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Novel SfM-DLT method for metro tunnel 3D reconstruction and Visualization
Journal Pre-proofs Novel SfM-DLT Method for Metro Tunnel 3D Reconstruction and Visualization Yadong Xue, Sen Zhang, Mingliang Zhou PII: DOI: Reference:
S2467-9674(19)30099-6 https://doi.org/10.1016/j.undsp.2020.01.002 UNDSP 132
To appear in:
Underground Space
Received Date: Revised Date: Accepted Date:
28 December 2019 26 January 2020 26 January 2020
Please cite this article as: Y. Xue, S. Zhang, M. Zhou, Novel SfM-DLT Method for Metro Tunnel 3D Reconstruction and Visualization, Underground Space (2019), doi: https://doi.org/10.1016/j.undsp.2020.01.002
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2019 Tongji University and Tongji University Press. Production and hosting by Elsevier B.V. on behalf of Owner.
Novel SfM-DLT Method for Metro Tunnel 3D Reconstruction and Visualization Yadong Xue1,2, Sen Zhang2, and Mingliang Zhou1,2* 1
Key Laboratory of Geotechnical and Underground Engineering of Education Ministry, Tongji University, Shanghai 200092, China
2
Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China *[email protected]
Abstract: Metro tunnels play a crucial role in urban transportation. However, with growing tunnel operation periods, defects, and large deformations appearing, these are influencing tunnel structural performance and threatening public safety. Three-dimensional (3D) tunnel reconstruction is an effective way to highlight tunnel conditions and provide a basis for engineering management and maintenance. However, the current methods of tunnel 3D reconstruction do not sufficiently combine the qualitative and quantitative characteristics of tunnel states. In this study, a novel method for metro tunnel 3D reconstruction based on structure from motion (SfM) and direct linear transformation (DLT) is proposed. The dimensionless 3D reconstruction point cloud acquired through the SfM method showcases the qualitative characteristics (such as leakage and pipelines) of the tunnel state. The closerange photogrammetry DLT method provides scale information missing from the SfM method and quantitative characteristics (such as profile deformation) of the tunnel state. The SfM-DLT method was tested in a Shanghai metro tunnel, and proved to be feasible and promising for future tunnel inspections. Keywords Metro Tunnel; 3D Reconstruction; Visualization; Structure from Motion; Direct Linear Transformation
1
Introduction Congested traffic is a serious issue for megacities around the world, and public transportation is an
effective way to alleviate this problem. As a form of public transportation, metros utilize underground
2
space and do not occupy much above-ground space. They are also environmental-friendly, fast, and have a large transportation capacity. Accordingly, metro systems have played a crucial role in urban operations. With increasing metro tunnel operation periods, structural defects (such as leakages and cracks) begin to develop in the tunnel linings. Further, because of strata and train dynamic load actions, large deformations may appear in tunnel segments. These defects and deformations stimulate each other, causing deterioration of the structural performance of metro tunnels. This threatens tunnel operational safety and causes further social and environmental safety issues (Zhu and Huang, 2010; Zhang et al., 2014). Much of the existing research suggests that timely tunnel inspections help to locate potential danger zones in a metro tunnel (Wang and Huang, 2015; Gan and Zhou, 2019). Engineers can then make maintenance decisions according to the inspection results to ensure the structural safety of the tunnel (Masumi et al., 2016; Daniel et al., 2017; Zhang et al., 2019a). Tunnel inspection consists of defect inspection and deformation measurements. Machine learning techniques have demonstrated promising efficiency in detecting defects, but they cannot measure tunnel lining deformations (Huang and Li, 2017; Xue and Li, 2018; Zhang et al., 2019b). Laser scanning and photogrammetry methods have been applied to measure tunnel profiles, but they have a low capability in detecting tunnel lining defects (Xie et al., 2013; Xie and Lu, 2017). Therefore, a new method is required that combines both the defect and deformation aspects. Conducting an inspection on a reconstructed three-dimensional (3D) metro tunnel model is a potential method for achieving this aim. Leakages and cracks can be easily visualized in a fine 3D reconstruction tunnel model, and tunnel lining deformation information can also be obtained. Photogrammetry is a common technique for 3D reconstruction. However, most photogrammetry methods have demanding site requirements that many metro tunnels cannot fulfill. Laser scanning is another typical 3D reconstruction method. The problem with laser scanning is that the laser point cloud does not contain color and texture information of the lining surface. Therefore, detecting cracks is more difficult. Moreover, the inspection speed is slow, the equipment is expensive, and post-processing is time-consuming. Hence, a new 3D reconstruction method should be developed to conduct quick, automatic, and accurate inspections at low cost. In this study, a novel method for metro tunnel 3D reconstruction combining structure from motion (SfM) and direct linear transformation (DLT) is proposed. SfM is a 3D reconstruction method with low site requirements, and it is widely used in topography measurements (Snavely et al., 2006; Bi et al., 2017; Surya et al., 2018; Wang et al., 2018). DLT, a photogrammetry method, has been used for the past few years to measure tunnel profiles (Chen et al., 2014; Ai et al., 2015; Xue et al., 2017). Dimensionless 3D reconstruction point clouds that showcase the overall tunnel state are acquired using the SfM method and a consumer-level digital camera. The points cloud model contains color, texture, and shape
3
information but lacks scale information. The close-range photogrammetry DLT method is utilized to provide the missing scale information of the SfM model. The proposed SfM-DLT method was tested in a Shanghai metro tunnel, and the precision of the 3D reconstruction model was satisfying. The remainder of this paper is organized as follows. Section 2 describes the concepts and application of the SfM method. Section 3 introduces the DLT method for measuring tunnel deformation. Section 4 gives a specific project application case, and Section 5 presents the discussion and concluding remarks.
