## 2 Materials and Methods
### Proposed Method
#### 2.4.1 Encoder  
The present study constructed a DL encoder from scratch using a series of conv and max-pooling layers, repeated four times with the same number of filters. To prevent overfitting, we added a dropout layer after each max-pooling layer. Instead of a dense layer, we used a single conv layer that acted as a bottleneck in the network, separating the encoding and decoding networks. The Rectified Linear Unit (ReLU) activation function is employed to represent the non-linear mapping into the model [43, 44]. The SE block, which is exhibited in Figure 5, is then involved in enhancing the feature maps and learning accurate boundaries of Sella structures in cephalometric radiographic images [44, 45]. In the squeezing step \(Z_{squeeze,}\in R^{c}\) reduces the spatial dimensions of feature maps to a \(1\times 1\) representation using global average pooling, while in the exciting step \(Z_{excite}\in R^{c}\), learnable weights are applied to the squeezed feature maps to recalibrate channel-wise information. The mathematical equation below illustrates the SE combination:  
\[SE=\gamma_{2}\bigg{(}W_{2}\times\gamma_{1}\bigg{(}W_{1}\times\frac{1}{H\times W }\sum i\sum jX_{ijc}\bigg{)}\bigg{)}\otimes X, \tag{1}\]  
where \(\gamma_{2}\) denotes the softmax activation function, \(\gamma_{1}\) denotes the ReLU activation function, \(W_{1}\) and \(W_{2}\) are learnable weight matrices, H and W are spatial dimensions, and \(\times\) denotes matrix multiplication.  
Moreover, to enhance the encoder's ability to integrate context information, a recurrent residual convolutional layer (RrCL) is incorporated in individual steps [44, 46]. The RrCL consists of \(3\times 3\) convolutions, which allows for a deeper model and better accumulation of feature representations across different time steps. However, the use of RrCL leads to an increase in the number of feature maps and a reduction in size by approximately  
Figure 5: Outline of the proposed method. The proposed model contains an encoder part incorporated with recurrent residual convolutional layer RrCL, squeeze-and-excite SE block, attention gating modules AGM, discriminator D, and zero-shot linear classifier ZsLC.  
half. In addition, batch normalisation (BN) is applied after each convolution operation to regularise the model and reduce internal covariate shifts [44; 47]. In the RrCL block, the network output \(O_{i}\) at time step \(t_{s}\) can be mathematically described by the equation below, assuming \(\omega_{i}\) as the input of the \(i\)th layer and \((p,\ q)\) as the localised pixel in the input on the \(n\)th feature map, as illustrated in the accompanying figure.  
\[O_{i(p,d,t_{s})}\ =\ (W_{n}^{c})^{T}\times\omega_{i(p,d,t_{s})}+(W_{n}^{r})^{T} \times\omega_{i(p,d,t_{s-1})}+b_{n}, \tag{2}\]  
where \(O_{i}\) is the output at position \((p,\ q)\) in the \(n\)th feature map of the ith layer at time step \(t_{s}\), with \((W_{n}^{c})^{T}\) and \((W_{n}^{r})^{T}\) as weight matrices, \(\omega_{i}\) as the input at time step \(t_{s}\), \(\omega_{i(p,d,t_{s-1})}\) as the input at time step \(t_{s-1}\), and \(b_{n}\) as the bias term for the \(n\)th feature map. The recurrent convolutional unit's output \(\omega(i+1)\) is then sent to the residual unit, which is represented by the following equation:  
\[\omega(i+1)=\omega_{i}+F_{O(\omega_{i},\ \tau i)} \tag{3}\]  
The RrCL takes inputs \(\omega_{i}\) and produces outputs \(F_{O(\omega i,\tau i)}\), which are utilised in the encoder and decoder layers of the proposed network's down- and up-sampling layers. The subsequent sub-sampling or up-sampling layers rely on the final output \(\omega(i+1)\) as their input.