α=σ[C1(δ(U(g′+C2(x))))](2)

where C2 represents the convolution operation acting on x, using a Cx×2×2 kernel size and a stride of 2, U represents the bilinear interpolation upsampling and δ denotes the ReLU activation function. C1 denotes the convolution with kernel size of 1×1 and stride of 1. And σ stands for the sigmoid activation function.

Thus, the weights of the features can be adjusted by calculating the dot product between the attention-weighted map α and the feature map x. The re-weighted feature map x^ is shown in Eq. (3):

x^=x×α(3)

Since the values of the attention map α are in the range of [0, 1] after being normalized by the sigmoid function, this re-weighted process will cause the loss of detailed information and weaken the output of feature maps. Therefore, the input feature maps are added to the re-weighted results using identity mapping. The introduction of residual connection enhances the network’s segmentation performance rather than simply weighting the features. It can alleviate the vanishing gradient problem, which benefits training and accelerates convergence. The final output of RMDA is formatted in Eq. (4).

X^=x^+x(4)

3.5 RepVGG

In the decoder of our model, RepVGG blocks are utilized instead of regular convolutions to integrate feature information from shallow and deep layers, helping to restore image details and refine pancreas segmentation. In the multi-branch structure, different branches can learn various representations, which makes the fused representations enriched and enhanced. As is shown in Fig. 7, the RepVGG blocks use 3×3, 1×1 and identity branches, and as a result, the training-time information flow is y=f(x)+g(x)+x. If the dimensions of f(x) and x do not match, y=f(x)+g(x), where f(x) and g(x) are the operations of 3×3 convolution, 1×1 convolution in the same layer. In the inference stage, the branch module is equivalent to y=h(x), where h(x) is implemented only by a 3×3 convolutional layer, and parameters are transformed from the trained model by linear combination. Compared with the other convolution kernels, 3×3 convolutions have faster computational speed, use fewer memory units, and obtain better efficiency.

Figure 7: The process of structural re-parameterization in the RepVGG block

After training, the multi-branch structure is transformed through structural re-parameterization. Specifically, each branch in the RepVGG block passes through the BN layer during training, and the convolutional layers and BN layers can be merged. Eqs. (5) and (6) represent equations of the convolutional layer without bias and the BN layer, respectively. And Eq. (7) is the combination of the convolution and BN. The final fused operation is represented by Eq. (8).

Conv(x)=W(x)(5)

BN(x)=(x−μ)⋅γσ2+ϵ+β(6)

BN(Conv(x))=W(x)⋅γσ2+ϵ+(β−μ⋅γσ2+ϵ)(7)

BN(Conv(x))=Wfused(x)+bfused(8)

where μ,σ,γ, and β denote the accumulated mean, standard deviation, learned scaling factor, and bias of the BN layer. Wfused, bfused presents the convolution operator W⋅γσ2+ϵ and bias (β−μ⋅γσ2+ϵ) after fusion.

After combining convolution and BN, the RepVGG block has only one 3×3 convolution kernel, two 1×1 convolution kernels, and three parameters of bias, because the identity branch can be viewed as a special 1×1 convolution with an identity matrix as the kernel. The 1×1 convolution kernel can be filled with zero to obtain a 3×3 convolution. Therefore, the final convolution kernel can be obtained by adding the 1×1 convolution kernel parameter to the central point of the 3×3 convolution kernel, and adding up the three biases yields the final bias. The final convolution kernel and final bias will be assigned to a new 3×3 convolution with bias, followed by a ReLU activation function.

According to Ding et al. [30], it uses W(3)∈RC2×C1×3×3 to denote the kernel of a 3×3 convolution layer with C1 input channels and C2 output channels, and W(1)∈RC2×C1 for the kernel of 1×1 branch. And μ(3),σ(3),γ(3),β(3) denote the accumulated mean, standard deviation and learned scaling factor and bias of the BN layer following 3×3 convolution, μ(1),σ(1),γ(1),β(1) for the BN following 1×1 convolution, and μ(0),σ(0),γ(0),β(0) for the identity branch. Let M(1)∈RN×C1×H1×W1, M(2)∈RN×C2×H2×W2 represent the input and output of RepVGG block, and ∗ stands for the convolution operator. If C1=C2,H1=H2,W1=W2, the output can be

