## 2 Materials and Methods
### U-Net++ Network Architecture  
The H-denseunet network was proposed by [PERSON] et al. [22]. [PERSON] systematically studied the importance of short skip connections [23]. The network's redesigned skip connection can retain image features better, effectively preventing the features loss of the diverse lesions in medical image segmentation. Inspired by this, U-Net++ was proposed by [PERSON] et al., and has greatly improved the skip connection part of the U-Net network [24]. The network structure is shown in Figure 3, as follows:In the figure, the red part represents the original U-Net; the green and blue parts are respectively the skip connection and up-sampling parts of u-net + +, which are different from u-net; and the black part indicates the depth supervision. As can be seen from the figure, U-Net++ starts from the encoder sub-net or backbone network by the decoder sub-net. The redesigned skip connection of the pathways transforms the connectivity of the encoder and decoder sub-networks. In U-Net, the feature map of the encoder is directly received in the decoder, while they go through a dense convolutional block in U-Net++, and the number of convolutional layers depend on the pyramid level. Both the first and the second layer's structure diagrams of the network are shown in Figure 4:  
From Equation (1), the skip pathways are as follows. Let \(x^{(i,j)}\) represent the output of this layer, \(i\) refer to the down-sampling layer along the encoding direction, and \(j\) refer to the dense convolution layer along the skip path direction. This pile of feature maps is represented by \(x^{(i,j)}\), and the calculation is shown in Equation (1):  
\[x^{(i,j)}=\begin{cases}H\Big{(}x^{(i-1,j)}\Big{)},&j=0\\ H\Big{(}\Big{[}x^{(i,k)}\Big{]}_{k=0}^{j-1},U\Big{(}x^{(i+1,j-1)}\Big{)}\Big{)},&j=1\end{cases} \tag{1}\]  
Figure 3: U-Net ++ network structure diagram.  
Figure 2: The flow chart of the proposed method.  
where the function \(H(\cdot)\) is a convolution operation, an activation function \(U(\cdot)\) represents an up-sampling layer, and the bracket [ ] represents a cascade layer.  
Essentially, the dense convolutional blocks make the semantic level of the encoder feature map closer to the feature map required in the decoder. Assuming that the received encoder feature map is semantically similar to the corresponding decoder feature map, the optimizer will become an easier optimization problem.  
In terms of loss function, the combination of binary cross-entropy and Dice coefficient is referred to as the loss function, as shown in Equation (2).  
\[L(Y,\hat{Y})=-\frac{1}{N}\sum_{b=1}^{N}\frac{1}{2}Y_{b*}\log(\hat{Y}_{b})+\frac {2Y_{b}*\hat{Y}_{b}}{Y_{b}+\hat{Y}_{b}} \tag{2}\]  
where \(\hat{Y}_{b}\) and \(Y_{b}\) respectively represent the flattening prediction probability and flattening basic fact of the b image, and \(N\) refers to the batch size.  
Due to the nested skip path, U-Net ++ forms a full-resolution graph at multiple semantic levels [25], which can be deeply supervised, enabling the model to run in two modes: (1) precise mode, where the output is averaged from all split branches, and (2) fast model, where the final segmentation graph only selects one of the split branches; this selection determines the degree of model pruning and speed gain, and is simplified during prediction.