Adaptive Attention-Based U-Transnet Architecture with Optimized Metaheuristic Classifier for Early Liver Tumor Detection

The liver is one of the body's largest internal organ, located on the right side of the abdomen beneath the ribcage. Growth of liver cells in abnormal fashion above or within the liver can form a mass known as a liver tumor, signalling an underlying liver disease. The liver is susceptible to various diseases, including cirrhosis, hepatitis, and liver cancer [1]. Over the past two decades, the course of cirrhosis and liver cancer have collectively contributed to an estimated total of approximately 50 million deaths worldwide on an annual basis each year.

Metastatic liver cancer typically occurs when cancer spreads to the liver from other affected organs, or vice versa [2]. In such cases, the cancer cells present in the liver typically originate from the primary tumor site elsewhere in the body. Since this clearly indicates cancer progression, doctors usually classify it as advanced cancer of stage 4. Common cancers that frequently metastasize to the liver include colorectal, stomach, lung, pancreatic, breast, melanoma, and esophageal. In most instances, patients with liver metastases tend to develop tumors in both lobes of the liver [3].

1.1 Liver cancer: Cholangiocarcinoma and metastatic disease

Cholangiocarcinoma, a severe form of liver cancer, originates in the bile ducts. As the second most common primary hepatobiliary tumor, its global prevalence has been rising. Cholangiocarcinoma can be classified as intrahepatic (within the liver) or extrahepatic (outside the liver), but both types are collectively termed bile duct cancer due to their origin [4].

While numerous liver diseases exist, this study focuses on metastatic liver cancer and cholangiocarcinoma, both of which are life-threatening conditions.

1.2 Diagnostic challenges and advances in liver imaging

Computed Tomography (CT) is the preferred imaging modality for liver cancer due to its high lesion-to-liver contrast and non-ionising radiation benefits [5]. However, liver segmentation—a critical step in diagnosis—faces challenges such as:

•Scale diversity (varying tumour sizes)

•Complex backgrounds (overlapping tissues)

•Unclear tumour boundaries

•Low contrast in organ density

Accurate segmentation is essential for improving medical assessment and research outcomes [6]. Early and precise detection of cancer in the liver can definitely significantly reduce the rates of mortality and enhance the survival of the patient. Unfortunately, due to late diagnosis, liver disease remains the third leading cause of cancer-related deaths [7].

1.3 Limitations of current classification methods

Existing computerized tumor classification approaches often fail to accurately identify early-stage disease characteristics [8]. While deep learning (DL) networks show potential for classification, their computational demands make them impractical for time-sensitive clinical use. Alternatively, shape-based strategies leveraging historical data offer a promising solution [9].

1.4 The role of AI in liver segmentation

Deep learning through the use of AI can accelerate the formation of probabilistic segmentation models,  normally called as PSMs, assisting medical analysis. However, despite these advancements, clinical validation of AI-generated PSMs remains essential to ensure reliability [10]. Additionally, evaluating the clinical feasibility of automated liver segmentation—including the time required for clinically acceptable results—is crucial for real-world implementation [11].

Intensity-based strategies are widely recognised for their rapid implementation, particularly in zone growth, tiering, and threshold-based approaches [12]. However, these methods are predominantly semi-automatic, making them susceptible to noise and often requiring manual intervention when handling complex constraints. While they demonstrate significant improvements in segmentation accuracy when combined with machine learning (ML) techniques [13], most ML-based approaches still rely on manually designed features, which substantially limits their precision.

This limitation has helped in significant advancements not only in convolutional neural networks (CNNs) but also in other deep learning methods and the fully convolutional network (FCN) provides a prominent solution for image classification at pixel-level [14]. Also, the Deep learning techniques have been proved to be far more accurate than conventional ML-based methods. Yet both these architectures, the FCN and U-Net, have notable inherent drawbacks. The FCN-based approach many times fails to produce reliable results for liver segmentation both in case of single-network or cascaded training [15]. The primary reason is due to the fact that pixel-level analysis have a tendency to overlook subtle visual cues [16]. On the other hand, U-Net is efficient but its feature maps remains unrefined till the final convolution step. Additional challenges like vanishing gradients and repeated subsampling leading to the progressive degradation in features is found in deeper U-Net architectures which ultimately reduces output quality [17]. Category imbalance further compounds these issues, introducing errors and poorly defined boundaries in certain liver regions.