M(2)=bn(M(1)∗W(3),μ(3),σ(3),γ(3),β(3))+bn(M(1)∗W(1),μ(1),σ(1),γ(1),β(1))+bn(M(1),μ(0),σ(0),γ(0),β(0)).(9)

4  Experiments

4.1 Dataset

NIH pancreas dataset [45]. Our method is tested and evaluated on the NIH pancreas dataset, which is an open-source collection consisting of 82 enhanced abdominal CT scans with a resolution of 512×512 pixels. A medical student manually conducted slice-by-slice segmentations of the pancreas, which were subsequently verified or modified by an experienced radiologist to serve as ground truth (GT). 4-fold cross-validation (CV-4) strategy is performed on this pancreas dataset and all experiments follow this strategy. Concretely, the dataset is partitioned into 4 folds, consisting of 20, 20, 21, and 21 samples, respectively, and three portions are used for the training network while the remaining part is employed for testing the trained model each time.

MSD pancreas dataset [46]. Medical Segmentation Decathlon consists of ten medical image segmentation datasets, which are from different sections of the human body. The MSD pancreas tumor segmentation dataset contains labeled 281 volumetric data with the dimension of 512×512×L, L ∈[37,751]. In our experiments, it is divided into 70, 70, 70, 71 cases for 4-fold cross-validation. Following previous studies [26,47], we merge the pancreas and tumor into a unified target region for segmentation.

4.2 Implementation Details

All experiments are executed based on the environment of Python 3.7, PyTorch 1.7.1, and Ubuntu 20.04. Our models are trained on two Nvidia GeForce RTX 3090 GPUs, each with 24 GB of memory. We employ the learning rate scheduling strategy, Cosine Annealing, to dynamically adjust the learning rate, thereby improving the model’s convergence and overall performance. After preliminary experiments and considering both training time and model performance, the experimental parameters are set as shown in Table 2.

4.3 Evaluation Metrics

Four evaluation metrics Dice Similarity Coefficient (DSC), Intersection over Union (IoU), Precision, and Recall is leveraged to measure the model’s performance in segmenting the pancreas. Here are the definitions of these metrics:

(1) DSC calculates the spatial overlap between the predicted mask and ground truth.

DSC=2TP2TP+FP+FN(10)

(2) IoU computes the similarity between the segmentation mask and ground truth.

IoU=TPTP+FP+FN(11)

(3) Precision calculates the proportion of true positive predictions in the segmentation mask.

Precision=TPTP+FP(12)

(4) Recall calculates the true positive rate within the ground truth annotations.

Recall=TPTP+FN(13)

where TP, FN, and FP represent the true positives, false negatives, and false positives predicted for the pancreas, respectively.

4.4 Loss Function

In the experiments, Dice loss is employed to evaluate and optimize the training of segmentation models, which is derived from DSC. Because of the tiny volume of pancreas in the CT scans, there is a problem of class imbalance between the target and background. Therefore, Focal Loss [48] is utilized in our model to alleviate the pancreatic category imbalance problem. The combination of these two losses forms the final loss function of our network. It is writen as Eq. (14), where pn is the predicted probability that pixel n is the pancreas, and gn is the ground truth of pixel n. N is the total number of pixels in the CT images.

ℒ=ℒDice+ℒFocal=1−2TP2TP+FN+FP−∑n=1Ngn(1−pn)2log⁡pn(14)

4.5 Experimental Results

4.5.1 Comparison with the State-of-the-Art

In this section, we compare our segmentation results with state-of-the-art methods. Table 3 presents the comparative outcomes of mean DSC, IoU, Precision, and Recall, including their standard deviation. It also displays the parameters and inference time of models. All experimental outcomes of other methods are sourced from the original papers or related studies.

