## 2 Materials and Methods
### Proposed Method
#### 2.2.3 Root Rot Disease Identification  
Once the plant regions are segmented from the plant images, they are given as the input to the proposed deep learning model to identify whether the plants are infected with root rot disease. Image augmentation techniques such as random rotation and random rescaling were used during the model training. The architecture of proposed model is shown in Figure 5, and the details are presented in Table 1. Furthermore, transfer learning models were used to identify the plants infected by root rot disease. In transfer learning, deep learning models are trained to learn the features in a domain and the models are optimized to learn more features in a specific domain. The various transfer learning models used in our experimentation were AlexNet, VGG19, SqueezeNet, DarkNet19, ResNet18, and ResNet101. In the proposed model, there are four convolutional layers. Three of these convolutional layers are followed by the maxpooling layer. All these layers are followed by two fully connected layers. The second fully connected layer is followed by a softmax layer and a classification layer. The numbers of neurons in the first and second fully connected layers are 1024 and 2, respectively.  
The following is a brief discussion about the functions of the different layers in the deep learning models. The convolutional layer identifies the local feature maps from the input image. The size of the features can be calculated by the following equation:  
\[F=[(W-K+2P)/S]+1 \tag{3}\]  
where \(F\) denotes the feature map size, \(W\) is the input image size, \(K\) is the filter size, \(P\) denotes the padding, and \(S\) denotes the stride.  
The activation layer used in the proposed model is a ReLU layer. The ReLU function gives output the same as the input if the input is greater than 0. It is given by  
\[ReLU(x)=max(0,x) \tag{4}\]  
where \(x\) is the input to the ReLU function.  
Maxpooling is used to down-sample the obtained feature maps from the convolutional layer. The size of the output after maxpooling is given by the following equation:  
\[O=floor((I_{y}-L)/S) \tag{5}\]  
where \(O\) is the output size of the maxpooling function, \(I_{y}\) is the input shape, \(L\) is the pooling window size, and \(S\) is the stride.  
The fully connected layers generate the final features by integrating the output of previous layers, and these final features are used for classification or regression. The softmax layer assigns the probabilities for each class in the problem. It is given by the following equation:  
\[M(x)_{i}=\frac{exp(x_{i})}{\sum_{j=1}^{n}exp(x_{j})} \tag{6}\]  
where \(M\) is the softmax, \(x\) is the input vector, and \(exp(x_{i})\) and \(exp(x_{j})\) are the exponential function for input and output vectors, respectively.  
The classification layer calculates the loss and performs the classification tasks. The loss function used in the proposed model is cross-entropy. In our experiment, the loss function is given by the following equation:  
\[L_{C}=-\sum_{i=1}^{2}log(m_{i}),\text{ }for\text{ }2\text{ }classes \tag{7}\]  
where \(L_{C}\) is the cross-entropy loss; \(t_{i}\) is the truth value, having 0 or 1 as its value; and \(m_{i}\) is the \(i\)th class softmax probability.  
Figure 5: The proposed model Architecture.