## 3 Methods
### CNN-Based Identification  
Over the last few years, CNNs have made great advances in many fields, such as reducing noise, super-resolution reconstruction [55], pan sharpening [56], image segmentation [57; 58], object detection [59], change detection [60; 61], and classification [62; 63]. In these studies, the convolutional operation was applied in both the \(x\) and \(y\) dimensions to detect the potential architecture or patterns hidden in data. Similarly, in this study, a CNN is used to detect the distinctive characteristics of vineyards in both the time and scale dimensions in scalogram data because it has the following strengths: i) extreme versatility that allows it to approximate any type of linear or nonlinear transformation, including scaling or hard thresholding; ii) it is not necessary to design handcrafted filters, they are automatically learned by algorithms; and iii) high-speed processing because of parallel computing. In this study, a new CNN similar to LeNet [64], which combines small convolutional kernels with maximum or average pooling to learn high-level features, is built to identify vineyards. The convolution and pooling operations are conducted both on the frequency/scale and time axis in our experiment because the scalogram contains time-related frequency patterns of each planting condition. Specifically, Table 2 lists the CNN layers in order. For example, the first convolutional layer represents a convolutional kernel with three input channels, 12 output channels, and a size of 5; and the first pooling layer represents a max pooling kernel of a size of 4 and strides of 2. The activation functions for all convolutional layers and the first dense layer is an ReLU, whereas it is softmax for the last dense layer. The output of the last convolutional layer is concatenated into one vector, then fed into the fully connected layer with 100 units. Finally, there is a softmax layer with two units, which indicate non-vineyard and vineyard. To test an unknown pixel, the CNN takes its three VIs' (i.e., NDVI, EVI, and GCVI) scalograms, concatenated as a three-dimensional array, as the input, and the maximum unit of the last softmax layer is the result. For each scalogram, the size of \(x\) dimension is equal to the length of the reconstructed time series (i.e., 365), and the size of \(y\) dimension is dependent on the value of maximum scale of CWT (i.e., 200 in this research), which is determined by calculating the optimal entropy of scalogram. As three stacked scalograms are directly fed into the CNN without splitting them into several small patches, the input size of CNN is \(365\times 200\times 3\). The construction of CNN is implemented with the assistance of Keras, and TensorFlow is used as the backend of Keras in the research.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Layer (Type)** & **Output Shape** & **Kernel Size** & **Param \#** \\ \hline Input Layer & (None, 200, 365, 3) & - & 0 \\ Conv2D & (None, 196, 361, 12) & (5,5) & 912 \\ Max\_Pooling2D & (None, 97, 179, 12) & (4,4) & 0 \\ Conv2D & (None, 93, 175, 24) & (5,5) & 7224 \\ Max\_Pooling2D & (None, 46, 87, 24) & (2,2) & 0 \\ Conv2D & (None, 42, 83, 48) & (5,5) & 28,848 \\ Max\_Pooling2D & (None, 21, 41, 48) & (2,2) & 0 \\ Flatten & (None, 41328) & - & 0 \\ Dense & (None, 100) & - & 4,132,900 \\ Dense & (None, 2) & - & 202 \\ \hline \hline \end{tabular}  
* Total params: 4,170,086; Trainable params: 4,170,086; Non-trainable params: 0.  
\end{table}
Table 2: Convolutional neural network (CNN) architecture.