# A Deep Learning-Based Approach for Extraction of Positioning Feature Points in Lifting Holes
## 2 Methods
### The ADD Network Model
#### 2.3.3 Daspp  
DeepLabv3+ employs the ASPP module, which utilizes cascaded dilated convolutions. By stacking dilated convolutions with different dilation rates, the output feature maps are concatenated together, gradually achieving a larger receptive field. The ASPP module addresses the trade-off between resolution and receptive field by employing dilated convolutions, enabling a larger receptive field size without increasing the number of convolutional parameters, thus encoding high-level semantic information. The calculation of the receptive field size R for the ASPP module is as follows:  
\[\mathrm{R}=(\mathrm{r}-1)\times(\mathrm{k}-1)+\mathrm{k} \tag{4}\]  
where r represents the dilation rate of the atrous convolution, and k indicates the size of the convolutional kernel. It can be observed from above equation that, while keeping other factors constant, R increases with the increment of the dilation rate. In DeepLabV3+, three different dilation rates are employed with 3 \(\times\) 3 convolutional kernels, specifically 6, 12, and 18. The corresponding receptive fields for each convolutional kernel are as follows:  
\[\left\{\begin{aligned} \mathbb{R}_{3,6}&=(6-1)\times(3-1)+3=13 \\ \mathbb{R}_{3,12}&=(12-1)\times(3-1)+3=25\\ \mathbb{R}_{3,18}&=(18-1)\times(3-1)+3=37\end{aligned}\right. \tag{5}\]  
By parallelizing 3 atrous convolution layers with different dilation rates, ASPP processes the same input feature and combines the results together, indicating that the output features are a multi-scale sampling of the input. To acquire a wider receptive field, a larger dilation rate is needed. However, as the dilation rate increases, the sampling rate becomes sparser compared to traditional convolution, resulting in the loss of more detailed information. At this point, the effectiveness of dilated convolutions diminishes.  
The DASPP module addresses this issue by cascading multiple atrous convolution layers and densely connecting the output of each atrous convolution layer to subsequent ones. This cascading approach combines the advantages of both serial and parallel atrous convolution layers, enabling the generation of feature representations with more scales. As the dilation rate increases layer by layer, the output of each atrous convolution layer is combined with its input and the outputs of other layers, facilitating the fusion of multi-scale features and enlarging the receptive field [32].  
The original dilated convolution layers are retained and cascaded in this study, combined with 1 \(\times\) 1 convolutions to jointly encode and generate a denser feature pyramid. Furthermore, the concatenation of two dilated convolution layers enables the creation of a larger receptive field. Assuming that the receptive field sizes of the two dilated convolutions are R1 and R2, the resulting receptive field after concatenating these two dilated convolutions is illustrated in Figure 6.  
From Figure 6, it can be observed that the receptive field of two dilated convolution kernels with r = 2 and k = 3 becomes larger and denser. The specific calculation formula for the receptive field is as follows:  
\[\text{R}=\text{R}_{1}+\text{R}_{2}-1 \tag{6}\]  
It should be noted that in DASPP, the 1 \(\times\) 1 convolution does not affect the size of the receptive field. Additionally, the maximum receptive field for both ASPP and DASPP is:  
\[\text{ASPP}:\ \text{R}_{\text{max}}=\text{max}(\text{R}_{3,6},\text{R}_{3,12}, \text{R}_{3,18})=37 \tag{7}\]  
\[\text{DASPP}:\ \text{R}_{\text{max}}=\text{R}_{1,1}+\text{R}_{3,6}+\text{R}_{3,12 }+\text{R}_{3,18}-3=73 \tag{8}\]  
Figure 6: The impact of DASPP on receptive field.  
The comparison of maximum receptive field shows that the DASPP module used provides sufficient contextual information for pixel-level classification of the same image. This enables better segmentation details.