## 2 An ESNet of Real-Time Semantic Segmentation Based on DCNN
### Analysis of the Principle of Atrous Convolution  
(1) Receptive field  
The receptive field refers to the area of the original input image perceived by the pixels on the output feature image of a particular convolutional layer. It plays a significant role in the structure of DCNN. The larger the receptive field, the more global information contained in the NN features. The receptive field of DCNN can be enlarged in two ways:  
One is to expand the receptive field of the entire network structure through downsampled strategies such as the confluence layer with step size and convolutional layer; the other is to use the atrous convolution to expand the receptive field NN. This method can keep the image's resolution unchanged [26; 27]. The specific analysis of the calculation process of the receptive field is shown in Figure 5.  
The specific analysis of the calculation process of the receptive field is shown in Figure 5, the size of the image in the input network is \(7\times 7\), and the feature image of \(1\times 1\) is output after three convolutions, the step size of the convolution is 1, the padding is 0, and the size of the convolution kernel is \(3\times 3\). After n convolutions, the size of the receptive field of each unit in the feature image in the original image of the input network is recorded as \(r_{n}\), the step size of the convolution is recorded as \(s_{n}\), and the size of the convolution kernel is recorded as \(k_{n}\). As shown in Figure 5, the size of the receptive field of the image after the first convolution on the original image is the same as the size of the convolution kernel; that is, \(r_{1}=3\), and then the maximum receptive field of the image after the second convolution is \(3\times 3=9\)[28; 29; 30]. Since the step size of the first convolution is 1, the convolution kernels overlap during the moving process; thus, it is necessary to subtract the overlapping part \((k_{2}-1)\) from the feature image after the second convolution. The size of the receptive field of the overlapping part is \(r_{1}-s_{1}\), from which Equation (12) can be obtained:  
\[r_{2}=r_{1}\times k_{2}\ -(r_{1}-\ s_{1})\times(k_{2}-\ 1)=3\ \times\ 3\ -\ (3\ -\ 1)\ \times\ (3\ -\ 1)=5 \tag{12}\]  
Since the size of the convolutional receptive field is cumulatively affected by the step size of the previous convolution, Equation (13) can be obtained:  
\[r_{3}=r_{2}\times k_{3}-(r_{2}-\ s_{1}\times s_{2})\times(k_{3}-\ 1)=5\ \times\ 3\ -\ (5\ -\ 1\ \times 1)\ \times\ (3\ -\ 1)=7 \tag{13}\]  
By analogy, Equation (14) can be obtained:  
\[r_{n}=\ r_{n-1}\times k_{n}\ -\ \Big{(}r_{n-1}\ -\prod_{i=1}^{n-1}s_{i}\Big{)} \times(k_{n}\ -\ 1),\ n\ \geq\ 2 \tag{14}\]  
After simplifying the above equation, the specific calculation of the receptive field is obtained as shown in Equation (15). \[r_{n}=\ r_{n-1}+(k_{n}\ -1)\prod_{i=1}^{n-1}s_{i},\ n\ \geq\ 2 \tag{15}\]  
Figure 5: Receptive field. Dilated Convolutions  
When making predictions on dense images, it is necessary to perform extensive reasoning on the context, and it is necessary to ensure that the obtained prediction results have high resolution. To solve the above problems, a dilated convolution algorithm is proposed, which can expand the size of the network's receptive field, and the image's resolution will not change during this process [31; 32]. The one-dimensional calculation of dilated convolution is shown in Equation (16). \[g[i]=\sum_{l=1}^{L}\ f[i+r.l]h[l] \tag{16}\]  
In Equation (16), \(g[i],f[i]\) denote output and input signal; \(h[l]\) refers to the convolution kernel of length \(l\); \(r\) means the dilated convolution coefficient used to sample the input signal \(f[i]\). In the general convolution process, the dilated convolution coefficient is set to 1. The expansion of the size of the receptive field of the convolution kernel in the semantic segmentation system can be achieved through dilated convolution of a two-dimensional form. The specific way is to insert a \"hole\" between two adjacent pixels of a common convolution kernel.