Although 3D networks benefit from enhanced z-axis information, memory constraints complicate slice selection, limiting their practicality [18]. While existing methods perform well in many automated liver segmentation scenarios, their accuracy and robustness remain insufficient for direct clinical application, hindering widespread adoption.

To address these challenges, our proposed U-TransNet introduces two major advancements compared to existing U-Net variants such as ResUNet and Attention-UNet. While ResUNet improves feature extraction through residual connections, it often suffers from increased model complexity and limited ability to capture long-range dependencies. Similarly, Attention-UNet enhances focus on salient regions but still relies heavily on local contextual information, which restricts its performance in cases of small or obscured liver lesions. In contrast, U-TransNet integrates the strengths of U-Net with Transformer-based global self-attention, allowing the model to simultaneously preserve fine structural details and capture long-range dependencies across the CT volumes. This dual capability enables more accurate boundary delineation, robust detection of small lesions, and improved generalization across diverse imaging conditions, thereby overcoming the primary shortcomings of existing U-Net variants.

Liver tumor detection through medical imaging, particularly in its early stages, faces significant challenges. Medical Imaging techniques like CT and MRI often introduce noise and artifacts that compromise the accuracy of segmentation and classification models. To address the issues of noise and artefacts in medical images, the proposed method incorporates advanced noise reduction algorithms using anisotropic diffusion filtering (refer to Figure 1). This method is better than the traditional filtering as it can suppress noise effectively still preserving the intricate structures of liver tissues that are important for accurate detection. The enhanced image clarity sets the foundation for more precise segmentation and classification, overcoming over-smoothing limitations seen in earlier approaches. To address the inaccurate segmentation of liver boundaries, the proposed method integrates an Attention-based U-TransNet, which performs the initial segmentation, capturing key liver regions. With its attention mechanism, the transformer layer refines this by focusing on the boundaries and critical regions where early lesions might occur, even if they are small or obscured by noise. The integration of these ensures both macro-level segmentation and fine boundary precision, making it more accurate for early detection than existing models. Thus, the proposed method robustly capture spatial hierarchies, provides long-range attention while handling coarse segmentation, identifying fine liver abnormalities and distinguishing them from nearby tissues.

tu_pian_21.png

Figure 1. Proposed flow diagram

Figure 2 presents the detailed system architecture of the proposed framework, illustrating how segmentation, feature extraction, and classification modules interact. To enhance classification accuracy and overcome the imbalance in early-stage disease detection, we propose a metaheuristic-optimised classification model. A support vector machine (SVM) classifier is tuned using the Whale Optimisation Algorithm (WOA). WOA improves on the standard grid or random search techniques by intelligently exploring the hyperparameter space, leading to optimal model performance. Furthermore, cost-sensitive learning is incorporated to handle class imbalance, assigning higher weights to minority (early-stage disease) samples, thus ensuring they are not under-represented during training. The classification process begins by using the fused feature vector from the earlier step. The SVM classifier is optimised using WOA, which iteratively searches for the best kernel parameters. The combination of noise-resilient preprocessing, hybrid segmentation with attention mechanisms, and metaheuristic optimisation-based classification promises higher segmentation precision, robust feature extraction, and improved classification of early liver disease, making it a significant advancement over current techniques.

tu_pian_22.png

Figure 2. Comprehensive system architecture showing the interaction between preprocessing, segmentation, feature extraction, and classification modules

3.1 Anisotropic diffusion filtering

Anisotropic diffusion (Perona–Malik diffusion) is a process in which the image noise is decreased without removing the essential details of the image content for proper image interpretation. Magnetic resonance images normally have noise, and therefore, to remove it without damaging image details, an anisotropic diffusion filter is proposed using Eq. (1).