As indicated in Table 3, our approach demonstrates highly competitive performance compared to the state-of-the-art methods. Among the compared approaches, the suggested algorithm scores the greatest DSC of 85.59±4.11%, the greatest IoU of 75.03±5.92%, and the greatest Recall of 86.57±6.11%. In terms of mean DSC, our approach has significantly surpassed two strong baseline techniques [43,50], with gains of 1.06% and 0.69%, respectively. While the mean DSC of our method surpasses previous state-of-the-art [52] by a mere 0.02%, the enhancement over the second-best [25] is nearly 0.1%. Although ours mean Precision is inferior to that of Chen et al. [26], we achieve improvements of 0.4%, 0.84% and 1.99% in DSC, IoU and Recall, respectively. Similarly, our Precision is 0.51% lower than that of FPF-Net [39], but our method outperforms FPF-Net in DSC, IoU, and Recall by 0.18%, 0.23%, and 0.67%, respectively. Moreover, the standard deviation of each metric in our approach is the lowest, indicating the stability and robustness of our method. The high accuracy and robustness demonstrate the superiority of the proposed method.

It is worth noting that our method sharply lowers the network parameters compared with most algorithms. Although the model of Cao et al. [51] has the fewest parameters, our approach outperforms theirs by 2.55%, 3.38%, and 2.15% in terms of average DSC, Precision, and Recall, respectively. And our network has a remarkable reduction in inference time. With only 0.052 s needed for inferring each slice, the inference speed of our network is extremely quick. Compared to the method of Hu et al. [25], our model has one-third the number of parameters and achieves six times the inference speed. This proves that our model not only performs well in segmentation accuracy but also has fewer parameters and faster inference speed.

Furthermore, Fig. 8 indicates the qualitative comparison of our approach with labels, where the red line represents the contours of ground truth and the blue line indicates the predicted edges of our model, respectively. It is evident that the shapes and boundaries of the final segmentation closely match the ground truth, whether for small, large, or discontinuous pancreatic regions.

Figure 8: The segmentation results of our method compared with labels. The red solid line represents the ground truth, and the blue solid line represents the predicted results

Our approach is also experimentally validated on the MSD pancreatic dataset to verify its effectiveness and generalization ability. The data undergoes the same preprocessing as the NIH dataset. As presented in Table 4, our method achieves superior segmentation accuracy, reaching the highest average DSC, IoU, and Recall of 82.7%, 71.25%, and 84.79%, respectively. Although our average Precision is not among the highest, the proposed method scores 83.1% in Precision and 84.79% in Recall, demonstrating a relatively balanced overall segmentation performance.

4.5.2 Comparison with the Classical Segmentation Models

In this experiment, we contrasted our model with the classical segmentation networks. They are PSPNet [53], DeeplabV3+ [54], SegFormer [55], and TransUNet [56]. It can be seen in Table 5, when compared with the two CNN-based models, PSPNet and DeeplabV3+, the performance of ours exhibits a substantial improvement in segmentation accuracy. Compared with two Transformer [41]-based models, SegFormer and TransUNet, our model achieves better segmentation performance. Although our Precision is 0.03% lower than that of TransUNet, our model shows superior accuracy in DSC, IoU, and Recall, while also exhibiting the lowest standard deviation. And the parameter count and FLOPs of our network are significantly lower than those of TransUNet, indicating that our model achieves an effective trade-off between segmentation accuracy and computational resource usage.

In order to clearly display the distribution of the segmentation outcomes of five models on NIH 82 cases, we provide four Box-Scatter Plots to visualize the results of four metrics. As is indicated in Fig. 9, each boxplot displays a distribution of model segmentation results. For instance, the green boxplot stands for the distribution of our segmentation outcomes. It presents a box shape where the upper whisker indicates the maximum value and the lower whisker indicates the minimum value of the data, both of them containing no outliers. The bottom of the box stands for the first quartile and the top of it represents the third quartile. The black lines inside all boxes represent the median of the results. Besides, the specific results of each sample are visually presented in scatter plots, allowing for a comprehensive understanding of the performance of the five models. A jitter is applied to prevent point overlap, ensuring clarity in data representation.

Figure 9: Box-Scatter Plots of five segmentation methods on four evaluation index

By contrasting the boxplots of the segmentation outcomes of five models, it is obvious that the value of median DSC, IoU, and Recall of our model significantly exceed 85%, 75% and 85% respectively, outperforming the segmentation outcomes of other models. Furthermore, our model has the smallest box size among the four evaluation metrics, reflecting the stability and consistency of our segmentation performance. Although the median Precision of TransUNet marginally exceeds that of our network, the majority of the segmentation outcomes from the proposed approach surpass 80%.

