## 2 Materials and Methods
### Methods
#### 2.2.4 Leaf Pixel Classification Based on Multidimensional Fusion Atrous-CNN  
In conventional hyperspectral image processing, the conventional 1D-CNN network can only process the spectral information of hyperspectral data while ignoring the spatial information of hyperspectral data. Although 3D-CNN-based networks can synthesize hyperspectral data's spatial and spectral information, the model structure is complex and requires high hardware consumption. Figure 4 shows the process of CNN fusion in three dimensions--1D-CNN, 2D-CNN, and 3D-CNN. The network can effectively utilize the feature information of hyperspectral data extracted from three different dimensional CNNs with higher recognition accuracy and can further reduce hardware consumption. In the data fusion process, this paper utilizes the reshape method to adjust the dimensionality of the data and achieves the fusion of the data by connecting the CNNs of two dimensions.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Layer** & **Type** & **Output Shape** & **Param** & **Connected to** \\ \hline input & InputLayer & (None, 7, 7, 204, 1) & 0 & \\ Conv3\_1 & Conv3D & (None, 7, 7, 204, 8) & 224 & input \\ Conv3\_2 & Conv3D & (None, 7, 204, 8) & 1736 & Conv3\_1 \\ Conv3\_3 & Conv3D & (None, 7, 7204, 8) & 1736 & Conv3\_2 \\ Pool & MaxPooling3D & (None, 7, 7, 102, 8) & 0 & Conv3\_3 \\ reshape1 & Reshape & (None, 7, 7, 816) & 0 & Pool3 \\ Conv2 & Conv2D & (None, 3, 8) & 58,760 & reshape1 \\ reshape2 & Reshape & (None, 72, 1) & 0 & Conv2 \\ Conv1 & Conv1D & (None, 68, 16) & 64 & reshape2 \\ flatten & Flatten & (None, 1088) & 0 & Conv1 \\ Dropout & Dropout & (None, 1088) & 0 & flatten \\ D1 & Dense & (None, 50) & 54,450 & Dropout \\ out & Dense & (None, 4) & 204 & D1 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Multidimensional fusion of Atrous-CNN structure.  
Figure 4: Leafpixel classification based on multidimensional fusion of Atrous-CNN.  
Figure 3: Multidimensional fusion of Atrous-CNN.  
As shown in Figure 4, the multidimensional fusion Atrous-CNN makes full use of the spatial and spectral information of the hyperspectral data. In the 3D-CNN part, the \"null-spectral\" information of the hyperspectral data is extracted using the 3D convolution-pooling operation, with a feature size of (\(7\times 7\times 102\)) and many features of 8. In the 2D-CNN part, the hyperspectral data's spatial information is extracted using the 2D-hole convolution operation with the feature size of (\(3\times 3\)) and the number of features of 8. In the 1D-CNN part, the spectral information of the hyperspectral data is extracted by using the 1D-hole convolution operation with a feature size of 68 and many features of 16.  
Figure 5 shows the structural comparison of the three CNNs. As noted, 3D-CNN uses only 3D convolution (Conv3D) and 3D maximum pooling (MaxPooling3D) for feature extraction of hyperspectral data. Due to the large Conv3D computation with high hardware consumption during model training, the multidimensional fusion CNN and Atrous-CNN use 2D-CNN and 1D-CNN for feature extraction in the intermediate layer to reduce computational loss. Among the feature extraction methods in the middle layer, multidimensional fused CNN utilizes convolution-pooling operation and Multidimensional fusion Atrous-CNN with specific feature extraction capability. In the last two layers (D1, out) of the whole network, D1 acts as a fully connected layer to integrate and combine the features of the previous flattened layer spread out. Finally, the four neurons in the out layer correspond to the categories to which the four leaf pixels belong. Using the activation function softmax, the results of the four neurons can be processed as probability values between 0 and 1, and the one with the largest probability value is determined as the category to which they belong.  
Figure 5: Comparison of three CNN structures.