2
SfM for metro tunnel 3D reconstruction
2.1
Basic principle
The SfM algorithm is an off-line algorithm for 3D reconstruction that is based on a series of unordered images. The specific procedures and algorithm flow of SfM 3D reconstruction are described as follows (Fig. 1):
Fig. 1. The specific procedures and algorithm flow of SfM 3D reconstruction. (1) There are a few steps that must be completed before applying the SfM algorithm. The focal length is obtained from the original image exchangeable image file format (EXIF) information. The image features are extracted by the scale-invariant feature transform (SIFT) algorithm. The feature points are then paired between two images using the k-dimensional tree (KD-TREE) model. For each pair of matched images, the epipolar geometry is calculated. The random sample consensus (RANSAC) algorithm is used to optimize the image matching. If the same feature point is continuously detected in different image pairs, then the motion and track are formed. (2) The first step of the SfM algorithm is choosing the appropriate image pairs to initialize the bundle adjustment, which is a nonlinear least square optimization method. Once the bundle adjustment is completed for the initial image pair, new image pairs are repeatedly added to recursively execute new bundle adjustments. The bundle adjustment process is finished when there are no new image pairs. Then, the estimated camera parameters and sparse reconstruction points cloud are obtained (Wu et al., 2011; Wu, 2013). The initial image pair is required to have enough matched feature points and a large enough camera center distance.
4
(3) Clustering views for multi-view stereo (CMVS) takes the output (a set of images and camera parameters) of SfM as its input and then decomposes the input images into several clusters of a manageable size. A multi-view stereo (MVS) is used to independently and parallelly process each cluster and then reconstruct the 3D structure of the object or scene visible in the images. CMVS outputs a set of oriented points instead of a polygonal (or mesh) model. (4) By solving the Poisson equation, the implicit equation representing the surface information of the points cloud model is obtained. Through isosurface extraction, the surface model with the geometric entity information is obtained. This model can be used in other analyses such as the finite element method (FEM). VisualSfM is an automated graphical user interface (GUI)-based end-to-end 3D reconstruction system distributed by Zheng and Wu (2015). The system integrates several algorithms: SiftGPU, multicore bundle adjustment (BA) (Wu et al., 2011), SfM (Snavely et al., 2006; Bi et al., 2017; Surya et al., 2018), and CMVS which is distributed by Furukawa and Ponce (2010). In this study, VisualSfM is used to fulfill the first three procedures of SfM 3D reconstruction, and the final procedure is fulfilled by MeshLab (Cignoni et al., 2008), which is an open-source system for processing and editing 3D triangular meshes. 2.2
Reconstruction examples
As shown in Fig. 2, two shooting schemes are explored for metro tunnel reconstruction. The blue dot signifies the camera position, and the red arrow signifies the shooting direction. Shooting Scheme 1 shoots images at one tunnel cross-section using six different stations. Three images were shot at three different heights at each station, resulting in 18 original images at each cross-section. Shooting Scheme 2 shoots forward at the center of the lining and moves along the tunnel in the longitudinal direction with a fixed distance interval. Shooting Scheme 1 is applicable for precise and stationary measurements, while Shooting Scheme 2 is for quick and moving measurements. The original images taken by the two schemes are shown in Fig. 3. In this study, a Fujifilm XPRO-2 camera with a Laowa 9 mm f2.8 lens was used to obtain the required images. The camera has a 24 mega-pixel ad-hoc positioning system (APS)-C sensor, and its Laowa 9 mm lens provides a diagonal view angle of approximately 114°. There was no supplementary lighting, and the surrounding scene of the tunnel was illuminated by the site lighting equipment. The illuminance recorded on the site was 100 lux. The exposure parameters of the images were an aperture of 2.8, ISO of 3200 and shutter speed of 1 s.
5
Fig. 2. Two types of shooting schemes.
(a) images taken by Shooting Scheme 1
(b) images taken by Shooting Scheme 2
Fig. 3. The original images taken by the two different schemes. All original images of both shooting schemes were fed into the VisualSfM software without any camera calibration. The estimated camera position, shooting direction, and camera parameters were calculated automatically, and the results are shown in Fig. 4. The calculation environment was a I76700HQ CPU desktop. The time elapsed during the calculation process for Shooting Schemes 1 and 2 were 56 and 58 s, respectively. Then, the dense reconstruction was carried out, and the CMVS results were fed into the MeshLAB, which is visualized in Fig. 5. This process was more time-consuming than the last process with a time elapse of 483 and 475 s for Shooting Schemes 1 and 2, respectively. Some process techniques were used to accelerate the calculation. For an image sequence (like continuous
6
frames of a video), an interval was set to calculate the correspondence points of an image with only a few nearby images instead of with all the other images. The computational demand then decreased significantly. A few factors influencing the reconstruction precision should be noted. (1) The original images need to have appropriate exposure, accurate focus, and more than 60% overlapping area taken from different directions and positions. (2) Higher resolution images are expected to produce a more precise model. (3) The lighting device in the tunnel caused different lens flare shapes in different images, which caused some errors in reconstruction. The reconstruction model obtained through the SfM does not contain scale information. In practice, it needs a ruler to be projected to the actual size. For this study, the DLT method is proposed to provide the reference ruler.
(a) SFM results from Shooting Scheme 1
(b) SFM results from Shooting Scheme 2.
Fig. 4. The visualized results of sparse reconstruction in the VisualSfM.
(a) CMVS results from Shooting Scheme 1
(b) CMVS results from Shooting Scheme 2
Fig. 5. The visualized results of dense reconstruction in MeshLAB.
7
3
DLT for tunnel lining measurement Most photogrammetry methods have demanding site requirements that metro tunnels cannot fulfill.