$\partial I /_{\partial t}=\operatorname{div}(c(x, y, t) \nabla I)=\nabla_C . \nabla I+c(x, y, t) \Delta$    (1)

where I is the original image, the gradient operator is denoted by ∇, Laplacian operator is given by ∆, the divergence operator is donated by div(…) and the coefficient of diffusion is given by c(x,y,t).

In medical image segmentation, enhancing tissue contrast is critical for accurate analysis. As a first pre-processing step, we employ anisotropic diffusion filtering on the original CT images to reduce noise while preserving structural boundaries. This advanced filtering technique offers significant advantages over conventional Gaussian blurring by maintaining edge sharpness during the smoothing process. The method operates through an iterative diffusion process governed by the partial differential Eq. (2):

$\begin{aligned} I_{t+1} & =I_t+\lambda\left(c N_{x, y} \nabla_N\left(I_t\right)+c S_{x, y} \nabla_S\left(I_t\right)\right. \\ & \left.+c E_{x, y} \nabla_E\left(I_t\right)+c W_{x, y} \nabla_W\left(I_t\right)\right)\end{aligned}$     (2)

where the original image is I, the number of iterations carried out is given by t. The diffusion coefficients in the four directions (North (N), West (W), South (S) and East (E)) are indicated by cN,cW,cS, and cE respectively. The following Eqs. (3)-(6) are for anisotropic diffusion:

 $c N_{x, y}=\exp \left(-\left\|\nabla_N(I)\right\|^2 / k^2\right)$     (3)

$c S_{x, y}=\exp \left(-\left\|\nabla_S(I)\right\|^2 / k^2\right)$      (4)

$c E_{x, y}=\exp \left(-\left\|\nabla_E(I)\right\|^2 / k^2\right)$     (5)

$c W_{x, y}=\exp \left(-\left\|\nabla_W(I)\right\|^2 / k^2\right)$     (6)

In anisotropic diffusion, the k and λ are two parameters that regulate the level of smoothing, with larger values leading to smoother images, but the edges are not retained as much.

To evaluate how robust the anisotropic diffusion preprocessing is, we performed a sensitivity analysis by testing different values of the edge-stopping parameter (k), the time step (λ), and the number of iterations (N). Specifically, we tested k values of 5, 10, 20, and 40; λ values of 0.05, 0.10, 0.15, and 0.25; and N values of 5, 10, 20, and 40. For each combination of these parameters, we measured segmentation performance using the Dice coefficient, Intersection over Union (IoU), and Mean Squared Error (MSE). Key findings from this analysis are discussed in Section 4.4.

3.2 Anisotropic diffusion filtering

Medical image segmentation typically processes 3D volumetric data x ∈ ℝ^(D×H×W×C). Here spatial dimensions are represented as D, H, W and channel depth is donated by C which is used to generate pixel-wise label maps of matching resolution. Conventional U-Net architectures process this input through sequential encoding and decoding stages, extracting hierarchical features while maintaining spatial resolution. However, these traditional approaches often struggle to capture extensive contextual relationships across medical volumes. Our proposed architecture addresses this limitation by strategically incorporating attention mechanisms throughout the U-shaped network’s encoder and decoder pathways. The enhanced design combines convolutional layers' local feature extraction capabilities with transformer modules' global self-attention mechanisms. This synergistic integration improves modelling of anatomical relationships across different scales while preserving precise spatial details, ultimately achieving more accurate segmentation of complex tissue structures in medical imaging.

Image sequentialization: For 3D medical image processing, we implement volume tokenization by partitioning the input tensor x$\in $ℝ^D×H×W×C into non-overlapping cubic patches of size P×P×P. This transformation reshapes the volumetric data into a sequence of flattened patch vectors $\left\{x_p^i \in \mathbb{R}^{\wedge^{\mathrm{P}^3} \cdot \mathrm{C}} \mid \mathrm{i}=1, \ldots, \mathrm{~N}\right\}$, where N = (D×H×W)/P³ represents both the total number of patches and the sequence length for subsequent processing. Following established practices in vision transformer architectures, this pacification step serves as the fundamental operation for converting the spatial 3D medical image into a sequence suitable for transformer-based processing, while maintaining all original voxel information through the flattened vector representation.

