BTS-NEUNET: Brain Tissue Segmentation via White Shark Optimized Features Based Nested U-Net

In this section, the T1W and T2W MRI images of the brain are pre-processed using the WTBB filter and the PWI, and DWI images of the brain are pre-processed using the CTBAGN filter to enhance the quality of the images.

In this section, the denoised MRI images are processed using DenseGoogLeNet for feature extraction. It is a combination of DenseNet and an inception model from GoogLeNet. It uses a hierarchical feature-extraction approach, combined with effective feature reuse, to extract relevant characteristics from images. DenseNet is a cutting-edge CNN architecture for visual object detection that uses fewer parameters. With a few key differences, DenseNet and ResNet are relatively comparable. The architecture of DenseGoogLeNet is shown in Fig. 2.

Fig. 2.

Architecture of DenseGoogLeNet.

The output layers (i^th) are often calculated using conventional CNNs, applying the output of the previous layer Y_i−1 to a non-linear transformation R_i(.). (6) Yi=Ri(Yi−1) {Y_i} = {R_i}({Y_{i - 1}})

The layer output functionality maps are concatenated by DenseNets rather than summarizing them with the inputs. To enhance information flow across layers, DenseNet offers a straightforward approach: The features of the previous layers' inputs are transmitted to the i^th layer. The equation (6) is then changed to: (7) Yi=Ri(Y0,Y1,Y2,…,Yi−1) {Y_i} = {R_i}\left[ {({Y_0},{Y_1},{Y_2}, \ldots,{Y_{i - 1}})} \right] where [Y₀, Y₁, Y₂, … . . , Y_i−1] is a single tensor created by integrating the maps produced by the previous layers. The GoogLeNet, on the other hand, extracts deep features and widens the convolutional network to enhance training results.

The model parameters are significantly reduced by two auxiliary classifiers, dimensionality reduction, and mapping using a 1 × 1 convolutional kernel and a fully connected layer instead of the average pooling layer. The model was created to classify the original image in the domain (𝒟₁). The dataset of the labelled images is shown as (8) D1={xj,yj}j=1106 {{\cal D}_1} = \{{x_j},{y_j}\}_{j = 1}^{{{10}^6}} where y_j ∈ {1, … … 1000} for class labels. The transfer learning concept can be applied to a deep CNN method to learn image features from a different domain. This technique adapts GoogLeNet to our application domain (𝒟₂) using transfer learning methods. GoogLeNet transfer learning is the concept behind the suggested application. (9) D2={xj,yj}j=13064 {{\cal D}_2} = \{{x_j},{y_j}\}_{j = 1}^{3064} where the class labels, y_j ∈ {1,2,3}, represent the segmentation process. The CBMIR system uses pooling-layer activations to represent image features. An image's feature vector, x_i, is represented as (10) H(xi)∈H1024 H({x_i}) \in {H^{1024}}

The output of the feature-extraction functions is represented by H applied to input x_i. H¹⁰²⁴ represents the output in a vector with 1024 dimensions. The detection sequence is converted into a feature vector by extracting each pixel using DenseGoogLe Net.

