# LRP-DS: Lightweight RepPoints with Decoupled Sampling Point Set
## 4 The Lightweight RepPoints with Decoupled Sampling Point Set
### Decouple the Sampling Point Set between the Localization and the Classification Tasks  
The localization and classification tasks of RepPoints share the same feature sampling location, which ignore the difference of feature concerns between localization and classification. The main idea of this paper is to decouple the task of localization and classification, and give the feature sampling points of classification a certain degree of freedom. The initial point set \(P\) obtained by the localization branch is the sampling position set. Due to the supervision signal of the ground truth, it is actually more a geometric boundary characteristic of the object, such as the edge of the object. However, the classification task focuses more on the semantic information of the object, so it is not appropriate for them to share a set of sampling point sets. Therefore, two classification free sampling methods are proposed which are based on the idea of task decoupling, as shown in Figure 4. The sample set of the original RepPoints can be described as \(L_{d}=\{P+R_{i}+O_{i}\,|\,R_{i}\in R,\,O_{i}\in O\}\). The first scheme, LRP-DS-V1, is shown in Figure 4a. On the basis of the sampling position \(L_{d}\), a sampling free function for sample point set of classification is introduced to separate the sampling positions of the localization branch and the classification branch. With the influence of classification free sampling, the sampling point set of classification branch is described as \(L_{c}=\{P+F(R_{i}+O_{i})\,|\,R_{i}\in R,\,O_{i}\in O\}\), where \(F(. )\) is the coordinate transformation function based on the degrees of freedom. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**No** & **Input Channel** & **Operator** & **t** & **c** & **n** & **s** \\ \hline
1 & 3 & conv2d & - & 32 & 1 & 2 \\
2 & 32 & bottleneck & 1 & 16 & 1 & 1 \\
3 & 16 & bottleneck & 6 & 24 & 2 & 2 \\
4 & 24 & bottleneck & 6 & 32 & 3 & 2 \\
5 & 32 & bottleneck & 6 & 64 & 4 & 2 \\
6 & 64 & bottleneck & 6 & 96 & 3 & 1 \\
7 & 96 & bottleneck & 6 & 160 & 3 & 2 \\
8 & 160 & bottleneck & 6 & 320 & 3 & 1 \\
9 & 320 & bottleneck & 6 & 480 & 3 & 2 \\ \hline \hline \end{tabular}  
* The conv2d represents a 3 \(\times\) 3 regular convolution; the bottleneck represents the inverse residual structure in MobileNetV2; \(t\) represents the expansion rate of the number of channels in the inverse residual structure; \(c\) represents the number of channels of the output feature; \(n\) represents the number of times the structure is repeated; \(s\) represents a multiple of reduction relative to the input image.  
\end{table} 
Table 1: The struct of adjusted MobileNetV2. Furthermore, this paper designs two kinds of coordinate transformation functions \(F(.)\). The two coordinate transformation functions are shown in formula 3 and formula 4. \[F_{1}(R_{i}\,^{\prime})=\gamma^{*}R_{i}\,^{*}\!f_{i}=\gamma^{*}(x_{i}\,^{*}\!f_{xi },\,y_{i}\,^{*}\!f_{yi}), \tag{3}\]  
\[F_{2}(R_{i})=R_{i}\,^{\prime}+f_{i}=(x_{i}\,^{\prime}+f_{xi},y_{i}\,^{\prime}+ f_{yi}), \tag{4}\]  
where, \(R_{i}\,^{\prime}=R_{i}+O_{i}=(x_{i}\,^{\prime},y_{i}\,^{\prime});f_{i}=(f_{xi }.\,f_{yi});f_{xi}\) and \(f_{yi}\) are the free offsets in \(x\)-axis and \(y\)-axis respectively, and the value range is \([0,\,1]\); the \(\gamma\) is the relaxation factor of the coordinate transformation range. The set of sampling points on the localization branch is \(L_{d}\). When the coordinate transformation function \(F(. )\) is an identity function, the sampling position \(L_{c}\) based on the degree of freedom degenerates to the original \(L_{d}\). Figure 4: Overview of the proposed LRP-DS: (**a**) the LRP-DS-V1; (**b**) the LRP-DS-V2. Although the design of LRP-DS-V1 can decouple the sampling point set of classification and localization tasks, it may cause the classification task to confuse the object that really needs to be classified, that is, excessive decoupling. Take the left figure of Figure 5 as an example; the yellow rectangle is the current object.