The DLT method requires no camera calibration, and the calculation is based on the original images themselves. A novel method for using DLT in tunnel profile measurements was proposed by the author research group (Xue and Zhang, 2020), and a device called moving tunnel profile measurement (MTPM1) was developed. The developed device was used in this study for tunnel profile measurements. 3.1
Basic principle of DLT
The goal of photogrammetry is to convert from pixel to world coordinates. The DLT method directly converts these coordinates, as shown in Eqns. (1) and (2). Some of the control points are set to calculate the unknown m matrix. Then, the world coordinates of the target points are calculated. The difficulty in applying the DLT method to tunnel profile measurement mainly lies in setting the points. Setting fixed points such as reflectors is inefficient. A novel moveable point setting method was proposed by the author research group (Xue and Zhang, 2020). 1
i wi i wi uZ i wi uY ui Xwi Ywi Zwi 1 0 0 0 0 uX m1m11111 0 0 0 0 Xwi Ywi Zwi 1 vX , vY vZ vi i wi i wi i wi 2i11 2i1
(1)
i wi uY i wi uZ i wi Xwi Ywi Zwi 1 0 0 0 0 uX ui T m1 m11 , 0 0 0 0 Xwi Ywi Zwi 1 vX 111 viZwi vY i wi i wi vi 2i1 2i11
(2)
T
where Xwi, Ywi, Zwi signify the world coordinates of the i-th point; ui, vi signify the pixel coordinates of the i-th point; m1 to m11 are the unknown parameters defining the m matrix. Figure 6 presents the MTPM-1 device components. The main concept is to use a rotatable laser range finder to provide a series of control points and to use a linear laser source to provide the target points that then form the profile. In Fig. 6, 1 denotes the tunnel lining, 2 is the circular profile projected by a linear laser source onto the lining, 3 is a linear laser source, 4 is a laser range finder, 5 is a rotating shaft, 6 is a power supply, 7 is a wheel, 8 is a working panel, 9 is a camera and wide-angle lens, and 10 is a tripod.
8
Fig. 6. The MTPM-1 device components. 3.2
Measurement example
A typical set up of the MTPM-1 in the metro tunnel is shown in Fig. 7. During the field test, the laser range finder was rotated 20° after each shot for a total of seven times. An image was taken after each rotation; hence, a total of eight images were taken at each location. Eight control points were obtained, with corresponding image coordinates, measured distance, and angle information, to perform the DLT calculation. Then, the DLT fitting result was obtained. The laser range finder had a measuring precision of 1.5 mm ± 20 ppm. The measuring point diameter was 4mm, and the laser wavelength was 620–690 nm. After the shooting was completed, the laser range finder was rotated back to the original position and was then rotated slowly and continuously 180° with a rotation speed of 1°/s. The measurement frequency was set to 1 Hz. A total of 180 distance values were recorded for each tunnel lining section to form the ground truth profile for evaluating the DLT precision. There were eight measured profiles with a 5 m interval in a 40 m tunnel section, as shown in Fig. 8. A blue curve was constructed based on the 180 measured range values of each tunnel lining section, and is shown as a comparison reference in Fig. 8. In Fig. 8, the green points are the DLT fitting results. To evaluate the DLT fitting precision, an ellipse fitting was performed. The ellipse fitting results consist of five parameters: a long axis, a short axis, ellipse center x/y coordinates, and an x-axis rotation angle. To conduct the ellipse fitting, disturbance points were removed manually (such as the points on the bottom floor). The ellipse fitting of the DLT profile was completed using the remaining points, and a red curve was drawn. The blue curves are the ground truth profiles, and they highly coincidence with the red curve. Working parameters including control point number, control point layout, and image resolution are set to 8, a uniform distribution, and 24 megapixels, respectively. According to the comparison between the measured profile and laser scanning results, the maximum axis error is 5 mm.
9
Fig. 7. A typical original image taken in the field.
Fig. 8. A series of measured profiles.
4
Engineering application of the SfM-DLT method The SfM-DLT method can produce two outputs: the SfM reconstruction results provide the
qualitative characteristics of the tunnel state, and the DLT measurement results provide the quantitative characteristics of tunnel deformations. Therefore, the proposed method can acquire both the qualitative and quantitative characteristics of the metro tunnel state. Analyses of the proposed method results are performed for the following four aspects: precision, economy cost, field operation time cost, and internal operation time cost.
10
The original images taken using the SfM-DLT method are shown in Fig. 9. The shooting scheme is the same as Shooting Scheme 1. A total of 18 field images were taken. The qualitative characteristics of the tunnel state using the SfM-DLT method are shown in Fig. 10. The leakage location is clearly visible and is marked by a red square in the 3D reconstructed model. The missing scale information in the SfM model can be provided by the DLT results. This information is filled in by setting the distance value between two picked points, and an example is shown in Fig. 11. The distance is acquired from the DLT results. The SfM model is then scaled to the actual size based on the quantitative measurements. Once the scale information is acquired, the precise leakage area can be calculated. The quantitative characteristics of the tunnel state using the SfM-DLT method are shown in Fig. 12. The horizontal axis of the tunnel is approximately 5521 mm, and the vertical axis of the tunnel is approximately 5486 mm, which is a typical “duck egg” deformation pattern. After comparing the DLT results with those of the true profile, the axis error is approximately 4 mm; the distance between the two picked points is 5093 mm. The profile can then be utilized to detect the metro gauge to ensure train safety. In the SfM model, the error is mainly derived from the lens flares, initial EXIF parameters, image distortions. and image quality. In the DLT model, the error mainly comes from the image distortions and laser distance measurements. The self-made equipment is mainly composed of eight laser range finders, a moving vehicle. and a camera system. The laser range finders cost approximately 2500 US dollars, the moving vehicle costs approximately 3000 US dollars, and the camera system (Fujifilm X-PRO2 and LAOWA 9 mm f2.8) costs approximately 1500 US dollars. The total cost is approximately 8000 US dollars. Typically, a set of commercial laser scanning equipment costs approximately 100 000 US dollars to 150 000 US dollars. Therefore, the proposed system in the study costs only around 6% to 8% of the commercial one. Shooting Scheme 1 is more time-consuming in the field than Shooting Scheme 2 as the camera must be moved more, but it also provides a finer model. In practice, Shooting Scheme 1 is applicable to inspections of a certain location, whereas Shooting Scheme 2 is applicable to faster inspections of a tunnel section. The time consumption situation is similar for both schemes in the internal operation stage. Nevertheless, many techniques can be used to accelerate the calculation process such as GPUbased calculation or setting optimal parameters in the software.
