# Implicit-Explicit Coupling Enhancement for UAV Scene 3D Reconstruction
## 2 Implicit-Explicit Coupling-Enhancement-Based 3D Reconstruction
### Implicit Synthetic Co-Visibility-Cluster-Guided Dense 3D Reconstruction
#### 2.1.1 Implicit Representation of UAV Large-Scale Scenes
The exact method for calculating similarity \(\xi\) is as follows:  
\[\xi=\frac{2N_{fit}}{N_{I_{i}}^{LoFTR}+N_{I_{j}}^{LoFTR}} \tag{1}\]  
where \(N_{I_{i}}^{LoFTR}\) represents the number of LoFTR features in image \(I_{i}\), and \(N_{fit}\) represents the number of matched feature pairs. Due to the decreasing similarity between \(I_{1}\) and nearby images \((I_{2},I_{3},\ldots,I_{i})\), the last image \(I_{i}\) with a similarity greater than or equal to \(\xi_{covisibility}\) is selected as the central scene for the co-visible cluster. Using \(I_{i}\) as the reference, subsequent images are compared for scene overlap. Images in the sequence are sampled based on their temporal relationship with \(I_{i}\), and those with a similarity exceeding \(\xi_{covisibility}\) are added to the co-visible cluster sequence \(C_{i}\{I_{i},\ldots\}\). This completes the selection of the first co-visible cluster. Similarly, we need to find the last image among the frames before and after \(I_{i}\), where the regional overlap is greater than \(\xi_{covisibility}\), and this image becomes the central scene for the second co-visible cluster. This process is repeated until the last co-visible center in the vicinity still has a similarity greater than \(\xi_{covisibility}\) when compared to the end image \(I_{n}\) of the image sequence. At this point, all co-visible clusters within the existing image sequence have been identified, and the subsequent neural radiance field training phase begins. The method for establishing an individual neural radiance field is as follows: First, obtain the depth map \(D_{i}\) and camera parameters \(T_{i}\) for each frame based on Droid SLAM. Next, use an autoencoder structure to encode the input image into a latent vector and decode this latent vector into parameters for a multi-plane NeRF. These NeRF parameters include color and density for each plane. Then, employ a renderer to generate the image for each frame based on the parameters of the multi-plane NeRF and the camera pose. The renderer uses the same volumetric rendering formula as Instant NGP [38], taking into account the color and density of each plane and the distance between the camera and the planes to compute the color of each pixel. Finally, minimize the reprojection loss function to minimize the L1 norm between the rendered image and the input image. The reprojection loss function is as follows:  
\[L_{rep}=\sum_{i}\left\|I_{i}-\widehat{I}_{i}\right\|_{1} \tag{2}\]where \(I_{i}\) is the input image, and \(\widehat{I_{i}}\) is the rendered image. To generate more accurate modeling results, the neural implicit representation not only requires providing color images from new viewpoints but also needs corresponding dense depth maps to eliminate the impact of holes in textureless surface models caused by MVS methods. However, the output dimensions of the neural radiance field model do not directly contain depth information, but only include scene opacity information, which is related to the three-dimensional position of the described point and independent of the selected viewpoint. Clearly, we cannot simply use opacity information as depth information for calculation. Therefore, it is necessary to derive the correspondence between density predictions from the neural radiance field and depth. First, let us assume a ray originates from a point \(x\) in space. To obtain depth information from a specific viewpoint \(v_{i}\) to the point \(x\), we need to sample along the direction of the ray. Let \(x_{i}\) be a sampling point along the ray, and each point has its corresponding density value \(\sigma(x_{i})\), which represents the probability of the point emitting or reflecting rays. To calculate depth, we need to determine the position where the ray terminates when it encounters an opaque object. In the neural radiance field, when a ray encounters an opaque object, it is completely absorbed or reflected and cannot continue to propagate. At this point, the final position the ray reaches is the depth.