# 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 FFT-SIFT Algorithm for Feature Point Extraction  
The new method of Gaussian pyramid construction based on fast Fourier transform proposed in this paper can speed up the calculation speed of image two-dimensional convolution, thus accelerate the SIFT feature extraction process, and because it does not change the subsequent process of SIFT algorithm, it will not affect its scale and rotation invariance, and will not affect the number of feature points extraction in theory. The advantages of FFT-SIFT are summarized as follows:  
1. The construction time of Gaussian difference pyramid is reduced, and the speed of feature point extraction is accelerated as a whole. 2. Not only the speed is accelerated, but also the number of feature points is not reduced. In order to prove that the FFT-SIFT algorithm has the above characteristics, images collected in the printing process are selected to carry out comparative tests respectively between the traditional SIFT feature point extraction algorithm and the improved FFT-SIFT algorithm. The five images of the printing process are collected and the effect of feature point extraction is compared and analyzed, as shown in Figure 7. The a\({}_{i}\), b\({}_{i}\) and c\({}_{i}\) (\(i\) = 1-5) from left to right are the original image of the printing process, the feature point extraction of the traditional SIFT algorithm and the feature point extraction of the FFT-SIFT algorithm. The experimental results show that the extraction effect of feature points is nearly the same, because the FFT-SIFT algorithm only changes the calculation method of Gaussian filter template convolution, and speeds up the calculation speed of convolution without changing other steps of SIFT. The comparison results of feature points of the two algorithms are shown in Table 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**The Sequence Number of** & **The Number of Feature** & **Time Consumption of SIFT** & **Time Consumption of Feature Points** \\
**the Picture** & **Points Extracted** & **Algorithm to Extract Feature Points** & **Extraction by FFT-SIFT Algorithm** \\ \hline a\({}_{1}\) & 2634 & 4.31 s & 3.21 s \\ a\({}_{2}\) & 1927 & 3.62 s & 2.87 s \\ a\({}_{3}\) & 2879 & 4.43 s & 3.34 s \\ a\({}_{4}\) & 2015 & 3.98 s & 3.12 s \\ a\({}_{5}\) & 2960 & 4.51 s & 3.57 s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the feature points extraction by the different algorithms. Figure 7: Comparison of the feature point extraction results in the printing process. (**a\({}_{1}\)**–**a\({}_{5}\)**) The original image of the printing process; (**b\({}_{1}\)**–**b\({}_{5}\)**) The feature point extraction of the traditional SIFT algorithm; (**c\({}_{1}\)**–**c\({}_{5}\)**) The feature point extraction of the FFT-SIFT algorithm. It can be seen from Table 1 that the speed of feature point extraction by the FFT-SIFT algorithm is higher than that of the traditional SIFT algorithm, but it is not obvious from a single image. Therefore, the FFT-SIFT algorithm is applied to the actual reconstruction system for the overall time statistics, and each image set has 48 photos. As can be seen from Table 2, with the increase of the number of pictures, the FFT-SIFT algorithm has a higher speed of feature point extraction. The efficiency of feature point extraction is obviously improved. Based on the above experiments, the characteristics of the FFT-SIFT method are summarized as follows:  
1. Compared with the traditional SIFT algorithm, the extraction speed of feature points is faster, and the extraction speed is increased by 25.0% in the application of this system
2. The number of feature points extraction does not change while accelerating the speed of feature points extraction.