The renal dynamic imaging data used in this study were obtained from the Department of Nuclear Medicine, Shaanxi Provincial Cancer Hospital, and were used after hospital approval for anonymization. The data format is a static multi-frame DICOM sequence image format, which contains the changes in renal perfusion and excretion under different time phases. In order to simplify the experimental process, the images of 3 - 4 key time phases (optimal contrast time phases) were mainly selected for the segmentation study in this paper.

The criteria for selecting key temporal phases in this study are shown in Figure 1 . As for the experimental sample size, data from 100 patients were collected, and about 3 - 4 suitable single-frame images were selected for each patient, which ultimately resulted in about 300 - 400 images that could be used for training and testing. In order to ensure the accuracy of segmentation annotation, all kidney regions were manually labeled under the guidance of a professional physician to form the Ground Truth (GT).

The renal dynamic imaging data used in this study were stored in DICOM standard format, and its SPECT image data can be represented as a four-dimensional matrix X ∈ (W, H, C, F), in which each dimension characterizes the image’s lateral resolution, longitudinal resolution, the number of channels, and the number of frames of the time series, respectively. It contains a total of 90 frames of image information. The first 30 frames are fast dynamic imaging data with acquisition parameters set to 2 s/frame and continuous scanning for 1 minute, and the last 60 frames are slow dynamic imaging data with acquisition parameters set to 20 s/frame and continuous scanning for 20 minutes.

This study mainly analyzes the slow dynamic imaging data, and in order to perform the semantic segmentation task, a single-frame 2D image needs to be extracted from the time-series image. By processing the renal dynamic images of 100 patients, a total of about 400 single-frame images in PNG format with 64 × 64 resolution were obtained. The annotation of all images after denoising and zooming was done under the guidance of professional physicians and these annotation data will be used for network parameter optimization and segmentation performance evaluation.

In the model training stage, the data preprocessing process is shown in Figure 2 . Specifically, the study first scales the original images uniformly to 224 × 224 resolution and manually annotates them, followed by expanding the samples using spatial transformation (including mirror flip, random rotation, etc.) techniques [3] . By constructing a standardized training set and validation set, not only is the data scale effectively increased, but the generalization performance of the model is also significantly improved.

The allocation ratio of this study for the dataset is 60% training set, 20% validation set, and 20% test set. At the end of the model training, the validation set is used to manually adjust the hyper-parameters of the model to get the final network model, and finally, the test set is used to evaluate the final effect of the model. Images from the same patient (with different phases) are not allowed to appear in different sets.

UNet was proposed by Ronneberger et al. in 2015 and designed for medical image segmentation, which is characterized by a symmetric encoder-decoder structure and jump connections.

The classical UNet consists of two main parts, the encoder (down-sampled branch) and the decoder (up-sampled branch), and splices the features in the corresponding layer of the encoder with the corresponding scales in the decoder through jump connections. The structure of the network is shown in 3. This allows the network to fully integrate the low-level spatial information with the high-level semantic information in the process of up-sampling, thus improving the segmentation accuracy.

As shown in Figure 3 , the UNet network architecture adopts the classical encoder-decoder structure. The encoder module implements feature extraction by stacking convolutional layers, batch normalization layers, and maximum pooling layers and gradually captures high-level semantic information during downsampling; accordingly, the decoder module consists of multiple up-sampling operations (or transposed convolution) with convolutional units and reconstructs the spatial details through level-by-level up-sampling. In particular, the network introduces a jump-joining mechanism in the decoding process, which cascades and fuses the features of each layer of the encoder with the corresponding decoding layer, thus effectively preserving the fine-grained feature information.

The output layer of the network uses a 1 × 1 convolutional kernel for feature dimensionality reduction to compress the number of channels to the number of target categories (this study contains 3 categories: left kidney, right kidney, and background region). Eventually, the model outputs a segmentation result map that is consistent with the size of the input image, realizing accurate classification at the pixel level.

The traditional UNet model mainly consists of a simple convolutional layer and a pooling layer and usually uses a 3 × 3 convolutional kernel for feature extraction. The architecture includes an encoder (down-sampling part) and a decoder (up-sampling part), where the encoder gradually reduces the spatial dimensions of the feature maps, and the decoder gradually restores these dimensions. The feature maps are passed directly to the decoder via jump connections to help recover detailed information. However, due to the small number of convolutional layers, the feature extraction capability of traditional UNet is limited and suitable for handling relatively simple tasks, which mainly rely on the network depth and the number of convolutional layers to extract features.

The UNet model proposed in this study uses the VGG16 network as a feature extractor in the encoder part.VGG16 is a deep convolutional neural network with multiple convolutional layers and pooling layers, which is capable of extracting richer features, and its network structure is shown in Figure 4 . Compared with the simple convolutional layers of traditional UNet, VGG16 has a stronger feature extraction capability and is able to capture more complex image features. By using the pre-trained weights of VGG for migration learning, the model performance is significantly improved. The UNet architecture based on the VGG16 backbone network is capable of extracting multi-level features and is suitable for handling more complex image segmentation tasks, while the multiple convolutional layers of VGG16 capture richer contextual information and detailed features.

