## 2 Stereo Reconstruction Algorithm for Unstructured Scenes
### GVDS Feature Extraction Algorithm  
The calculation of the depth value is the process of finding the set of spatial 3D points and includes two parts: the selection of feature points and the calculation of the depth value. When conducting a stereo 3D reconstruction project, the stereo camera can generally use a fixed camera position and parallel structure pose to shoot the scene to be reconstructed. The schematic diagram of the depth value calculation with the stereo parallel optical axis structure is shown in Figure 6.  
As shown in Figure 6, point \(P(X_{w},Y_{w},Z_{w})\) is an observed point in 3D space that corresponds to points \(P(u_{l},v_{l})\) and \(P(u_{r},v_{r})\) on the imaging planes of the left and right cameras, respectively, and points \(O_{CL}\) and \(O_{CR}\) indicate the optical centers of the left and right cameras, respectively. It is obvious from observation that the relationship between these five points in space is in accordance with the triangulation principle. Since the main ray axes of the left and right cameras are horizontal and parallel, the x-axes of the coordinate systems of the two cameras overlap: that is, disparity only exists in the direction of \(x\). The formula for calculating disparity \(d\) is:  
\[d=L_{l}\ \ \ \ L_{r} \tag{14}\]  
According to Figure 6, using the similar triangle determination property, we can conclude that:  
\[\frac{f}{Z_{w}}=\frac{L_{l}}{B/2+X_{w}}=\frac{L_{r}}{B/2\ X_{w}} \tag{15}\]  
Combining the above two equations, the depth value \(z\) of point \(P\) can be expressed as:  
\[z=\frac{B\ f}{L_{l}\ L_{r}}=\frac{B\ f}{d} \tag{16}\]  
Combined with the depth calculation formula, the depth information for point \(P\) can finally be determined as follows:  
\[\left\{ \begin{array}{l}X_{w}=\frac{B\ u_{l}}{u_{r}}\ u_{l}\\ Y_{w}=\frac{B\ u_{l}}{v_{r}}\frac{y}{u_{l}}\\ X_{w}=\frac{B\ f}{u_{r}}\frac{y}{u_{l}}\end{array} \right. \tag{17}\]  
where \(f\) is the camera focal length, \(B\) indicates the distance between the left and right camera optical centers, and \(d\) is the disparity value. The formula shows that the depth  
Figure 6: Principle diagram for parallel optical axis depth value calculation. information for the object can be determined with only the corresponding point positions of the spatial points on the left and right images when the relevant parameters of the camera are known. The above solution process can accurately obtain the 3D coordinates of a point in space. In order to reach the accuracy and efficiency required for scene reconstruction, it is necessary to first consider the distribution of the extracted feature point set and then calculate the 3D coordinates of the feature points. However, it is difficult to reconstruct the scene with weak texture information because this area contains very little information compared to the surrounding scene, and it is extremely difficult to guarantee the reconstruction quality while ensuring scene reconstruction efficiency. In the usual, fixed depth value calculation step, the feature points are extracted mechanically only in the areas with strong texture information and depth variation, and it is extremely difficult to extract feature points in the weak-texture and low-comparison areas with the same scene background. When faced with a scene that itself occupies a large number of weakly textured areas, the difficulty of extracting feature points can be the primary problem that prevents the formation of an effective visual 3D model. To meet the dual criteria of accuracy and efficiency, it is necessary to consider the distribution of extracted feature points and then calculate the 3D coordinates of feature points to form a more efficient 3D point cloud.