The White Shark Optimizer (WSO) is an advanced metaheuristic model used to select relevant features from medical images. The movements of great white sharks, which use their extraordinary senses of smell and hearing for navigation and foraging, have influenced the main idea and basic notion of this algorithm. These special components can be theoretically and numerically studied to balance the analysis and execution of this strategy effectively. The supporting search agents explore and use each possible zone within the search area to improve optimization. To eventually achieve the desired results, WSO's search agents may arbitrarily adjust their positions based on the closest optimal possibilities. Some of the functional linkages involved in the WSO are evaluated in this investigation. A white shark's location can be estimated using (11). (11) v=v21v21⋯vf1v12v22⋯vf2⋮⋮⋮⋮v1mv2m⋯vfm v = \left\{{\matrix{{v_2^1} & {v_2^1} & \cdots & {v_f^1} \cr {v_1^2} & {v_2^2} & \cdots & {v_f^2} \cr \vdots & \vdots & \vdots & \vdots \cr {v_1^m} & {v_2^m} & \cdots & {v_f^m} \cr}} \right\} where the i^th white shark location in relation to the i^th dimension is indicated by vji v_j^i . The algorithm search region's upper (wd_j ) and lower (ℓd_j) bounds in the jth dimension can be utilized for determining it as follows: (12) vji=ℓdj+rand×(wdi−ℓdj) v_j^i = \ell {d_j} + rand \times (w{d_i} - \ell {d_j}) where the rand indicates a random integer between 0 and 1. An upgrade phase is also employed when a fresh site is better suited than a previous version. The great white shark can oscillate its way toward its prey, depending on its speed, which is represented as follows, when it determines the location of the prey based on its wave frequency: (13) up+1i=ψ(upi+b1[vebestk−vpj]×a1+b2[vbestupi−vpi]×a2 u_{p + 1}^i = \psi (u_p^i + {b_1}[{v_{{ebest}_k}} - v_p^j] \times {a_1} + {b_2}[v_{best}^{u_p^i} - v_p^i] \times {a_2} where b₁ and b₂ show the effects of white sharks that maintain monitors on v_ebestk and vbestupi v_{best}^{u_p^i} , the values of up+1i u_{p + 1}^i and upi u_p^i are the improved i^th white shark current velocities. The i^th optimal position with relation to the swarm during the frequency p iteration process is best represented by the parameter vupi {v^{u_p^i}} , and the WSO factor u is used to examine white sharks' convergence behavior in the manner described below: (14) u=[m×rand(1,m)]+1 u = [m \times rand(1,m)] + 1 where the vector with arbitrary interval numbers [0, 1] is called rand(1, m). The following relationships can be used to compute the variables p₁ and p₂ given in (15): (15) b1=bmax+(bmax−bmin)×c−4pp2 {b_1} = {b_{max}} + ({b_{max}} - {b_{min}}) \times {c^{- {{\left({{{4p} \over p}} \right)}^2}}} (16) b2=bmin+(bmax−bmin)×c−4pp2 {b_2} = {b_{min}} + ({b_{max}} - {b_{min}}) \times {c^{- {{\left({{{4p} \over p}} \right)}^2}}}

The maximum and minimum speeds at which great white sharks can move are denoted by b_max and b_min. In this scenario, p_max and p_min are assumed to be 1.5 and 0.5, respectively. The flowchart of White Shark Optimization Algorithm is shown in Fig. 3.

Fig. 3.

Flowchart of White Shark Optimization Algorithm.

In the meantime, P is the present version, identified by p and the maximum iteration. The following formula is employed to update the white shark position: (17) vp+1i=vpi∘¬vq+wd∘oif rand<nuvpi+upirif rand≥nu v_{p + 1}^i = \left\{{\matrix{{v_p^i \circ \neg {v_q} + wd \circ o} \hfill & {if\;rand < nu} \hfill \cr {v_p^i + {{u_p^i} \over r}} \hfill & {if\;rand \ge nu} \hfill \cr}} \right. where t is the white shark's wavy motion frequency, o and d are binary vectors, wd and ℓd are the search space's upper and lower bounds, v_o is a logical vector, and ¬ is the negation operator.

The process of finding the best shark was described as follows: (18) v´p+1i=vebestp+k1G→v×sgn(k2−0.5)if k3<SS \matrix{{{\acute v}_{p + 1}^i = {v_{{ebest}_p}} + {k_1}{{\vec G}_v} \times sgn ({k_2} - 0.5)} & {if\,{k_3} < {{\cal S}_{{\cal S}}}} \cr} where k₁, k₂, and k₃ are random values between 0 and 1, and v´p+1i {\acute v}_{p + 1}^i is the white shark's new attitude toward its victim. The search can be redirected because sgn (k₂ − 0.5) returns either 1 or −1. 𝒮_𝒮 indicates the white shark and smell, and G→v {\vec G_v} indicates how far away the prey is from the white shark.

