# Dense Robust 3D Reconstruction and Measurement for 3D Printing Process Based on Vision
## 5 Comparison and Analysis of 3D Reconstruction Experiments in 3D Printing Process
### Experimental and Comparative Analysis of Integrated SFM  
In order to prove the effectiveness and feasibility of the integrated SFM algorithm, the paper compares it with the incremental and global SFM algorithm. The images collected in the printing process are used as the experimental picture set, each picture set has 48 pictures. Some picture sets of the printing process are selected for display as shown in Figure 11a,b: \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Feature Extraction Algorithm** & \begin{tabular}{c} **Average Number of Feature** \\ **Points Extracted** \\ \end{tabular} & \begin{tabular}{c} **Time Consuming of Feature** \\ **Point Extraction (s)** \\ \end{tabular} & \
\begin{tabular}{c} **Time Consuming of Feature** \\ **Point Matching (s)** \\ \end{tabular} &
\begin{tabular}{c} **Average Matching Number** \\ **of Feature Points** \\ \end{tabular} \\ \hline FFT-SIFT & 2578.2 & 73.67 & 24.89 & 263.5 \\ AKAZE & 1396.7 & 70.39 & 16.67 & 215.1 \\ The algorithm in this paper & 3974.9 & 75.35 & 25.58 & 453.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of different algorithms in the printing process. Figure 10: The 3D reconstruction point cloud of traditional SIFT matching algorithm and the 3D reconstruction point cloud of FFT-SIFT-AKAZE. (**a**) The 3D reconstruction point cloud of traditional SIFT matching algorithm; and (**b**) the 3D reconstruction point cloud of FFT-SIFT-AKAZE. Figure 11: Captured images of 3D printing process. (**a**) Photo Gallery 1; (**b**) Photo Gallery 2. The comparison results of the three SFM reconstruction methods are shown in Table 4. The root mean square error of the reverse projection error optimized by the beam adjustment method is taken as the error evaluation standard, and the reconstruction time is taken as the reconstruction efficiency, where the root mean square of projection error is calculated as:  
\[e=\sqrt{\frac{1}{n}{\sum\limits_{i=1}^{n}}\|u_{i}-v_{i}\|^{2}} \tag{17}\]  
where \(n\) is the total number of matching feature points, \(u_{i}\) is the coordinate of feature points, and \(v_{i}\) is the coordinate of projection. In Table 4, \(T_{i}\) is the reconstruction time of incremental SFM, \(e_{I}\) is the reconstruction error of incremental SFM, \(T_{G}\) is the reconstruction time of global SFM, \(e_{G}\) is the reconstruction error of global SFM, \(T_{H}\) is the reconstruction time of comprehensive SFM, \(e_{H}\) is the reconstruction error of comprehensive SFM, and \(\times\) is the reconstruction failure of this image set. Table 4 shows that incremental SFM has the longest running time and global SFM has the shortest reconstruction time. The integrated SFM proposed in this paper is between the two, and the average reconstruction time is 39.3% shorter than incremental SFM. The main reason is that incremental SFM adds image registration camera in turn, locates the feature points through triangulation, and finally performs beam adjustment to optimize the reconstruction model. However, it takes a lot of time to perform beam adjustment optimization continuously. The global SFM is to calculate the pose parameters of all camera views at the same time, triangulate the positioning, and finally perform a global beam adjustment optimization, which reduces the calculation amount and improves the overall reconstruction efficiency. The integrated SFM proposed in this paper adopts the method of grouping similar images to carry out fast global reconstruction of related images within the group, and only incremental reconstruction of images that are not grouped into the group. In this way, compared with incremental SFM, the reconstruction efficiency is improved and the problem of scene drift that may occur in incremental SFM is alleviated. In terms of reconstruction error, the incremental SFM reconstruction error is smaller, and the global SFM reconstruction error is larger. The integrated SFM reconstruction error is between the two, and the reconstruction error is 33.2% less than that of global SFM.