# Multi-Scale Aggregation Stereo Matching Network Based on Dense Grouping Atrous Convolution
## 2 Related Work and Methods
### Related Work
#### 2.1.2 Atrous Convolution  
Atrous convolution is a method of increasing the receptive field without increasing the computation or reducing the resolution of the feature map [10; 11]. In atrous convolution, the receptive field refers to the size of the area mapped from the original image by pixels in the feature map output by each layer of the convolution neural network [10], and the size of the receptive field is closely related to the dilation rate. In order to increase the receptive field and reduce the calculation in a deep network, it is always necessary to carry out down-sampling and pooling operations, which can increase the receptive field but reduce the spatial resolution. Therefore, if you wish to increase the receptive field while maintaining the resolution, you can use atrous convolution. By this method, the receptive field and resolution can be balanced, and multi-scale information can be obtained by adjusting the dilation rate. The similarity between atrous convolution and ordinary convolution is that the size of convolution kernel is the same, and the number of parameters in the neural network remains unchanged. The difference is that atrous convolution preserves the original image information while increasing the receptive field. The structure is shown in Figure 1.  
Figure 1: The comparison of ordinary convolution and atrous convolution: (**a**) schematic diagram of ordinary convolution; (**b**) schematic diagram of atrous convolution. The interval between adjacent convolution kernels is \(d-1\). The receptive field size of a convolution kernel can be formulated using the following equation:  
\[R=(d-1)\times(K-1)+K \tag{1}\]  
where \(d\) represents the dilation rate and \(K\) represents the size of a kernel. \(R\) is the size of the receptive field. Obviously, atrous convolution increases the receptive field without losing the size of the feature map, but it has an inherent problem known as the grid effect. In the result of a certain layer of atrous convolution, adjacent pixels are obtained from the convolution of mutually independent subsets, and the lack of dependence on each other leads to the loss of local information, which is harmful to the segmentation of small objects [27]. In order to solve this problem of atrous convolution, the ASPP method proposes connecting the feature maps generated by hole convolution under different dilation rates so that the neurons in the output feature map contain multiple acceptance domain sizes, encode multi-scale information, and finally improve the matching accuracy. However, with the increase in dilation rate, atrous convolution becomes more and more ineffective and gradually loses its modeling ability. Therefore, it is very essential to design a network structure that can encode multi-scale information and obtain a large receptive field. In order to obtain a large enough receptive field and avoid convolution degradation, [PERSON] et al. [10] proposed DenseASPP, which combines the advantages of the parallel and cascading usage of the atrous convolution layer, which obtains a larger receptive field and denser features, along with improving the recognition ability of the algorithm when the target ratio changes. This leads to an improvement of the robustness of the matching. Regarding the DenseASPP method, stacking the two convolution layers together can provide a larger receptive field. Suppose we have two convolution layers. The convolution kernel size is \(K_{1}\) and \(K_{2}\) respectively, and the new receptive field \(R\) is calculated as follows:  
\[\left\{ \begin{aligned} R_{1}&=(d_{1}-1)\times(K_{1}-1 )+K_{1}\\ R_{2}&=(d_{2}-1)\times(K_{2}-1)+K_{2}\\ R&=R_{1}+R_{2}-1\end{aligned} \right. \tag{2}\]  
where \(R_{1},d_{1}\) are the receptive field and dilation rate of the first convolution layer, respectively, and \(R_{2},\ d_{2}\) are the receptive field and dilation rate of the second convolution layer, respectively.