# A Benchmark for Water Surface Jet Segmentation with MobileHDC Method
## 4 Method
### MobileHDC: A Novel Hybrid MobileNetV2 Backbone  
Hybrid Dilated Convolution Layers. Jets typically exhibit dynamic variations and irregular shapes, manifesting at different scales in images--sometimes fine and compact, and at other times wide and diffuse. A larger receptive field enables the model to better capture and maintain the continuity of the jet across different regions, thereby reducing the occurrence of segmentation discontinuities or incompleteness caused by insufficient local information. Dilated convolution is a distinctive convolutional technique that expands the receptive field by introducing \"dilations\" into the convolutional kernel. The dilation rate of this operation is controlled by the parameter a. As shown in Figure 6, when a = 1, dilated convolution behaves identically to standard convolution. However, when a exceeds 1, certain intermediate pixels are skipped, which may adversely affect network performance. Some previous works, such as Auto-DeepLab [32], were hesitant to use dilated convolutions in the shallow layers of the encoder. On the one hand, this may cause \"The Gridding Effect\" [33]. On the other hand, just like a large kernel [34], dilated convolution struggles to maintain a balance between contextual and detailed information, which can affect the model's performance. Therefore, to mitigate the gridding effect, the design of the hybrid dilated convolution layers in this work follows an odd-even mixing strategy, ensuring that the dilation rates do not share a common divisor. Additionally, to prevent the loss of fine details due to overly large dilation rates during the first dilated convolution, the dilation rates must satisfy the condition described in Equation (10). \[M_{i}=max[M_{i+1}-2r_{i},M_{i+1}-2(M_{i+1}-2r_{i}),r_{i}] \tag{10}\]  
wherein \(r_{i}\) denotes the dilation rate of the \(i\)-th layer and \(M_{i}\) represents the maximum dilation rate in that layer. Assuming that there are \(n\) dilated convolution layers in total, it is set by default that \(M_{n}=n\), and it is required that \(M_{2}\leq k\), where \(k\) represents the kernel size. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Input** & **Operator** & \(\mathbf{t}\) & \(\mathbf{c}\) & \(\mathbf{n}\) & \(\mathbf{s}\) \\ \hline \(512^{2}\times 3\) & conv2d & - & 32 & 1 & 2 \\ \(256^{2}\times 32\) & bottleneck & 1 & 16 & 1 & 1 \\ \(256^{2}\times 16\) & bottleneck & 6 & 24 & 2 & 2 \\ \(128^{2}\times 24\) & bottleneck & 6 & 32 & 3 & 2 \\ \(64^{2}\times 32\) & bottleneck & 6 & 64 & 4 & 2 \\ \(32^{2}\times 64\) & bottleneck & 6 & 96 & 3 & 1 \\ \(32^{2}\times 96\) & bottleneck & 6 & 160 & 3 & 1 \\ \(32^{2}\times 160\) & dilated & - & 256 & - & 1 \\ \(32^{2}\times 256\) & dilated & - & 256 & - & 1 \\ \(32^{2}\times 256\) & dilated & - & 256 & - & 1 \\ \(32^{2}\times 256\) & dilated & - & 256 & - & 1 \\ \(32^{2}\times 160\) & conv2d \(1\times 1\) & - & 256 & - & 1 \\ \(32^{2}\times 256\) & conv2d \(1\times 1\) & - & 256 & - & 1 \\ \(32^{2}\times 512\) & conv2d \(3\times 3\) & - & 512 & - & 1 \\ \(32^{2}\times 512\) & conv2d \(3\times 3\) & - & 512 & - & 1 \\ \(32^{2}\times 512\) & conv2d \(3\times 3\) & - & 512 & - & 1 \\ \(32^{2}\times 512\) & conv2d \(1\times 1\) & - & k & - & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Specification for our proposed model. Each line describes a sequence of 1 or more identical (modulo stride) layers, repeated \(n\) times. Here, \(t\), \(c\), and \(s\) denote expansion factor, output channels, and stride, respectively. To achieve better perceptual capability across different scales and enhance the model's ability to capture global information, inspired by STDC [35], we designed four hybrid dilated convolution layers in the backbone network based on the first seven feature maps \(x_{s}\) of MobileNetV2. As illustrated in Figure 7, each dilated convolution layer employs different dilation rates to expand the receptive field.