## 3 The Proposed Transferable Texture Convolutional Neural Network (TTCNN) Method
### Network Architecture
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Layers** & **Types** & **Input Size** & **Kernel Size to Form Each Feature Map** & **Stride** & **Padding** & **Output Size** \\ \hline
1 & Convolutional Layer 1 & 64 \(\times\) 64 \(\times\) 1 & 5 \(\times\) 5 & [1 1] & [1 1 1 1] & 62 \(\times\) 62 \(\times\) 16 \\ \hline
2 & Max Pooling Layer 1 & 62 \(\times\) 62 \(\times\) 16 & 2 \(\times\) 2 & [2 2] & [1 1 1 1] & 32 \(\times\) 32 \(\times\) 16 \\ \hline
3 & Convolutional Layer 2 & 32 \(\times\) 32 \(\times\) 16 & 5 \(\times\) 5 & [1 1] & [1 1 1 1] & 30 \(\times\) 30 \(\times\) 32 \\ \hline
4 & ReLU & & & & & \\ \hline
5 & Max Pooling Layer 2 & 30 \(\times\) 30 \(\times\) 32 & 2 \(\times\) 2 & [2 2] & [1 1 1 1] & 16 \(\times\) 16 \(\times\) 32 \\ \hline
6 & Convolutional Layer 3 & 16 \(\times\) 16 \(\times\) 32 & 3 \(\times\) 3 & [1 1] & [1 1 1 1] & 16 \(\times\) 16 \(\times\) 64 \\ \hline
7 & ReLU & & & & & \\ \hline
8 & EL & 16 \(\times\) 16 \(\times\) 64 & - & - & - & 128 \(\times\) 1 \\ \hline
9 & Dropout & 128 \(\times\) 1 & - & - & - & 128 \(\times\) 1 \\ \hline
10 & FC1 & 128 \(\times\) 1 & - & - & - & 1024 \(\times\) 1 \\ \hline
11 & Dropout & 1024 \(\times\) 1 & - & - & - & 1024 \(\times\) 1 \\ \hline
12 & FC2 & 1024 \(\times\) 1 & - & - & - & 2 \(\times\) 1 \\ \hline
13 & Softmax Layer & & - & - & - & \\ \hline
14 & Classification Layer & & - & - & - & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Proposed texture CNN architecture layers. where \(S_{\theta}\) represents the output feature maps, \(C_{\theta}\) represents the input feature maps, and \(T\) denotes the weighted map. Afterwards, an energy descriptor is utilized for the output of the final convolution layer. Energy layers are combined after the third convolution layer, taking into account the requirements of the energy descriptor. Its functionality is similar to a dense, messy texture descriptor. The connection is given in Equation (12) as:  
\[EL(\xi,\theta)=\rho\left[\sum_{i=1}^{j}T_{i}^{w}\theta_{i}+P\right], \tag{12}\]  
where \(EL(\xi,\theta)\) represents the EL output layer, \(j\) represents the input connections, and \(T\) represents the EL weighted vector. Compared to the last conventional convolution layer interconnection, the interconnection between the EL and FC layers is much smaller and leads to a reduction in learnable parameters. In addition, EL retains energy information from the preceding layer and learns during forward and backward propagation. Furthermore, to reduce the vector size of the next FC layer, EL also improves the overall learning ability of the network and diminish the complication of the proposed system. Use Equation (13) to calculate the learnable parameters of EL as:  
\[\xi_{EL}=\eta^{m}\times\eta^{m-1}, \tag{13}\]  
where \(\xi_{EL}\) is the EL learnable parameters, \(\eta^{m}\) is the current FC layer neuron, and \(\eta^{m-1}\) is the previous FC layer neuron. To speed up the training process the batch normalization and activation function is used between the convolution layer and rectified linear unit (ReLU) layer. Batch normalization is used to remove the internal covariate shift [50]. This can be done by normalizing the mean and standard deviation. The bulk normalization calculation uses the following Equations (14) and (15) to calculate mean and variance. \[\tau_{Q}=\frac{1}{n}\sum_{i}^{n}\iota_{i}, \tag{14}\]  
\[v_{Q}=\frac{1}{n}\times\sum_{i}^{n}(\iota_{i}-\tau_{Q})^{2}, \tag{15}\]  
where \(\tau_{Q}\) and \(v_{Q}\) represents the mean and variance respectively, \(n\) is the mini batch size of \(\iota_{i}\) element of features. In our work the value of \(n\) is 64. The batch normalization is calculated in Equation (16) as:  
\[\lambda_{i}=\frac{\theta_{i}-\tau}{\sqrt{v^{2}+\phi}}\alpha+A, \tag{16}\]  
where \(\alpha\) and \(A\) are initial learnable parameter values of each output layer.