Patch embedding: Our patch embedding process transforms the vectorised image patches bold x to the p into a d-dimensional latent space through a trainable in-line projection, where p denotes patch size and c represents input channels. To preserve critical spatial information, we augment these patch embeddings with learned positional encodings formulated as Eq. (7):

${{z}_{0}}=\left[ x_{1}^{p}E;x_{2}^{p}E;\cdots ;x_{N}^{p}E \right]+{{E}^{pos}}$     (7)

where, $\mathbf{E}\in {{\mathbb{R}}^{\left( {{P}^{3}}\cdot C \right)\times {{d}_{enc}}}}$ is the patch embedding projection, and $\mathbf{E}^{p o s} \in \mathbb{R}^{N \times d_{\mathrm{enc}}}$ denotes the position embedding.

A standard Transformer layer contains two primary components: The first is Multi-head Self-Attention mechanism (MSA) and second is Multi-Layer Perceptron block (MLP) which are given using Eqs. (2) and (3). Consequently, the l-th layer output zₗ is computed using Eqs. (8) and (9) as:

$\mathbf{z}_{\ell }^{\text{ }\!\!'\!\!\text{ }}=\text{MSA}\left( \text{LN}\left( {{\mathbf{z}}_{\ell -1}} \right) \right)+{{\mathbf{z}}_{\ell -1}}$   (8)

${{\mathbf{z}}_{\ell }}=\text{MLP}\left( \text{LN}\left( \mathbf{z}_{\ell }^{\text{ }\!\!'\!\!\text{ }} \right) \right)+\mathbf{z}_{\ell }^{\text{ }\!\!'\!\!\text{ }},$   (9)

Our framework employs layer normalization (LN(⋅)) to process the encoded image representation zₗ. Departing from conventional pixel-wise segmentation, we reformulate medical image analysis as a mask classification task. Central to our approach are learnable d-dimensional 'organ query' vectors, each representing potential anatomical structures in a given image. Using a fixed set of N organ queries (where N ≫ K, with K being the true number of target classes), the model partitions the image into N candidate regions before assigning appropriate class labels. This design choice, inspired by recent advances in set prediction architectures, deliberately over-generates candidate regions to reduce false negative detections while maintaining computational efficiency. Consider d_dec as the dimension of the object queries, the dot product between the initial green queries ${{\mathbf{P}}^{0}}\in {{\mathbb{R}}^{N\times {{d}_{dec}}}}$ and the embedding the last block feature of the U-Net as $\mathbf{F}\in {{\mathbb{R}}^{D\times H\times W\times {{d}_{dec}}}}$that computes the coarse predicted segmentation map: With d_dec as the dimension of the object queries predicted coarse segmentation map can be calculated by the dot product of ${{\mathbf{P}}^{0}}\in {{\mathbb{R}}^{N\times {{d}_{dec}}}}$(the initial organ queries) and $\mathbf{F}\in {{\mathbb{R}}^{D\times H\times W\times {{d}_{dec}}}}\text{ }\!\!~\!\!\text{ }$(U-Net last block feature ) as in Eq. (10):

${{\mathbf{Z}}^{0}}=g\left( {{\mathbf{P}}^{0}}\times {{\mathbf{F}}^{\top }} \right)$    (10)

The activation function g(⋅) combines sigmoid nonlinearity with a 0.5 threshold for binarization, chosen over SoftMax to accommodate overlapping classes in our datasets. The Transformer decoder progressively refines organ queries to improve the initial prediction through multiple layers, each comprising: (1) a self-attention mechanism (MSA block) that captures inter-query relationships, and (2) a cross-attention module that integrates localized, multi-scale CNN features. This dual-path design synergistically combines the Transformer's global contextual understanding with CNN's precise spatial localization capabilities, enabling comprehensive feature representation while preserving anatomical details. The cross-attention mechanism specifically allows each query to dynamically attend to relevant spatial regions in the CNN feature maps, facilitating accurate boundary delineation for overlapping structures.