11
Fig. 9. The original images taken using the SfM-DLT method.
(a) the 3D reconstructed model
(b) the leakage location Fig. 10. The qualitative characteristics of the tunnel state using the SfM-DLT method.
12
Fig. 11. Setting the distance value between two picked points.
Fig. 12. The quantitative characteristics of the tunnel state using the SfM-DLT method.
5
Discussion and conclusion The SfM method mainly focuses on 3D reconstruction but lacks scale information, whereas the DLT
method focuses on profile measurement but lacks environmental information. Therefore, by combining these two methods for tunnel inspection, the proposed SfM-DLT method presents several advantages, such as not requiring prior camera calibration, low site requirements, reduced equipment costs, and greater applicability in the tunnel environment. Future metro tunnel inspections will require faster inspection speeds, and unmanned aerial vehicles (UAVs) could be used to carry out tunnel inspections. UAVs are light, portable, and relatively cheap.
13
As the SfM method only needs a series of field images, it is possible to combine SfM with UAVs. The UAV-SfM is a highly promising tunnel inspection method. After the UAV flies along the tunnel and collects a large number of images, SfM is used to generate a 3D reconstruction model of the monitored sites quickly. Then, the model can be inputted into the FEM or other software to perform additional structure analyses and provide information for engineering decisions. That is the projected development direction for this proposed method. The proposed method still has some limitations. For example, lens flare had a significant influence on the reconstruction precision. This issue may be solved by using supplementary lighting and adjusting the exposure parameters to attenuate the environmental light. Additionally, in the DLT calculation process, some manual work is required such as extracting the pixel coordinates of the control points, which increases the time consumption of the method. This may be mitigated by using an automatic pixel extraction algorithm in future work. In conclusion, a novel SfM-DLT method of tunnel 3D reconstruction was proposed. It can aid field engineers in conducting tunnel inspections automatically and intelligently. More importantly, the proposed method can provide not only the qualitative characteristics (leakage) but also quantitative characteristics (deformation) of metro tunnel linings.
Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements The work presented in this article was supported by the Science and Technology Commission of Shanghai Municipality (Grant No. 18DZ1205902), the Key innovation team program of innovation talents promotion plan by MOST of China (No. 2016RA4059), and the National Key R&D Program of China (Grant No. 2018YFB2101000).
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Chen, Z.H., Zhao, M., & Qiao, D.L. (2014). Study on a method of metro tunnel deformation monitoring based on the theory of close range photogrammetry. Special Structures, 31(5), 61–65. (in Chinese) Cignoni, P., Callieri, M., Corsini, M., Dellepiane, M., Ganovelli, F., & Ranzuglia, G. (2008). Meshlab: an open-source mesh processing tool. In Eurographics Italian chapter conference 2008, ISBN 978-3905673-68-5, The Eurographics Association, 129–136. Daniel, L., Pierre, B., & Claude, B. (2017). Improving the diagnosis methodology for masonry tunnels. Tunnelling and Underground Space Technology, 70, 55–64. Furukawa, Y., & Ponce, J. (2010). Accurate, dense, and robust multiview stereopsis. IEEE transactions on Software Engineering, 32(8), ISSN 0162-8828, IEEE, 1362–1376. Gan, Q.Y., & Zhou, J. (2019). Current research on tunnel monitoring and measurement technology. Chinese Journal of Underground Space and Engineering, 15(S1), 400–415. (in Chinese) Huang, H.W., & Li, Q.T. (2017). Image recognition for water leakage in shield tunnel based on deep learning. Chinese Journal of Rock Mechanics and Engineering, 36(12), 2861–2871. (in Chinese) Masumi, T., KoiChi, K., Shinji, K., Takanori, M., & Kosuke, F. (2016). Development of maintenance indicator to evaluate soundness of subway tunnels. Procedia Engineering, 165, 155–165. Snavely, N., Seitz, S., & Szeliski, R. (2006). Photo tourism: exploring photo collections in 3D. ACM Transactions on Graphics, 25(3), 835–846. Surya, S.C., Anand, J.P., & Cody, L.L. (2018). Total system error analysis of UAV-CRP technology for monitoring transportation infrastructure assets. Engineering Geology, 247, 104–116. Wang, M.Z., & Huang, H.W. (2015). Monitoring and pre-warning of risk visualization for civil engineering. Journal of Disaster Prevention and Mitigation Engineering, 35(5), 612–616. (in Chinese) Wang, Z.J., Ma, H.F., Xiong, Y.D., Yang, Q.P., & Zheng, J.Y. (2018). The method of tunnel 3D reconstruction based on changeable photography. Science of Surveying and Mapping, 43(6), 72–77. (in Chinese) Wu, C.C., Agarwal, S., Curless, B., & Seitz, S. (2011). Multicore bundle adjustment. IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), IEEE, Providence, RI, USA, 2011, 3057–3064. Wu, C.C. (2013). Towards linear-time incremental structure from motion. Proceedings of the International Conference on 3D Vision (3DV) 2013, ISSN 1550-6185, IEEE, Seattle, WA, USA,2013, 127–134. Xie, X.Y., & Lu, X.Z. (2017). Development of a 3D modeling algorithm for tunnel deformation monitoring based on terrestrial laser scanning. Underground Space, 2(1), 16–29. Xie, X.Y., Lu, X.Z., Tian, H.Y., Ji, Q.Q., & Li, P. (2013). Development of a modeling method for monitoring tunnel deformation based on terrestrial 3D laser scanning. Chinese Journal of Rock Mechanics and Engineering, 11, 2214–2224. (in Chinese) Xue, Y.D., Zhang, S., & Qi, Z.T. (2017). A novel method for measuring shield tunnel cross sections. In: Zhao Y., Kong X., Taubman D. (eds) Image and Graphics. ICIG 2017. Lecture Notes in Computer Science, vol 10668. Springer, Cham, Shanghai, 2017, 47–57.