Attention mechanisms originally originated from the field of natural language processing and were later introduced into computer vision tasks. In the field of image segmentation, attention mechanisms are divided into three main categories: spatial attention, channel attention, and hybrid attention.

Spatial attention focuses on learning the importance of spatial regions of an image, such as non-local Neural Networks [5] and Spatial Attention Modules [6] . Channel attention, on the other hand, focuses on the inter-channel relationships of feature maps, and representative works include Squeeze-and-Excitation Networks (SENet) [7] . Hybrid attention considers both spatial and channel dimensions, such as the Convolutional Block Attention Module (CBAM) [6] and Efficient Channel Attention (ECA) [8] .

Traditional attention mechanisms usually focus on a single dimension (e.g., channel or spatial dimension) and cannot fully capture the complex relationships in the feature map. In medical image segmentation tasks, the target structures often have complex morphology and fuzzy boundaries, requiring the model to focus on feature relationships in multiple dimensions simultaneously.

Based on this, this study proposes a triple-attention mechanism to model feature relationships simultaneously from three orthogonal dimensions: Channel-Width dimension, Height-Channel dimension, and Height-Width dimension, which achieves an all-round perception of the feature map.

The working principle of the triple attention mechanism can be seen in Figure 5 .

1) Channel-width attention: Transform the input tensor from [B, C, H, W] to [B, H, C, W] by permute operation so that the attention gate pays attention to the relationship between the channel and width dimensions

2) Height-channel attention: transform the input tensor to [B, W, H, C] through the permute operation so that the attention gate focuses on the relationship between the height and channel dimensions.

3) Height-width attention: Apply directly on the original input [B, C, H, W] to focus on the feature distribution of the spatial dimension.

The results of the three dimensions of attention are averaged and fused to obtain a fully enhanced feature representation. This design enables the model to capture feature relationships from three different dimensions simultaneously, which significantly improves the feature representation capability and is particularly suitable for dealing with complex structures and fuzzy boundaries in medical images.

In this study, the optimization strategy of combining depth-separable convolution with mixed-accuracy training is adopted. Depth separable convolution significantly reduces the parameter scale and computational complexity while ensuring the model performance by decomposing the standard convolution into two independent operations: depth convolution and point-by-point convolution. Experiments show that the method can reduce about 70% of the computation.

During the training process, we innovatively introduce a mixed-precision training mechanism, which achieves training acceleration by dynamically allocating the computational tasks of 16-bit floating point (FP16) and 32-bit floating point (FP32). Among them, FP16 is mainly used to reduce memory consumption and improve computational efficiency, while FP32 precision is retained for critical computation to ensure numerical stability. This mixed-precision strategy can increase the training speed by about 40% while maintaining model convergence stability.

By organically combining the above two techniques, this study achieves a significant effect of reducing the computational resource consumption by more than 50% and improving the training efficiency by 35% while ensuring segmentation accuracy. This optimization scheme is particularly suitable for task scenarios such as medical image segmentation that require processing high-resolution images.

The TAMUNet network model is shown in Figure 6 . From the figure, it can be seen that the TAMUNet network follows the encoder-decoder structure of the classical UNet, but there are many changes, choosing VGG16 as the backbone network for feature extraction, using depth-separable convolution instead of the standard convolution to reduce the number of references and the computational complexity; and adding triple-attention mechanism at the jump connection to enhance the feature representation capability and focus on the multidimensional feature relationships.

The network model is trained with a freeze training strategy for the first 50 Epochs. This is because the features extracted from the feature extraction part of the neural network backbone are generic, and freezing this part can improve the training efficiency and prevent the weights from being corrupted. In the freezing phase, the backbone of the model remains unchanged, and only the feature extraction network is fine-tuned, so the memory footprint is small.

After entering the unfreezing phase, the backbone of the model will no longer be frozen, and the feature extraction network will change accordingly, at which time the memory footprint increases, and all parameters in the network are updated.

In the training task, Dice loss is used as the loss function of the model for optimization. The choice of Dice loss is usually based on its high fit with the task characteristics. Dice loss directly optimizes the segmentation objective: maximization of the overlap region. The core metrics of the segmentation task (e.g., Dice coefficients, IoUs) directly measure the overlap region of the predicted and the real masks. The Dice loss is consistent with the evaluation metrics, and there is no need to optimize the proxy objective indirectly. Boundaries are often unclear in nuclear medicine images, and the gradient computation of Dice loss relies on both predicted and true masks, which is more stable to fuzzy boundaries.

As shown in Table 1 , these are the hardware devices used in this research experiment and some training parameter Settings of the algorithm.

In the classification task of the semantic segmentation model, the prediction results can be categorized into four basic cases: true positive examples (TP), false positive examples (FP), true negative examples (TN), and false negative examples (FN). Specifically, TP denotes the samples that the model correctly predicts as positive cases, FP is the negative samples that the model misjudges as positive cases, FN refers to the positive case samples that the model fails to recognize, and TN is the negative samples that the model correctly judges.

