# Bounding Volume Hierarchy-Assisted Fast SAR Image Simulation Based on Spatial Segmentation
## 4 Discussion of Simulation Results
### Analysis of Simulation Results
As shown in Figure 11 (right), both geometric features can almost be fit together, and the amplitude distribution is generally consistent, with some local differences in details. Meanwhile, Table 5 gives some common structural similarity metrics including the normalized correlation coefficient, mean hash similarity, and cosine similarity, indicating that there is a high degree of structural similarity between the simulation results and the real SAR images. Through the above qualitative and quantitative comprehensive analysis, it can be effectively verified that the target simulation results obtained using the proposed method have good fidelity. Based on the above simulation test of the Japanese helicopter carrier, the simulation study of the composite scenario of multiple ships and the sea surface proceeded, as shown in Figure 12a, by selecting the ship 1 (length 305 m \(\times\) width 75 m \(\times\) height 60 m, 53,499 surface facets), the ship 2 (length 200 m \(\times\) width 120 m \(\times\) height 30 m, 127,443 surface facets), the ship 3 (length 167 m \(\times\) width 22 m \(\times\) height 57 m, 204,362 surface facets), and \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**SAR Image Size**} & \multicolumn{2}{c}{**Lattice**} & \multirow{2}{*}{**CPU Time**} & \multirow{2}{*}{**GPU Time**} & \multirow{2}{*}{**Speedup**} \\  & & **(HH)** & & & & \\ \hline \multirow{2}{*}{Japanese helicopter carrier} & \multirow{2}{*}{Azimuth samples} & 680 & \multirow{2}{*}{125,972} & \multirow{2}{*}{65.14 h} & \multirow{2}{*}{0.31 h} & \multirow{2}{*}{210.1\(\times\)} \\  & & samples & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Time consumption. Figure 10: Amplitude difference between single scattering and multiple scattering. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Reference Image**} & \multicolumn{2}{c}{**Normalized Cross-Correlation**} & \multirow{2}{*}{**Mean Hash Similarity**} & \multirow{2}{*}{**Cosine Similarity**} \\  & & & & \\ \hline Real SAR image & 0.89 & 0.91 & 0.93 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Quantitative evaluation of simulation results. ship 4 (length 127 m \(\times\) width 16 m \(\times\) height 40 m, 48,766 surface facets) for sea surface posture simulation. As shown in Figure 12b, we use a directional spectrum of the sea wave made up of the JONSWAP spectrum and Donelan directional extension function to construct the 3D sea surface background [27; 28]. The sea area is set to 1200 m \(\times\) 1200 m, the wind speed is 10 m/s, the wind direction is 45\({}^{\circ}\), and the number of sea surface facets is 289,040, which can be flexibly replaced according to different sea conditions and application requirements. The test selects the parameters in Table 1 (No. II). The total facet number in the composite model of the multi-ships targets and sea surface is 723,110. The interval of lattices is set to half the system sampling space, which is less than the theoretical resolution and higher than the requirement of the Naquist sampling law; the latticed radiation area is shown in Figure 12c, and the number of lattices is 3,928,125. Figure 13 shows the SAR image simulation results of the composite model of the sea surface and ships. Usually, there is a \"four-path\" scattering phenomenon between the sea surface and the ships, including the single and multiple scattering of the ship self-body, the second scattering from the sea surface to the ship, the second scattering from the ship to the sea surface, and the multiple scattering among the sea surface, ship, and sea surface. The backscatter field of the composite scene is the vector superposition of the \"four paths\" backscatter field. As shown in Figure 13, the geometry of the carrier's command tower on the sea surface is more complex and prone to multiple scattering, with stronger backscatter and higher display brightness. The flight deck is mostly a planar structure with only single scattering occurring, and it is relatively darker.