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Xue, Y.D., & Li, Y.C. (2018). A method of disease recognition for shield tunnel lining based on deep learning. Journal of Hunan University (Natural Sciences), 45(3), 100–109. (in Chinese) Xue, Y.D., & Zhang, S. (2020). A fast metro tunnel profile measuring method based on close-range photogrammetry. In: Antonio, G.G., Joaquim, T., Paulo, C., Luis, L. (eds) Information technology in Geo-Engineering, ICITG Springer, Portugal, 2020, 57–69. Zhu, L., & Huang, H.W. (2010). Review on the influence of shield tunneling in soft soil on adjacent existing tunnel. Chinese Journal of Underground Space and Engineering, 6(S2), 1692–1695. (in Chinese) Zhang, D.M., Zou, W.B., & Yan, J.Y. (2014). Effective control of large transverse deformation of shield tunnels using grouting in soft deposits. Chinese Journal of Geotechnical Engineering, 36(12), 2202– 2212. (in Chinese) Zhang, Q., Huang, X., Zhu, H., Li, J., (2019a). Quantitative assessments of the correlations between rock mass rating (RMR) and geological strength index (GSI). Tunnelling and Underground Space Technology, 83, 73–81. Zhang, W., Zhang, R., Wu, C., Goh, A. T. C., Lacasse, S., Liu, Z., & Liu, H. (2019b). State-of-the-art review of soft computing applications in underground excavations. Geoscience Frontiers (in Press). DOI: 10.1016/j.gsf.2019.12.003. Zheng, E.L., & Wu, C.C. (2015). Structure from motion using structure-less Resection. 2015 IEEE International Conference on Computer Vision (ICCV), ISSN 2380-7504, IEEE, Santiago, Chile, 2015, 2075–2083.
S2467-9674(19)30099-6 https://doi.org/10.1016/j.undsp.2020.01.002 UNDSP 132
To appear in:
Underground Space
Received Date: Revised Date: Accepted Date:
28 December 2019 26 January 2020 26 January 2020
Please cite this article as: Y. Xue, S. Zhang, M. Zhou, Novel SfM-DLT Method for Metro Tunnel 3D Reconstruction and Visualization, Underground Space (2019), doi: https://doi.org/10.1016/j.undsp.2020.01.002
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2019 Tongji University and Tongji University Press. Production and hosting by Elsevier B.V. on behalf of Owner.
Novel SfM-DLT Method for Metro Tunnel 3D Reconstruction and Visualization Yadong Xue1,2, Sen Zhang2, and Mingliang Zhou1,2* 1
Key Laboratory of Geotechnical and Underground Engineering of Education Ministry, Tongji University, Shanghai 200092, China
2
Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China *[email protected]
Abstract: Metro tunnels play a crucial role in urban transportation. However, with growing tunnel operation periods, defects, and large deformations appearing, these are influencing tunnel structural performance and threatening public safety. Three-dimensional (3D) tunnel reconstruction is an effective way to highlight tunnel conditions and provide a basis for engineering management and maintenance. However, the current methods of tunnel 3D reconstruction do not sufficiently combine the qualitative and quantitative characteristics of tunnel states. In this study, a novel method for metro tunnel 3D reconstruction based on structure from motion (SfM) and direct linear transformation (DLT) is proposed. The dimensionless 3D reconstruction point cloud acquired through the SfM method showcases the qualitative characteristics (such as leakage and pipelines) of the tunnel state. The closerange photogrammetry DLT method provides scale information missing from the SfM method and quantitative characteristics (such as profile deformation) of the tunnel state. The SfM-DLT method was tested in a Shanghai metro tunnel, and proved to be feasible and promising for future tunnel inspections. Keywords Metro Tunnel; 3D Reconstruction; Visualization; Structure from Motion; Direct Linear Transformation
1
Introduction Congested traffic is a serious issue for megacities around the world, and public transportation is an
effective way to alleviate this problem. As a form of public transportation, metros utilize underground
2
space and do not occupy much above-ground space. They are also environmental-friendly, fast, and have a large transportation capacity. Accordingly, metro systems have played a crucial role in urban operations. With increasing metro tunnel operation periods, structural defects (such as leakages and cracks) begin to develop in the tunnel linings. Further, because of strata and train dynamic load actions, large deformations may appear in tunnel segments. These defects and deformations stimulate each other, causing deterioration of the structural performance of metro tunnels. This threatens tunnel operational safety and causes further social and environmental safety issues (Zhu and Huang, 2010; Zhang et al., 2014). Much of the existing research suggests that timely tunnel inspections help to locate potential danger zones in a metro tunnel (Wang and Huang, 2015; Gan and Zhou, 2019). Engineers can then make maintenance decisions according to the inspection results to ensure the structural safety of the tunnel (Masumi et al., 2016; Daniel et al., 2017; Zhang et al., 2019a). Tunnel inspection consists of defect inspection and deformation measurements. Machine learning techniques have demonstrated promising efficiency in detecting defects, but they cannot measure tunnel lining deformations (Huang and Li, 2017; Xue and Li, 2018; Zhang et al., 2019b). Laser scanning and photogrammetry methods have been applied to measure tunnel profiles, but they have a low capability in detecting tunnel lining defects (Xie et al., 2013; Xie and Lu, 2017). Therefore, a new method is required that combines both the defect and deformation aspects. Conducting an inspection on a reconstructed three-dimensional (3D) metro tunnel model is a potential method for achieving this aim. Leakages and cracks can be easily visualized in a fine 3D reconstruction tunnel model, and tunnel lining deformation information can also be obtained. Photogrammetry is a common technique for 3D reconstruction. However, most photogrammetry methods have demanding site requirements that many metro tunnels cannot fulfill. Laser scanning is another typical 