Fig. 10 provides a 3D qualitative comparison of the predicted outcomes from five different models. And the green circle highlights areas where other classical segmentation networks do not perform as well as ERR-Net. The displayed cases include Case 67, Case 71, and Case 79. In the three instances, PSPNet’s segmentation outcomes are subpar and different regions of each example display under-segmentation. For Case 67 and Case 79, DeepLabv3+ suffers from inaccurate boundary recognition when segmenting the pancreas, while an apparent over-segmentation occurrs in Case 71. In Case 67, it is obvious that both SegFormer and TransUNet show considerable over-segmentation. Our prediction result in Case 67 is closer to GT, despite the fact that our model also encounter a minor over-segmentation. Additionally, ERR-Net is capable of segmenting the pancreas more accurately, particularly in cases with intricate features, compared to the segmentation results of SegFormer and TransUNet in Case 79. As we can see, in the three cases, ERR-Net produces segmentation masks that are very similar to GT. This implies that our model can not only effectively extract pancreatic features of various shapes and sizes, but also maintain stability under complex backgrounds interference, and achieve more accurate segmentation of the pancreas.

Figure 10: Comparison of 3D segmentation outcomes from different models. The green circles mark the regions where the segmentation masks of other models are less precise than ours

4.5.3 Ablation Study

Several ablation experiments are carried out in order to evaluate the contributions of each component in our model. Table 6 summarizes the experimental results of different network configurations. For fair comparisons, we keep the training parameter settings unchanged with only modules being replaced or added. And all of them are running in the same environment.

The first group represents the segmentation results of U-Net. By replacing the encoder of U-Net with the adjusted EfficientNetV2, the metrics increase 1.83% on DSC, 2.63% on IoU, and 3.51% on Recall, respectively. The significant increments reflect the powerful feature extraction capability of EfficientNetV2. From the third and fourth groups, it can be seen that simply adding the RMDA or RepVGG module leads to improvements in the average DSC, IoU, and Recall. On the basis of EfficientNetV2, by incorporating the RMDA module to the skip connections, the segmentation accuracy sees an increase of 0.13% on DSC, 0.19% on IoU, 0.22% on Precision, and 0.05% on Recall. Similarly, the use of RepVGG blocks boosts accuracy over EfficientNetV2 by 0.34% on DSC, 0.5% on IoU, 0.28% on Precision, and 0.37% on Recall. With the inclusion of EfficientNetV2, RepVGG, and RMDA, our model produces superior performance for pancreas segmentation. Compared with the baseline U-Net, the mean DSC, IoU, Precision, and Recall of our model achieve the growths of 2.34%, 3.38%, 0.35%, and 4.06%, respectively. In addition, all segmentation indicators of our network have the smallest standard deviation. The growth in these metrics suggests the modules we utilized can enhance pancreatic segmentation accuracy.

We qualitatively illustrate the segmentation outcomes of different network settings using three scenarios, namely Case 20, Case 57, and Case 68. Fig. 11 visualizes their 3D segmentation results. Specifically, the comparison between the columns (a) and (b) indicates that EfficientNetV2, as the encoder, outperforms U-Net in fitting the overall shape of the pancreas and is better equipped to handle complex situations with significant variations in pancreatic shape and size, leading to a more precise overall segmentation of the pancreas modality. When analyzing the columns (b) and (c), by combining the designed RMDA module with EfficientNetV2, certain pancreatic regions are segmented more accurately. Similarly, the introduction of RepVGG improves the recovery of pancreas detail information compared to using EfficientNetV2 alone, as evidenced by the contrast of the columns (b) and (d). As seen in the last two columns, our model performs more effectively when segmenting the three cases of the pancreas with varying morphologies.

Figure 11: Comparison of 3D prediction results of different network structures. (a) U-Net; (b) U-Net+EV2; (c) U-Net+EV2+RMDA; (d) U-Net+EV2+RepVGG; (e) Ours; (f) Ground truth

4.6 Model Re-Parameterization

In this section, we have accomplished re-parameterization on the trained model. As mentioned in Section 3.5, the structural re-parameterization technique makes it feasible to convert the RepVGG modules, into single path modules containing only 3×3 convolutions. Through this strategy, the model’s computational and storage overhead can be decreased while maintaining its performance, making it more suitable for deployment in resource constrained environments. Inspired by this technique, we have carried out re-parameterization on both the RMDA module and the EfficientNetV2. Specifically, the adjacent convolutional layers and BN layers are fused to improve the inference speed of our model. Although the primary aim of the BN layer is to accelerate network convergence, adding it increases memory consumption during inference, which slows down the inference speed. Therefore, it is necessary to integrate convolutional and BN layers.

