# Dense Robust 3D Reconstruction and Measurement for 3D Printing Process Based on Vision
## 1 Introduction  
The emerging additive manufacturing methods represented by 3D printing have changed the traditional manufacturing mode [1, 2, 3]. 3D printing has the advantages of rapid prototyping, simple use, low cost, and high material utilization [4, 5, 6]. Due to the limitations of the process and the structure of the molding equipment, 3D printing manufacturing is still an open-loop manufacturing in essence. The parts model is uploaded to the printing device, and the tolerance of the structure cannot be measured during the printing process, leading to the failure of closed-loop control in the manufacturing process and the difficulty of guaranteeing the forming accuracy. At present, the research on the 3D printing molding accuracy mainly focuses on the model design in the early stage of printing [7, 8], such as model improvement [9, 10], optimization of printing path [11, 12], and so on. Therefore, it is of great practical significance to carry out the real-time detection of printing parts process precision and realize the process precision control. Existing detection methods for 3D printing process parts mainly use indirect detection. For example, the fused deposition modeling process can indirectly reflect defects by detecting the working current change of wire feeding motor, transmission mechanism tension, and other indicators, and detect specific defects of specific 3D printing structure through CT and X-ray [13, 14]. However, the printing process is affected by many factors, and these methods have limitations in application. Obviously, the panoramic 3D informationof the structure surface in the 3D printing process can better reflect the quality of the printed structure. Compared with the existing panoramic 3D reconstruction methods, the monocular vision 3D reconstruction method based on structure motion recovery (SFM) is suitable for 3D detection in the 3D printing process because of its low cost, simple structure and high reconstruction accuracy [15; 16].The process of 3D reconstruction based on SFM generally includes image acquisition preprocessing, feature point extraction and matching, 3D sparse point cloud densification and surface texture reconstruction. The extraction and matching of feature points is the key of reconstruction, which determines the final accuracy of 3D reconstruction. The classic algorithm for feature point extraction is the SIFT algorithm [17], which has good robustness and stability when dealing with the change of image scale and image rotation, but involves a large amount of computation and has low efficiency. The SURF algorithm solves the shortcomings of SIFT algorithm, such as high computational complexity and long time-consuming, and improves the speed of feature extraction [18], but it is inferior to SIFT in the robustness of illumination and deformation. The KAZE algorithm is the most effective feature point extraction algorithm in recent years [19]; its efficiency is similar to that of SIFT algorithm, and its stability is better than the SIFT, but its scale robustness is not as good as the SIFT. Most of the 3D printed parts are of single color, and require high robustness and accuracy in the printing process detection, so the existing feature extraction algorithms are not fully applicable. The key to solve this problem is to improve the speed of feature extraction and acquire as many feature points as possible, especially to preserve the edge feature information. The generation methods of sparse point cloud mainly include the incremental SFM method and global SFM method [20; 21]. The reconstruction accuracy of incremental SFM is higher, but it is greatly affected by initialization, and it is easy to accumulate errors with the reconstruction process, especially when the motion trajectory of the image collected by the camera is in loop state. The global SFM method is less affected by the initial model, less affected by drift and faster in reconstruction, but sensitive to noise.