3D reconstruction method. The problem with laser scanning is that the laser point cloud does not contain color and texture information of the lining surface. Therefore, detecting cracks is more difficult. Moreover, the inspection speed is slow, the equipment is expensive, and post-processing is time-consuming. Hence, a new 3D reconstruction method should be developed to conduct quick, automatic, and accurate inspections at low cost. In this study, a novel method for metro tunnel 3D reconstruction combining structure from motion (SfM) and direct linear transformation (DLT) is proposed. SfM is a 3D reconstruction method with low site requirements, and it is widely used in topography measurements (Snavely et al., 2006; Bi et al., 2017; Surya et al., 2018; Wang et al., 2018). DLT, a photogrammetry method, has been used for the past few years to measure tunnel profiles (Chen et al., 2014; Ai et al., 2015; Xue et al., 2017). Dimensionless 3D reconstruction point clouds that showcase the overall tunnel state are acquired using the SfM method and a consumer-level digital camera. The points cloud model contains color, texture, and shape
3
information but lacks scale information. The close-range photogrammetry DLT method is utilized to provide the missing scale information of the SfM model. The proposed SfM-DLT method was tested in a Shanghai metro tunnel, and the precision of the 3D reconstruction model was satisfying. The remainder of this paper is organized as follows. Section 2 describes the concepts and application of the SfM method. Section 3 introduces the DLT method for measuring tunnel deformation. Section 4 gives a specific project application case, and Section 5 presents the discussion and concluding remarks.
2
SfM for metro tunnel 3D reconstruction
2.1
Basic principle
The SfM algorithm is an off-line algorithm for 3D reconstruction that is based on a series of unordered images. The specific procedures and algorithm flow of SfM 3D reconstruction are described as follows (Fig. 1):
Fig. 1. The specific procedures and algorithm flow of SfM 3D reconstruction. (1) There are a few steps that must be completed before applying the SfM algorithm. The focal length is obtained from the original image exchangeable image file format (EXIF) information. The image features are extracted by the scale-invariant feature transform (SIFT) algorithm. The feature points are then paired between two images using the k-dimensional tree (KD-TREE) model. For each pair of matched images, the epipolar geometry is calculated. The random sample consensus (RANSAC) algorithm is used to optimize the image matching. If the same feature point is continuously detected in different image pairs, then the motion and track are formed. (2) The first step of the SfM algorithm is choosing the appropriate image pairs to initialize the bundle adjustment, which is a nonlinear least square optimization method. Once the bundle adjustment is completed for the initial image pair, new image pairs are repeatedly added to recursively execute new bundle adjustments. The bundle adjustment process is finished when there are no new image pairs. Then, the estimated camera parameters and sparse reconstruction points cloud are obtained (Wu et al., 2011; Wu, 2013). The initial image pair is required to have enough matched feature points and a large enough camera center distance.
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(3) Clustering views for multi-view stereo (CMVS) takes the output (a set of images and camera parameters) of SfM as its input and then decomposes the input images into several clusters of a manageable size. A multi-view stereo (MVS) is used to independently and parallelly process each cluster and then reconstruct the 3D structure of the object or scene visible in the images. CMVS outputs a set of oriented points instead of a polygonal (or mesh) model. (4) By solving the Poisson equation, the implicit equation representing the surface information of the points cloud model is obtained. Through isosurface extraction, the surface model with the geometric entity information is obtained. This model can be used in other analyses such as the finite element method (FEM). VisualSfM is an automated graphical user interface (GUI)-based end-to-end 3D reconstruction system distributed by Zheng and Wu (2015). The system integrates several algorithms: SiftGPU, multicore bundle adjustment (BA) (Wu et al., 2011), SfM (Snavely et al., 2006; Bi et al., 2017; Surya et al., 2018), and CMVS which is distributed by Furukawa and Ponce (2010). In this study, VisualSfM is used to fulfill the first three procedures of SfM 3D reconstruction, and the final procedure is fulfilled by MeshLab (Cignoni et al., 2008), which is an open-source system for processing and editing 3D triangular meshes. 2.2
Reconstruction examples
As shown in Fig. 2, two shooting schemes are explored for metro tunnel reconstruction. The blue dot signifies the camera position, and the red arrow signifies the shooting direction. Shooting Scheme 1 shoots images at one tunnel cross-section using six different stations. Three images were shot at three different heights at each station, resulting in 18 original images at each cross-section. Shooting Scheme 2 shoots forward at the center of the lining and moves along the tunnel in the longitudinal direction with a fixed distance interval. Shooting Scheme 1 is applicable for precise and stationary measurements, while Shooting Scheme 2 is for quick and moving measurements. The original images taken by the two schemes are shown in Fig. 3. In this study, a Fujifilm XPRO-2 camera with a Laowa 9 mm f2.8 lens was used to obtain the required images. The camera has a 24 mega-pixel ad-hoc positioning system (APS)-C sensor, and its Laowa 9 mm lens provides a diagonal view angle of approximately 114°. There was no supplementary lighting, and the surrounding scene of the tunnel was illuminated by the site lighting equipment. The illuminance recorded on the site was 100 lux. The exposure parameters of the images were an aperture of 2.8, ISO of 3200 and shutter speed of 1 s.
