# Gaussian Dynamic Convolution for Semantic Segmentation in Remote Sensing Images
## 3 Method
### Gaussian Dynamic Convolution Network  
To further illustrate the advantages of GDConv in the field of image segmentation for remote sensing, we construct a novel Gaussian Dynamic Convolution Network (GDCN) as shown in Figure 3. The input image is first passed through a deep convolutional neural network for feature extraction to obtain both the low-level and high-level features. Then, the high-level features are subjected to our Gaussian pyramid pooling (GPP) module for mining the multi-scale contextual information content. The GPP module is shown in  
Figure 2: Illustration of the Gaussian dynamic convolution with kernel size 3.  
Figure 4. It is worth mentioning that it is quite different from the Gaussian dynamic pyramid pooling [15]. The feature pyramid module mentioned in [15] is composed of multiple dilated convolutions with different dilation factors and Gaussian dynamic convolutions with fixed offsets, which does not break the shape limitation. Our GPP module is composed of Gaussian dynamic convolution and dilated convolution. The Gaussian dynamic convolution ensures features of different scales and natural shapes of objects. Therefore, our GDCN can better extract the multi-scale features in high-resolution remote sensing images.  
Figure 4. Illustration of the Gaussian Pyramid Pooling.  
Figure 3. Illustration of the Gaussian Dynamic Convolutional Network.  
Many segmentation tasks use dilated convolution with different dilation rates to fuse information at different scales. As shown in Figure 4, the large red box represents an atrous convolution with a large dilation factor used to collect large-scale information in the image, while the small yellow square indicates a small dilation rate used to collect small scale information in the image. In order to fuse the mesoscale information, people often use a layer of dilated convolution with a moderate dilation rate or multiple layers of atrous convolution with increasing dilation factor in order, such as Atrous Spatial Pyramid Pooling (ASPP) module. We do a different job. We use GDConv to capture the information at different scales. GDConv can break the limitation of the expansion factor by randomly generating Gaussian offsets to extract information at various scales instead of limiting it to extracting intermediate scales. This is the reason why our GPP module can produce richer feature maps.  
We concatenate the feature layers of different scales obtained by the GPP module, and then adjust the number of channels via an \(1\times 1\) convolution layer to obtain the blue feature layer as shown in Figure 3. This feature layer is first subjected to \(4\times\) upsampling and fused with the low-level feature layer having the same spatial resolution. We downsample the low-level features with another \(1\times 1\) convolutional layer before fusion, because low-level features often contain a large number of channels. The fused feature layers are then passed through several \(3\times 3\) convolutional layers for feature extraction and finally subjected to \(4\times\) upsampling to restore the feature layer to the same size as the original image, which gives the final prediction result.