# A CSAR 3D Imaging Method Suitable for Edge Computation
## 3 A CSAR 3D Imaging Method Suitable for Edge Computation
### Algorithm Flow
IRT is performed on \(s_{\mathrm{rj\_sub,i}}(\tau,\varphi)\) along the slow time direction to obtain \(I_{\mathrm{rj\_sub,hk,i}}\), which is a 2D image of each sub-aperture at height \(h_{k}\):  
\[I_{\mathrm{rj\_sub,hk,i}}=\mathrm{IRT}\Big{[}s_{\mathrm{rj\_sub,j}}(\tau, \varphi)\Big{]} \tag{16}\]  
where \(\mathrm{IRT}[\cdot]\) denotes the IRT. (4) Sub-aperture image fusion. To reduce the average effect of sub-apertures in incoherent processing and the influence of scattering center intensity in different sub-apertures,sub-aperture images are fused based on the generalized likelihood ratio test (GLRT) [16], and the largest pixel in each sub-image is taken as the pixel of the final 2D image:  
\[I_{\rm final,hk}(x,y)=\underset{i}{\rm argmax}\Big{|}I_{\rm f_{\rm final,sub,hk}(x, y)}\Big{|} \tag{17}\]  
where \(I_{\rm final,hk}\) is the CSAR 2D image representing the height \(h_{k}\). CSAR 2D images with different heights are then superimposed to form a CSAR image volume \(\mathbf{I}_{\rm final}\). **Step 3**: Extract the CSAR 3D point cloud. Hough transform is used to extract the intersection points of the height slices of the defocused circle in the X and Y directions, respectively. Lastly, 3D point cloud extraction is completed after voting fusion. (1) Layering along the X (Y) direction. Firstly, the CSAR image volume \(\mathbf{I}_{\rm final}\) obtained in step 2 is layered along the X direction and the Y direction, respectively, as shown in Figure 4a. Each layer's data \(I_{\rm Yj}\) (\(I_{\rm Yj}\)) represent a change in the Z\(-\)Y (Z\(-\)X) direction, where \(j=1,2,\cdots,J\). Then, the Canny operator is used to binarize each layer of data \(I_{\rm Yj}\) (\(I_{\rm Yj}\)) to obtain \(I_{\rm X0j}\) (\(I_{\rm Y0j}\)), which prepares the data for the Hough transform;  
(2) Hough transform along the Z direction. Carry out a one-dimensional Hough transform on \(I_{\rm X0j}\) (\(I_{\rm Y0j}\)) along the Z direction and extract the peak points \((\rho_{i},\vartheta_{i})\) of the Hough transform in each layer, where \(i\geq 2\). The upper limit needs of \(i\) can be set according to the number of targets to be extracted in this layer;  
(3) Output intersection points. According to Formula (14), calculate the intersection points of the straight lines in \(I_{\rm X0j}\) (\(I_{\rm Y0j}\)), as shown in Figure 4b;  
Figure 3: Schematic diagram of climber position prediction: (**a**) \(pos(t_{k})\) at a non-boundary; (**b**) \(pos(t_{k})\) at the boundary. (4) Voting fusion to extract the 3D point cloud. In the 3D grid composed of the CSAR image volume \(\mathbf{I}_{\text{final}}\), according to the Hough transform, the output intersection coordinates are voted for in the corresponding grid. As seen in Figure 4c, only when the height of the imaging plane is consistent with the actual height of the target will the output intersection coordinates in the X and Y directions completely coincide when the target is entirely focused. If the grid voting result exceeds a certain threshold, the CSAR 3D point cloud extraction is considered complete.