DBNs are probabilistic generative models containing several Restricted Boltzmann Machines (RBMs). Discriminative supervised fine-tuning is used to train DBNs with greedy unsupervised layer-wise pre-training. In DBN, weight connections only exist between neighboring layers; buried neurons do not share any connections within the same layer. An RBM with one visible and one hidden layer is the basic building block of a DBN. The hidden layer of a prior RBM is assumed to be the visible layer of the subsequent RBM when building a DBN. Pre-training each RBM layer by layer, from the bottom to the top, is typically how a DBN is learned. Then, supervised learning techniques are employed to optimize the entire network. The output layer uses the probability distribution from the preceding layer to produce the expected forecast. Fig. 4 shows the DBN architecture.

Fig. 4.

Architecture of a DBN.

An RBM is an undirected generative model that is based on energy. The formula for its energy function for a given set of states (w, t) is as follows: (19) Aϕ(w,t)=−∑i=1mwpiwi−∑j=1mtejtj−∑i=1mw∑j=1mtvijwitj {A_\phi}(w,t) = - \sum\nolimits_{i = 1}^{{m_w}} {{p_i}{w_i}} - \sum\nolimits_{j = 1}^{{m_t}} {{e_j}{t_j}} - \sum\nolimits_{i = 1}^{{m_w}} {\sum\nolimits_{j = 1}^{{m_t}} {{v_{ij}}} {w_i}{t_j}}

There is a connection between the i neurons in the hidden layer and the j neurons in the visible layer, represented by v_ij . The component form is displayed earlier; however, the matrix form is an alternative: (20) Aϕ(w,t)=−pHt−eHw−Vwt {A_\phi}(w,t) = - {p^H}t - {e^H}w - Vwt

The joint probability distribution of the state (W, T) can be obtained by using the following energy function: (21) Bϕ(w,t)=1Xϕ*a−Aϕ(w,t) {B_\phi}(w,t) = {1 \over {{X_\phi}}}*{a^{- {A_\phi}(w,t)}}

Data are normalized using a normalization factor, also referred to as a partition function. The four types of brain tissues such as white matter, cerebrospinal fluid, grey matter, and ischemic lesions are classified.

A Nested Attention-based U-Net is used to segment the brain tissue diseases of the classified white matter, cerebrospinal fluid, grey matter, and ischemic lesions. Combining task-related selections with features extracted at other craters is possible. Fig. 5 depicts the Nested Attention U-Net topology. The Nested Attention U-Net is composed of a decoder and an encoder, connected by a series of thick nested convolutional blocks.

Fig. 5.

Structure of Nested Attention U-Net.

In addition, the model was more flexible by having the final outputs of X_0,1, X_0,2, and X_0,3 connected directly at the same time, which is equivalent to the network trim. Additionally, by using skip connections to propagate feature information more efficiently, attention gates (AG) can be used. The portion of the encoder that corresponds to the augmenting path and its up-sampling function is the AG inputs. The former serves as a gating signal to suppress regions unrelated to the mission and to enhance the target area's learning related to the segmentation objective.

Thus, AG can improve the productivity of producing semantic data by removing linkages. Furthermore, the focus coefficient α is obtained by training the Gate's parameters to converge using the sigmoid activation function. To obtain the output, multiply each pixel of the encoder characteristic by coefficient α. The decoder retrieves the feature in a bottom-up way, using the circular edge feature at each layer. The output of node X_p is represented by the matrix X_p,q, where p and q are the convolutional layer of dense blocks in conjunction with the skip connection index and the sampling layer beneath the encoder index. The formula that follows is used to ascertain the characteristic graph stack that X_p,q represents: (22) Xp,q=∲[xp−1,q]q=0∲[∫r=0q−1A(Xp,r),up(xp−1,q−1)]q>0 {X_{p,q}} = \left\{{\matrix{{\varointclockwise {[{x^{p - 1,q}}]}} \hfill & {q = 0} \hfill \cr {\varointclockwise {[\int_{r = 0}^{q - 1} {A({X_{p,r}}),{u_p}({x^{p - 1,q - 1}})} ]}} \hfill & {q > 0} \hfill \cr}} \right. where A(·) signifies the attention gate selection, function ∲ (·) is the activation function's convolution operation, and u_p(·) stands for the fully connected layer.