An important metric for assessing the performance of the model is the mean Intersection over Union (mIoU), which is calculated as the average of the ratio of the intersection and concatenation of the prediction results and the true values for each category. Mathematically, mIoU can be expressed as the ratio of true cases (TP) to the sum of prediction error (FP+FN) and true cases, i.e., IoU = TP/(FP + FN + TP). This metric can effectively reflect the accuracy of the model in pixel-level classification tasks.

$mIoU=\frac{1}{k+1}\underset{i=0}{\overset{k}{{\displaystyle \sum }}}\frac{p_{ii}}{{{\displaystyle \sum }}_{j=0}^k{p}_{ij}+{{\displaystyle \sum }}_{j=0}^k{p}_{ji}-p_{ii}}$

$p_{ij}$ denotes the number of true values of i that are predicted to be j. K + 1 is the number of categories (including the empty category). $p_{ii}$ is the true number, $p_{ij}$ and $p_{ji}$ denote false positive and false negative, respectively. mIoU is generally computed based on classes, and the global-based evaluation is obtained by accumulating the IOUs of each class after computation and then averaging them. Larger values represent better segmentation accuracy.

Mean Pixel Accuracy (mPA): the proportion of the number of correctly categorized pixels within each class, after which the average of all classes is sought. That is, PA = (TP + TN)/(FP + FN + TP + TN).

$mPA=\frac{1}{k+1}\underset{i=0}{\overset{k}{{\displaystyle \sum }}}\frac{p_{ii}}{{{\displaystyle \sum }}_{j=0}^k{p}_{ij}}$

In semantic segmentation model evaluation, Precision and Recall are two key metrics. Precision reflects the accuracy of the positive samples in the prediction results, which is expressed as the category pixel accuracy (CPA), Precision = TP/(TP + FP) or TN/(TN + FN), and is used to measure the probability of correct prediction for a certain category. Recall, on the other hand, characterizes how well the model covers the true positive sample and is calculated as Recall = TP/(TP + FN) or TN/(TN + FP).

Accuracy, as a global evaluation metric, characterizes the proportion of correct predictions to the total samples, accuracy = (TP + TN)/(TP + TN + FP + FN), which is equivalent to pixel accuracy (PA). However, in the case of uneven sample distribution, a single reliance on accuracy may lead to assessment bias, and thus, a combination of other metrics is needed for a comprehensive evaluation of the model.

In order to verify the effectiveness of the proposed model, the following baseline methods are selected for comparison experiments in this study:

Threshold Segmentation Method: as a traditional method in the field of image segmentation, it realizes segmentation by setting a threshold combined with post-processing. Although it has the advantage of simple computation, it is often difficult to obtain ideal results when dealing with complex images.

Standard UNet [9] : as a benchmark model in the field of medical image segmentation, this architecture has become the de facto standard for all kinds of medical image segmentation tasks, and its encoder-decoder structure provides an important reference for subsequent research.

Attention UNet [10] (AttUNet): this model innovatively introduces the attention gating mechanism on the basis of UNet, optimizes the jump connections through the attention gate, effectively solves the noise problem in medical images, and is one of the earlier models that apply the attention mechanism to medical image segmentation.

The method in this paper (TAMUNet): the improved model proposed in this study adopts the VGG network as the encoder feature extractor and introduces a triple attention module at the jump connection, which significantly improves the segmentation accuracy by adaptively adjusting the feature channel weights. The model realizes the effective integration of feature extraction and attention mechanism while maintaining the basic architecture of UNet.

From Table 2 , it can be seen that this paper’s method has obvious improvement in core indexes such as mPA and mIoU compared with other models. Meanwhile, compared with the traditional method, which is prone to wrong segmentation in the edge region, this paper’s method can visually fit the kidney contour better, indicating that the introduction of the VGG16 backbone network as well as the non-local triple attention mechanism, positively helps the segmentation performance.

AttUNet only increases the inference time by a small amount compared to the original UNet. The TAMUNet triple attention mechanism increases the inference time accordingly due to the need to compute the attention in three dimensions (channel-width, height-channel, and height-width), but reduces the computation amount to a certain extent due to the use of ZPool for feature compression. In practice, if the inference speed requirement is high, partial attention gates can be selectively disabled, and the use of the complete triple attention mechanism can be weighed according to the specific task requirements and hardware conditions.

In Figure 7 , some examples from renal dynamic imaging are used to demonstrate the actual segmentation effect of the model. From the figure, it can be seen that the TAMUNet model constructed in this study achieves good segmentation results under different conditions, while the segmentation results of AttUNet and standard UNet are less satisfactory when the development is not clear (the second and the third renal images) and when the background noise is serious and the contrast is low (the fourth renal image). It can be seen that the model performs well on injured or postoperatively changed kidneys.

The experimental results show that the TAMUNet segmentation model exhibits excellent performance in kidney dynamic image processing, and its segmentation results are highly consistent with the real labeling. This effect is mainly attributed to the designed non-local triple attention module, which effectively suppresses the background noise interference and enhances the attention to the target region of the kidney through the adaptive feature weighting mechanism, and finally realizes the automated and accurate segmentation of the double kidney region.