## 3 Progressive Full Data Convolutional Neural Networks
The final output processed with GAN and without GAN results had its advantages and disadvantages, and one may choose whether to add it according to the actual requirements. Finally, we had our current network structure, a progressive and hierarchical U shaped neural network. Its global schematic diagram is shown Figure 2.  
Our system's input was a color image with alpha channel \(X\in\mathbb{R}^{H\times W\times 4}\), which presented the original anime-style illustration. The output of the system was \(\hat{Y}\in\mathbb{R}^{H\times W\times 4}\), which was the line extraction result. Our CNN model \(F_{CNN}\) is specified in Figure 2, and parameterized by \(\theta\), trained to minimize the object function in Equation (1) with database \(D\), which contained the source illustrations and the corresponding line extraction outputs. The loss function \(\mathfrak{L}\) calculated in Equation (2) describes the accuracy of our model. \[\theta^{*}=\operatorname*{arg\,min}_{\theta}\mathbb{E}_{X,Y\sim D}\left[ \mathfrak{L}(F_{CNN}(X,\theta),Y)\right] \tag{1}\]  
**Progressive full data convolutional neural network:** The purpose of our network structure was to include all the detailed information in the convolution process. We merged all the important layers into each convolution process. For example, in the bottom of the gradual structure diagram, we connected \(L4_{X}\), \(L4_{0}\), \(L4_{1}\), \(L4_{2}\), \(L4_{3}\) layers together and used them to generate \(L4_{4}\) layer. Where \(L4_{0}\) was  
Figure 3: The conceptual view of our progressive full data neural network for extracting lines in anime-style illustrations. generated by the convolution of \(L4_{X}\), and \(L4_{1}\) was generated by the merged layer of \(L4_{X}\) and \(L4_{0}\), they were proceeded step-by-step, as shown in the following equations. \[L4_{0}=F_{conv}(L4_{X}),\]  
\[L4_{1}=F_{conv}(F_{concat}(L4_{X},L4_{0})),\]  
\[L4_{2}=F_{conv}(F_{concat}(L4_{X},L4_{0},L4_{1})),\]  
\[L4_{3}=F_{conv}(F_{concat}(L4_{X},L4_{0},L4_{1},L4_{2})),\]  
\[L4_{4}=F_{conv}(F_{concat}(L4_{X},L4_{0},L4_{1},L4_{2},L4_{3})),\]  
The reason why so many layers were set is that different layers could be extrapolated to the data of different natures. These data were becoming abstract layer-by-layer, and we chose the more meaningful first four or five layers to do the calculation. The structure of the last level is shown in Figure 2:0  
The key concepts in different stages of the network structure are explained here and depicted in Figures 3 and 4. 1. Full data: Our purpose was to keep all the data, so that all the previous convolutional outputs would participate in the outputs of the next convolutional layers, and the original input would also be added; in this case, the system's computational burden would increase, but it ensured that the following layers of the neural network would generate the result with the whole information in the original input. 2. Progressive full data: After ensuring that the source data could be obtained by each convolutional layer, as many as possible, we also considered the interim results produced as important information; from the visualization results of a neural network analysis [33], we could know that interim results represented different levels of feature data; therefore, in the same resolution, we used the layer concatenation function, as much as possible to make the convolution layer the same level that could refer to the results generated before. 3. Globally progressive full data: Finally, we needed to refer to and modify the U-Net network structure. We could not use layer concatenation to connect the output of different resolutions, thus all the concatenations must be completed at the same resolution, and finally, we had our neural network structure depicted in Figure 2:1  
According to the ideas provided in [33], the first five layers contained rich information such as color, edge, texture, and abstraction information. However, the information contained after the fifth layer was more abstract and of lower value.