The Nested Attention U-Net gives each output node a brief introduction to the sigmoid function and the convolution layer. The loss function in DL measures how discordant the actual results are from the predictions. The stronger the model's robustness, the less the function's loss value as training time increases. Consequently, the Nested Attention U-Net training process's loss function has adapted the binary cross-entropy (BCE) loss: (23) Lc=zp+zptp+log(1+exp(−zp)) {L_c} = {z_p} + {z_p}{t_p} + \log (1 + \exp (- {z_p}))

In the Nested Attention U-Net prediction output, z_p represents the predicted label at pixel p, The total of all pixel losses is the loss to the image. Greater significance will be attributed to the loss if there is a notable discrepancy between the marked and the expected images. Finally, the Nested Attention U-Net segmented the grey matter, white matter, cerebrospinal fluid, and ischemic lesions features from the Brain MRI images.

The performance of the proposed model is evaluated using the following statistical metrics: Accuracy, Precision, Recall, Specificity, and F1-Score. (24) Accuracy=True++True−True++True−+False++False− Accuracy = {{{True}^ + + {True}^ -} \over {{True}^ + + {True}^ - +{ False}^ + + {False}^ -}} (25) Precision=True+True++False+ Precision = {{{True}^ +} \over {{True}^ + +{ False}^ +}} (26) Recall=True+True++True− Recall = {{{True}^ +} \over {{True}^ + + {True}^ -}} (27) Specificity=True−True−+False+ Specificity = {{{True}^ -} \over {{True}^ - +{ False}^ +}} (28) F1−Score=2(Precision*Recall)(Precision+Recall) F1 - Score = 2{{(Precision*Recall)} \over {(Precision + Recall)}}

True-Positive, False-Positive, True-Negative, and False-Negative are all represented by the symbols True⁺, True⁻, False⁺, and False⁻, respectively.

Table 1 shows the performance evaluation of the proposed BTS-NEUNET approach for brain tissue segmentation. The overall Accuracy, Precision, Recall, Specificity, and F1-Score of the proposed BTS-NEUNET approach are 99.60 %, 98.95 %, 98.18 %, 97.11 %, and 97.03 %, respectively.

Fig. 7 shows an accuracy curve with epochs on the x-axis and accuracy rate on the y-axis. A high accuracy level of 99.60 % based on the epochs is shown by the training and testing accuracy curves. Fig. 8 displays the loss curve, with epochs on the x-axis and the loss rate on the y-axis. The proposed BTS-NEUNET performs well during testing and training.

Fig. 7.

Accuracy curve of the proposed BTS-NEUNET method.

Fig. 8.

Loss curve of the proposed BTS-NEUNET method.

The deep network was determined to be the most effective method after evaluating the effectiveness of previous methods. Four deep learning networks, such as ShuffleNet, ResNet, GhostNet, and MobileNet, as well as the proposed network, were tested. To assess the effectiveness of current methods and demonstrate the superiority of the proposed network technique, we use Accuracy, Precision, Recall, Specificity, and F1-Score. Table 2 shows the results of a comparative analysis conducted between existing techniques and the proposed model.

Table 2 compares the performance of different neural networks for feature extraction across Accuracy, Precision, Recall, Specificity, and F1-Score. The proposed DenseGoogLeNet method for feature extraction achieves an overall Accuracy of 1.64 %, 4.53 %, 0.76 %, and 3.94 % higher than ShuffleNet [26], ResNet [27], GhostNet [28], and MobileNet [29], respectively.

Table 3 illustrates the accuracy evaluation of the proposed technique with the existing DDSeg, optimal SVM, and CEFAFCM methods. The proposed BTS-NEUNET method improves overall Accuracy by 1.92 %, 1.34 %, and 1.74 % over existing methods such as DDSeg, optimal SVM, and CEFAFCM. However, the aforementioned techniques do not perform as well as the proposed method. The proposed method outperforms other models, achieving precise results with 99.60 % Accuracy.