# Focusing 3D Small Objects with Object Matching Set Abstraction
## 3 Methodology
### Cube Query  
In ball query, the points within a spherical range are typically regarded as the neighboring points. The shape of the ball differs significantly from that of the objects, leading to an under-consideration of informative points and an over-consideration of noise points. Motivated by this, we design a cube query to acquire neighboring points with fine-grained 3D information. The comparison is outlined in Figure 3.  
Figure 1: The framework of our approach OMSA.  
Figure 2: The diagram of the focus-based sampling.  
As shown in Figure 3, the geometric shapes of the ball and pedestrians are quite different, which makes it easy to ignore key points or introduce more noise. In addition, Pillar Query [28] considered the entire \(z\) axis range, leading to more noise injection. In contrast, the cube query can adjust the length, alleviating the impact of irrelevant points on learning. Concretely, we employ FocS to obtain the key points, and a cube-based grouping operation, i.e., cube query, is utilized to partition the points:  
\[\{GA(k)=\{p\in P|D_{X}(p,k)<l,D_{Y}(p,k)<l,D_{Z}(p,k)<l\},k\in K\} \tag{3}\]  
\[D_{X}(p,k)=|p(x)-k(x)| \tag{4}\]  
\[D_{Y}(p,k)=|p(y)-k(y)| \tag{5}\]  
\[D_{Z}(p,k)=|p(z)-k(z)| \tag{6}\]  
where \(GA(k)\) denotes the grouping results array; \(\mathbf{P}=\{\mathbf{P}_{j}\}_{j=1}^{N_{j}-1}\) represents the input points; \(\mathbf{K}=\{\mathbf{K}_{j}\}_{j=1}^{N_{w}-1}\) is the set of key points; \(N_{m}\) is the number of sampled points; and \(D_{X}(p,k)\), \(D_{Y}(p,k)\), and \(D_{Z}(p,k)\) represent the distances along the \(x\), \(y\), and \(z\) axes, respectively.  
Similar to the ball query, we can obtain multi-scale neighboring points by setting different values of \(l\), thereby promoting global feature learning. Compared with the ball query, the presented geometry-aware query operation can effectively capture the object-related points. We find that the results of the cube query are slightly better than the ball query, as shown in Table 1. The cube query exhibits a closer alignment with the geometric characteristics of pedestrians and cyclists, facilitating accurate feature extraction of small objects.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{3}{c}{**Car**} & \multicolumn{3}{c}{**Pedestrian**} & \multicolumn{3}{c}{**Cyclist**} \\  & **Easy** & **Moderate** & **Hard** & **Easy** & **Moderate** & **Hard** & **Easy** & **Moderate** & **Hard** \\ \hline Baseline (Ball Query) & 91.18 & 82.94 & 80.34 & 60.65 & 57.53 & 51.30 & 91.10 & 72.02 & 67.64 \\ Model A (FocS + Ball Query) & 90.37 & 80.49 & 77.75 & 62.02 & 58.10 & 50.96 & 92.16 & 72.50 & 66.96 \\ Model B (Cube Query) & 91.09 & 82.72 & 79.75 & 59.09 & 58.92 & 52.26 & 92.27 & 73.13 & 67.20 \\ Model C (FocS + Pillar Query) & 88.66 & 78.97 & 78.24 & 66.63 & 60.58 & 55.01 & 88.67 & 72.19 & 67.77 \\ Model D (Two SA Layers) & 91.25 & 82.68 & 80.15 & 66.93 & 59.90 & 54.03 & 91.46 & 71.74 & 67.03 \\ OMSA (FocS + Cube Query) & 91.53 & 82.81 & 80.25 & 69.59 & 62.47 & 56.77 & 92.41 & 73.24 & 68.85 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Effect of each presented module  
Figure 3: Comparison of the different methods. (**a**) Ball query; (**b**) pillar query; (**c**) cube query.