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Fig. 2. Two types of shooting schemes.
(a) images taken by Shooting Scheme 1
(b) images taken by Shooting Scheme 2
Fig. 3. The original images taken by the two different schemes. All original images of both shooting schemes were fed into the VisualSfM software without any camera calibration. The estimated camera position, shooting direction, and camera parameters were calculated automatically, and the results are shown in Fig. 4. The calculation environment was a I76700HQ CPU desktop. The time elapsed during the calculation process for Shooting Schemes 1 and 2 were 56 and 58 s, respectively. Then, the dense reconstruction was carried out, and the CMVS results were fed into the MeshLAB, which is visualized in Fig. 5. This process was more time-consuming than the last process with a time elapse of 483 and 475 s for Shooting Schemes 1 and 2, respectively. Some process techniques were used to accelerate the calculation. For an image sequence (like continuous
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frames of a video), an interval was set to calculate the correspondence points of an image with only a few nearby images instead of with all the other images. The computational demand then decreased significantly. A few factors influencing the reconstruction precision should be noted. (1) The original images need to have appropriate exposure, accurate focus, and more than 60% overlapping area taken from different directions and positions. (2) Higher resolution images are expected to produce a more precise model. (3) The lighting device in the tunnel caused different lens flare shapes in different images, which caused some errors in reconstruction. The reconstruction model obtained through the SfM does not contain scale information. In practice, it needs a ruler to be projected to the actual size. For this study, the DLT method is proposed to provide the reference ruler.
(a) SFM results from Shooting Scheme 1
(b) SFM results from Shooting Scheme 2.
Fig. 4. The visualized results of sparse reconstruction in the VisualSfM.
(a) CMVS results from Shooting Scheme 1
(b) CMVS results from Shooting Scheme 2
Fig. 5. The visualized results of dense reconstruction in MeshLAB.
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3
DLT for tunnel lining measurement Most photogrammetry methods have demanding site requirements that metro tunnels cannot fulfill.
The DLT method requires no camera calibration, and the calculation is based on the original images themselves. A novel method for using DLT in tunnel profile measurements was proposed by the author research group (Xue and Zhang, 2020), and a device called moving tunnel profile measurement (MTPM1) was developed. The developed device was used in this study for tunnel profile measurements. 3.1
Basic principle of DLT
The goal of photogrammetry is to convert from pixel to world coordinates. The DLT method directly converts these coordinates, as shown in Eqns. (1) and (2). Some of the control points are set to calculate the unknown m matrix. Then, the world coordinates of the target points are calculated. The difficulty in applying the DLT method to tunnel profile measurement mainly lies in setting the points. Setting fixed points such as reflectors is inefficient. A novel moveable point setting method was proposed by the author research group (Xue and Zhang, 2020). 1
i wi i wi uZ i wi uY ui Xwi Ywi Zwi 1 0 0 0 0 uX m1m11111 0 0 0 0 Xwi Ywi Zwi 1 vX , vY vZ vi i wi i wi i wi 2i11 2i1
(1)
i wi uY i wi uZ i wi Xwi Ywi Zwi 1 0 0 0 0 uX ui T m1 m11 , 0 0 0 0 Xwi Ywi Zwi 1 vX 111 viZwi vY i wi i wi vi 2i1 2i11
(2)
T
where Xwi, Ywi, Zwi signify the world coordinates of the i-th point; ui, vi signify the pixel coordinates of the i-th point; m1 to m11 are the unknown parameters defining the m matrix. Figure 6 presents the MTPM-1 device components. The main concept is to use a rotatable laser range finder to provide a series of control points and to use a linear laser source to provide the target points that then form the profile. In Fig. 6, 1 denotes the tunnel lining, 2 is the circular profile projected by a linear laser source onto the lining, 3 is a linear laser source, 4 is a laser range finder, 5 is a rotating shaft, 6 is a power supply, 7 is a wheel, 8 is a working panel, 9 is a camera and wide-angle lens, and 10 is a tripod.
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Fig. 6. The MTPM-1 device components. 3.2
Measurement example
A typical set up of the MTPM-1 in the metro tunnel is shown in Fig. 7. During the field test, the laser range finder was rotated 20° after each shot for a total of seven times. An image was taken after each rotation; hence, a total of eight images were taken at each location. Eight control points were obtained, with corresponding image coordinates, measured distance, and angle information, to perform the DLT calculation. Then, the DLT fitting result was obtained. The laser range finder had a measuring precision of 1.5 mm ± 20 ppm. The measuring point diameter was 4mm, and the laser wavelength was 620–690 nm. After the shooting was completed, the laser range finder was rotated back to the original position and was then rotated slowly and continuously 180° with a rotation speed of 1°/s. The measurement frequency was set to 1 Hz. A total of 180 distance values were recorded for each tunnel lining section to form the ground truth profile for evaluating the DLT precision. There were eight measured profiles with a 5 m interval in a 40 m tunnel section, as shown in Fig. 8. A blue curve was constructed based on the 180 measured range values of each tunnel lining section, and is shown as a comparison reference in Fig. 8. In Fig. 8, the green points are the DLT fitting results. To evaluate the DLT fitting precision, an ellipse fitting was performed. The ellipse fitting results consist of five parameters: a long axis, a short axis, ellipse center x/y coordinates, and an x-axis rotation angle. To conduct the ellipse fitting, disturbance points were removed manually (such as the points on the bottom floor). The ellipse fitting of the DLT profile was completed using the remaining points, and a red curve was drawn. The blue curves are the ground truth profiles, and they highly coincidence with the red curve. Working parameters including control point number, control point layout, and image resolution are set to 8, a uniform distribution, and 24 megapixels, respectively. According to the comparison between the measured profile and laser scanning results, the maximum axis error is 5 mm.