Our method includes simultaneous training of both decoders namely CNN and Transformer. At the t-th layer $\mathrm{P}^t \in \mathbb{R}^{N \times d_{\text {dec }}}$ represent the refined organ queries and concurrently the U-net feature at intermediate stage is mapped to a d_dec-dimensional feature space represented by F to simplify cross-attention computations. Also, multi-scale CNN topographies can be anticipated as $\mathcal{F}\in {{\mathbb{R}}^{\left( {{D}_{t}}{{H}_{t}}{{W}_{t}} \right)\times {{d}_{dec}}}}$, when the number of upsampling blocks line up with the number of Transformer decoder layers. In this ${{D}_{t}},{{H}_{I}}$, and ${{W}_{I}}$ represents t-th upsampling block spatial dimensions in the feature map. Further, the organ queries at $t+1$-th layer are refined by cross-attention with Eq. (11):

${{\mathbf{P}}^{\nu +1}}={{\mathbf{P}}^{l}}+\text{Softmax}\left( \left( \mathbf{{P}'}{{\mathbf{w}}_{q}} \right){{\left( {{\mathcal{P}}^{\nu }}{{\mathbf{w}}_{k}} \right)}^{\top }} \right)\times \mathcal{F}{{\mathbf{w}}_{v}}$     (11)

where the r-th query topographies are updated using linear projection so as to obtain queries for the subsequent layers by means of the weight matrix $w_q \in R^{\left(d_{d_e} e^{\mathrm{i} \times d_4}\right.}$. The U-Net feature, F, is likewise restructured into keys and values with ${{w}_{k}}\in {{R}^{{{d}_{d}}_{es}{{x}_{k}}}}$ and ${{w}_{v}}\in {{R}^{{{d}_{d}}_{oc}{{x}_{d}}}}$ that are parametric weight matrices. A residual path is used for this restructuring of P following earlier works [25]. Next, a attention refinement as coarse-to-fine is attempted to improve the segmentation accuracy.

Our approach incorporates a coarse-to-fine refinement strategy through a novel mask attention module within the Transformer decoder, specifically designed to enhance small target segmentation in medical images. The module leverages coarse predictions from previous stages to guide subsequent refinements by constraining the cross-attention method to focus primarily on probable foreground regions. This attention masking operation, formulated as A' = A ⊙ M + A (where A is the original attention map and M is the binarized mask from the preceding stage), progressively reduces background interference while preserving the Transformer's global contextual understanding. The iterative application of this mechanism enables precise boundary delineation, particularly for small anatomical structures, by successively refining the region of interest while maintaining computational efficiency through spatially-constrained attention computation. This dual advantage of focused local refinement and preserved global context represents a significant improvement over conventional coarse-to-fine approaches in medical image segmentation.

Concretely, the coarse level mask prediction and the organ queries are initially set as Z⁰ and P⁰ respectively followed by the iterative refinement process. At the r-th iteration coarse prediction Z' and the current organ query features P^' are used to calculate the masked cross-attention for refinement of P⁽⁺¹⁾ for the iterations in the later stages. The calculation includes the current coarse prediction Z^I into the affinity matrix as specified in Eqs. (12) and (13):

$\begin{gathered}\mathrm{P}^{\mathrm{N}+1}=\mathrm{P}^{\mathrm{N}}+ \operatorname{Softmax}\left(\left(\mathrm{P}^r \mathrm{w}_q\right)\left(\mathcal{F} \mathrm{w}_k\right)^{\top}+h\left(\mathrm{Z}^r\right)\right) \times \mathcal{F} \mathrm{w}_e\end{gathered}$      (12)

where,

$h\left(\mathbf{Z}^{\prime}(i, j, s)\right)= \begin{cases}0 & \text { if } \mathbf{Z}^l(i, j, s)=1 \\ -\infty & \text { otherwise }\end{cases}$   (13)

The coordinate indices (i,j,s) define the spatial constraints for our cross-attention mechanism, forcing it to operate exclusively within foreground regions while completely suppressing background interference. Through an iterative update scheme that simultaneously optimizes both organ queries and their associated mask predictions, our Transformer decoder progressively enhances segmentation accuracy across multiple refinement stages. As detailed in Algorithm 1, this cyclic process continues until completion at iteration t=T, where T corresponds precisely to the total number of decoder layers, ensuring comprehensive feature integration throughout the network's depth.