Table 7 displays the comparison results of our network on the NIH dataset before and after re-parameterization. According to Table 7, it can be seen that both before and after the re-parameterization procedure, the values of the four assessment indicators for the model’s segmentation accuracy remain the same. Compared with the training phase, the inference phase of the model has fewer parameters and requires less computation, with a reduction of 0.2 million parameters and 0.54 G FLOPs. This improves the efficiency of network inference and lightens the pancreatic segmentation model. Compared to the trained model, which has an inference time of 0.077 s per slice, the inference time of the re-parameterized model has been reduced to 0.052 s per slice. This indicates that our model can assist doctors in performing fast and accurate pancreatic segmentation in CT images, alleviate the pressure on doctors in clinical practice, and improve the efficiency of disease diagnosis. Additionally, the model’s memory requirement for reasoning has decreased by 326 MB, from 954 to 628 MB. This not only significantly lowers the amount of memory used, but it also lessens the reliance of the pancreas segmentation model on resources and equipment, which is more beneficial for segmentation model deployment and resource conservation in clinical applications.

5  Discussion

Although our model has improved in terms of accuracy and efficiency for pancreatic segmentation, the prediction results are not ideal in some specific cases. This negatively impacts the mean segmentation accuracy. As shown in Fig. 12, despite the preprocessing, the contrast between the pancreas and surrounding tissues remains extremely low. Due to the blurred boundaries, and small and discontinuous pancreatic region, it is difficult for the model to accurately segment the target. Additionally, the model does not incorporate pancreatic information from the coronal and sagittal views during segmentation, which leads to under-segmentation when constructing the 3D segmentation results. Improving the connection between pancreatic slices and the extraction of spatial three-dimensional context will be the main goal of future research.

Figure 12: (a) Original CT image; (b) preprocessed CT image; (c) ground truth; (d) predicted result

6  Conclusion

In this work, we propose a novel approach for segmenting the pancreas from CT images. Firstly, we generate candidate regions according to position distribution to remove certain unnecessary backgrounds. Then, an EfficientNetV2 is employed as the encoder to capture the diverse and multi-level pancreatic features, improving the modeling capability of the pancreas’s complex morphology. The RMDA module is crafted to emphasize the useful pancreatic features. After that, RepVGG is introduced in the decoder to fuse features from deep and shallow layers and restore detailed information about the pancreas. Additionally, the trained model has been re-parameterized, which not only reduces the number of parameters and FLOPs but also accelerates inference speed and saves memory usage. The quantitative and qualitative comparison with advanced methods and classical networks proves the superiority and stability of our approach.

Acknowledgement: Not applicable.

Funding Statement: This work was supported by the Science and Technology Innovation Program of Hunan Province (Grant No. 2022RC1021), the Hunan Provincial Natural Science Foundation Project (Grant No. 2023JJ60124), the Changsha Natural Science Foundation Project (Grant No. kq2202265), and the key project of the Hunan Provincial of Education (Grant No. 22A0255).

Author Contributions: Panru Liang: Conceptualization, Methodology, Software, Writing—original draft, Writing—review & editing, Visualization, Formal analysis. Guojiang Xin: Writing—review & editing, Supervision, Methodology, Resources. Xiaolei Yi: Validation, Formal analysis, Conceptualization. Hao Liang: Supervision, Investigation, Funding acquisition. Changsong Ding: Supervision, Formal analysis, Funding acquisition. All authors reviewed the results and approved the final version of the manuscript.

Availability of Data and Materials: The NIH dataset is openly available in the Cancer Imaging Archive (TCIA) at https://www.cancerimagingarchive.net/collection/pancreas-ct/ (accessed on 08 February 2025). The MSD dataset is available from http://medicaldecathlon.com/ (accessed on 08 February 2025).

Ethics Approval: Not applicable.

Conflicts of Interest: The authors declare no conflicts of interest to report regarding the present study.

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