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Fig. 7. A typical original image taken in the field.
Fig. 8. A series of measured profiles.
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Engineering application of the SfM-DLT method The SfM-DLT method can produce two outputs: the SfM reconstruction results provide the
qualitative characteristics of the tunnel state, and the DLT measurement results provide the quantitative characteristics of tunnel deformations. Therefore, the proposed method can acquire both the qualitative and quantitative characteristics of the metro tunnel state. Analyses of the proposed method results are performed for the following four aspects: precision, economy cost, field operation time cost, and internal operation time cost.
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The original images taken using the SfM-DLT method are shown in Fig. 9. The shooting scheme is the same as Shooting Scheme 1. A total of 18 field images were taken. The qualitative characteristics of the tunnel state using the SfM-DLT method are shown in Fig. 10. The leakage location is clearly visible and is marked by a red square in the 3D reconstructed model. The missing scale information in the SfM model can be provided by the DLT results. This information is filled in by setting the distance value between two picked points, and an example is shown in Fig. 11. The distance is acquired from the DLT results. The SfM model is then scaled to the actual size based on the quantitative measurements. Once the scale information is acquired, the precise leakage area can be calculated. The quantitative characteristics of the tunnel state using the SfM-DLT method are shown in Fig. 12. The horizontal axis of the tunnel is approximately 5521 mm, and the vertical axis of the tunnel is approximately 5486 mm, which is a typical “duck egg” deformation pattern. After comparing the DLT results with those of the true profile, the axis error is approximately 4 mm; the distance between the two picked points is 5093 mm. The profile can then be utilized to detect the metro gauge to ensure train safety. In the SfM model, the error is mainly derived from the lens flares, initial EXIF parameters, image distortions. and image quality. In the DLT model, the error mainly comes from the image distortions and laser distance measurements. The self-made equipment is mainly composed of eight laser range finders, a moving vehicle. and a camera system. The laser range finders cost approximately 2500 US dollars, the moving vehicle costs approximately 3000 US dollars, and the camera system (Fujifilm X-PRO2 and LAOWA 9 mm f2.8) costs approximately 1500 US dollars. The total cost is approximately 8000 US dollars. Typically, a set of commercial laser scanning equipment costs approximately 100 000 US dollars to 150 000 US dollars. Therefore, the proposed system in the study costs only around 6% to 8% of the commercial one. Shooting Scheme 1 is more time-consuming in the field than Shooting Scheme 2 as the camera must be moved more, but it also provides a finer model. In practice, Shooting Scheme 1 is applicable to inspections of a certain location, whereas Shooting Scheme 2 is applicable to faster inspections of a tunnel section. The time consumption situation is similar for both schemes in the internal operation stage. Nevertheless, many techniques can be used to accelerate the calculation process such as GPUbased calculation or setting optimal parameters in the software.
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Fig. 9. The original images taken using the SfM-DLT method.
(a) the 3D reconstructed model
(b) the leakage location Fig. 10. The qualitative characteristics of the tunnel state using the SfM-DLT method.
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Fig. 11. Setting the distance value between two picked points.
Fig. 12. The quantitative characteristics of the tunnel state using the SfM-DLT method.
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Discussion and conclusion The SfM method mainly focuses on 3D reconstruction but lacks scale information, whereas the DLT
method focuses on profile measurement but lacks environmental information. Therefore, by combining these two methods for tunnel inspection, the proposed SfM-DLT method presents several advantages, such as not requiring prior camera calibration, low site requirements, reduced equipment costs, and greater applicability in the tunnel environment. Future metro tunnel inspections will require faster inspection speeds, and unmanned aerial vehicles (UAVs) could be used to carry out tunnel inspections. UAVs are light, portable, and relatively cheap.
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As the SfM method only needs a series of field images, it is possible to combine SfM with UAVs. The UAV-SfM is a highly promising tunnel inspection method. After the UAV flies along the tunnel and collects a large number of images, SfM is used to generate a 3D reconstruction model of the monitored sites quickly. Then, the model can be inputted into the FEM or other software to perform additional structure analyses and provide information for engineering decisions. That is the projected development direction for this proposed method. The proposed method still has some limitations. For example, lens flare had a significant influence on the reconstruction precision. This issue may be solved by using supplementary lighting and adjusting the exposure parameters to attenuate the environmental light. Additionally, in the DLT calculation process, some manual work is required such as extracting the pixel coordinates of the control points, which increases the time consumption of the method. This may be mitigated by using an automatic pixel extraction algorithm in future work. In conclusion, a novel SfM-DLT method of tunnel 3D reconstruction was proposed. It can aid field engineers in conducting tunnel inspections automatically and intelligently. More importantly, the proposed method can provide not only the qualitative characteristics (leakage) but also quantitative characteristics (deformation) of metro tunnel linings.
Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements The work presented in this article was supported by the Science and Technology Commission of Shanghai Municipality (Grant No. 18DZ1205902), the Key innovation team program of innovation talents promotion plan by MOST of China (No. 2016RA4059), and the National Key R&D Program of China (Grant No. 2018YFB2101000).
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