In Fine segmentation updated organ queries ${{\text{P}}^{T}}$ is obtained after decoding the final iteration which can be mapped to the final refined binarized segmentation map ${{\text{Z}}^{T}}$ with the dot product of U-Net's last block feature $\text{F}$. Each binarized mask is linked with one semantic class using a linear layer of weight matrices. ${{\text{w}}_{fc}}\in {{\mathbb{R}}^{d\times K}}$ is used to project the refined organ embedding ${{\text{P}}^{T}}$ to the output class logits $\text{O}\in {{\mathbb{R}}^{N\times K}}$ using the Eqs. (14) and (15):

$\text{O}={{\text{P}}^{T}}{{\text{w}}_{{{f}_{c}}}}$     (14)

$\overset{}{\mathop{y}}\,=argma{{x}_{k=0,1,\ldots ,K-1}}O$     (15)

where k is the label index. The final class labels associated with the refined predicted masks ${{\text{Z}}^{T}}$ is $\hat{y} \in \mathbb{R}^N$.

Transformer hyperparameters: The Transformer module within U-TransNet was implemented with 4 encoder–decoder layers. Each multi-head self-attention (MSA) block employed 8 attention heads, each with an embedding dimension of 64, yielding a total hidden size of 512. The feed-forward network within each Transformer block had an intermediate dimension of 2048 with GELU activation. Positional encodings were learned and added to the patch embeddings of dimension 128 before entering the encoder. Layer normalization was applied before each attention and feed-forward block. Dropout with a probability of 0.1 was used throughout to reduce overfitting. These settings were selected after pilot hyperparameter tuning to balance segmentation accuracy with computational efficiency.

3.3 SVM with WOA

Whale Optimization Algorithm (WOA) is a new type of metaheuristic intelligent optimization algorithm proposed by Mirjalili and Lewis. It searches for the best possible solution by mimicking the ‘‘spiral bubble network’’ search strategy that is used humpback whales. The algorithm has the advantages of few adjustment parameters, simple operation, and easy understanding. The WOA mainly involves the following optimization steps: surround prey, spiral predation, and search for prey.

During cooperative hunting, humpback whales employ a strategic encircling behavior to capture prey. Once an individual identifies the optimal hunting position, the entire pod converges toward this location. The overall process is mathematically modeled in our optimization algorithm with the help of position update equations given as Eqs. (16) and (17), that controls the iterative refinement of search agents in the specified solution space.

$D=\left| CM\text{*}\left( t \right)-M\left( t \right) \right|$    (16)

$M\left( t+1 \right)=M\text{*}\left( t \right)-A\cdot D$      (17)

The optimization framework that is proposed has the position vector of the best solution as M*(t). This position vector is found by iteration t and is dynamically updated whenever superior solution is found. The position of current solution at iteration t is denoted by M(t) and the Euclidean distance (D) is calculated over each iteration as difference between M*(t) and M(t). Eqs. (18) and (19) are for the adaptive coefficient vector A that governs the magnitude and C gives direction of solution updates. These coefficients enable balanced exploration-exploitation tradeoffs throughout the optimization process.

$A=2a\cdot r1-a$     (18)

$C=2r2$     (19)

The parameter a given as $a\text{ }\!\!~\!\!\text{ }=\frac{2t}{maxgen}$, where the current iteration is t and the maximum allowed iterations are maxgen, controls the search intensity decreasing linearly from maximum of 2 to minimum of 0 across iterations carried out. This decay schedule balances exploration and exploitation. Additionally, r₁ and r₂ are randomisation vectors whose elements are uniformly distributed in [0,1], introducing stochastic variability to the search process.

During the search process whale is searcher and prey is required optimum solutiom. As the searcher gradually reaches the optimal solution then variable a decreases accordingly. Also, the coefficient A reduces linearly with the variable a according to Eq. (18). When A is [−1, 1] then subsequent position of the new searcher will be between the current position and the optimal position (optimum solution). The searcher will reach the optimal solution in a spiral way, updating its position according to Eq. (19), and gradually reach to the desired solution.

As the search agent converges toward the optimal solution, the control parameter' ‘a’ decreases linearly with iterations, causing coefficient A to similarly diminish. When A falls within [−1,1], the agent enters an exploitation phase where its next position is constrained to the convex space between its current location and the global optimum. For final convergence, the agent follows a logarithmic spiral trajectory that simultaneously maintains directional momentum toward the solution while progressively tightening the search radius. This dual-phase update strategy combines targeted local search with controlled oscillatory movements, ensuring both solution accuracy and convergence stability throughout the optimization process using Eq. (20).

$M\left( t+1 \right)={D}'\cdot eblcos\left( 2\pi l \right)+M\text{*}\left( t \right)$      (20)

where, ${D}'\text{ }\!\!~\!\!\text{ }=\text{ }\!\!~\!\!\text{ }\left| M\text{* }\!\!~\!\!\text{ }333\text{ }\!\!~\!\!\text{ }\left( t \right)\text{ }\!\!~\!\!\text{ }-\text{ }\!\!~\!\!\text{ }M\left( t \right) \right|$ specify the error in i-th searcher and optimal solution at current position; constant b defines logarithmic spiral shape, and random number l has the range [−1,1]. Humpback whales constantly narrow the search range while moving in spiral manner. Therefore with spiral mode and 50% probability of shifting is assumed and the searcher position is updated according to Eqs. (21) and (22).

$M\left( t+1 \right)=M\text{*}\left( t \right)-A\cdot D$      (21)

$M\left( t+1 \right)=D0\cdot eblcos\left( 2\pi l \right)+M\text{*}\left( t \right)$      (22)

where, ${D}'=\left| M\text{*}\left( t \right)-M\left( t \right) \right|$ is the error between the current optimal solution and the i-th searcher.

Random search capability of Humpback whales can enhance global search capabilities of algorithms. The updated Eq. (23) can be used for searching the solution randomly

$M\left( t+1 \right)={{M}_{rand}}\left( t \right)-A\left| C{{M}_{rand}}\left( t \right)-M\left( t \right) \right|$    (23)

where,$\text{ }\!\!~\!\!\text{ }{{M}_{rand}}$ is a position vector randomly selected from the 353 current population (representing a random whale).

SVM is a novel machine learning approach, proposed by Corinna Cortes and Vapnik in the year 1995, is a generalized linear classifier used for binary classification of data in a supervised learning mode. Over traditional neural networks, SVM has advantage of robustness, versatility, computational simplicity, effectiveness and theoretical support. On the contrary, when it is used for regression prediction or pattern recognition, no uniform standard method is available for the selection of its parameters c and g. In SVM fitting function, a minimum optimization problem and the penalty parameter c is introduced. The parameter c is used to fine-tune the objective function to achieve the balance between the minimum relaxation factor and maximum interval, that is, when the sample data is classified incorrectly, the larger the value of the parameter c, the more complex the algorithm will be, thus classification errors will not occur. However, if the parameter c is set too high, the algorithm’s generalization ability will be weakened, and the empirical risk may not change. On the contrary, a smaller value of parameter c reduces the complexity of the algorithm but increases the algorithm’s empirical risk. As a result, it is necessary to use an intelligent optimization algorithm to find a suitable parameter c, so that the support vector machine can perform better.

Coupling of segmentation and classification: The WOA-based SVM optimization is performed independently of the segmentation network training, i.e., the optimization process is decoupled from the U-TransNet training. First, the segmentation module generates complete binary masks of the liver tumor regions. From these segmentation outputs, we extract shape, texture, and intensity-based features that serve as inputs to the SVM classifier. Thus, the full segmentation output is used to drive feature extraction and classification. The WOA algorithm optimizes the SVM parameters (kernel type, C, and Γ) to maximize classification accuracy on the validation set. This design ensures that improvements in segmentation quality directly contribute to better classification, while keeping the optimization stages modular.