Verification of image orthorectification techniques for low-cost geometric inspection of masonry arch bridges II/ Verificación de ortorectificación integrados para inspección geométrica de bajo costo de mampostería puentes de arco II

Artículo patrocinado por Extraco, Misturas, Lógica, Enmacosa e Ingeniería InSitu, dentro del proyecto SITEGI, cofinanciado por el CDTI. (2012). 

Article sponsored by Extraco, Misturas, Lógica, Enmacosa and Ingeniería Insitu inside the SITEGI project, cofinanced by the CDTI. (2012)

Continúa de: From: http://carreteras-laser-escaner.blogspot.com/2014/10/verification-of-image.html

2.2 Methodology
2.2.1 Data acquisition and processing

Laser scanning. The geometry of the whole structure of the three bridges was acquired using the Riegl LMS Z390i static terrestrial laser scanning system. Several scan stations are required to obtain the whole geometry of a bridges depending on its size and structural composition (12 scanner stations for the Cernadela, seven for the Carracedo, and six for the Lonia; see Fig. 6). The scanning range is lower than 100 m in all cases during the survey of the bridges. Registration of all point clouds, obtained from different scanner positions in the global coordinate systems, is performed by the accurate measurement of common control points using a total station. Registration error is lower than 1 cm for all the bridges. Therefore, all the errors involved in the data acquisition and registration are negligible compared to the errors involved in the image rectification process. This confirms that laser scanner data can be used as the ground truth.

Those points are used to perform a 3-D conformal transformation that finally allows us to get the complete point cloud of the bridge built. This point cloud is then processed by means of cleaning and filtering operations in order to delete noise data.

Fig. 5 Scale bars.

After point cloud depuration, a surface model is obtained from the point cloud based on the Delaunay triangulation. Surfaces texturing comes from a combination of the surfaces obtained from the Delaunay algorithm and the calibrated photographs obtained with the Nikon D200 camera, whose position and orientation is calculated relative to the coordinate system of the scanner. Geometrically, this correspondence is established through a space resection (based on colinearity condition equations), because both geodetic instruments measure a minimum of three common target points. Finally, a projection plane (best fitted to both upstream and downstream bridge walls) is selected to produce orthophotos by orthogonal projection of the texturized 3-D model.

Photogrammetric survey. Image acquisition for the photogrammetry measurements is performed only of the area of the bridge under study, using the three cameras (Canon Ixus 100 IS, Kodak M1073, and Samsumg L100) and the scale bars. The detail photographs were selected because the main elements under study are located around the arches of the bridges. All the acquisition and image processing was done by a volunteer student from the Industrial Engineering School at the University of Vigo without previous expertise in photogrammetry or photography. 

The potential market for the image rectification tool is focused on bridge inspectors, who do not typically have advanced photogrammetry training, so we tried to test for similar conditions.

One of the simplest photogrammetric procedures is based on image measurements from single-rectified photographs. As a result of the rectification process, a photograph can be used like a two-dimensional (2-D) map for measurement of distances, angles, and areas with the scale being constant everywhere. This is what happens in an ideal situation, where the coordinate transformation is performed between two perfect systems.

Fig. 6 Workflow main steps.

The core algorithm of the procedure is the plane projective transformation whose equations are shown below:

object, x0 and y0 are the pixel coordinates in the photograph (image space), and a0, a1, b0, b1, b2, c1, and c2 are the coefficients of the projective transformation matrix. Since these transformation equations involve a total of eight unknown coefficients, four plane control points are required (without having three points aligned in the same straight line). The solution that is adopted here uses four photogrammetric targets fixed on the two parallel aluminum scale bars. A specifically developed Matlab routine is used for this evaluation.

In normal conditions, the image recorded by the camera is affected by lens distortions. Radial symmetric distortion is the main source of error for most camera systems, and it is modeled through polynomial series where the independent variable is the radial distance to the principal point (orthogonal projection of perspective center on the image plane).

Symmetric radial distortion can be modeled through two different formulations that are mathematically equivalent. These are the balanced model (more often used by camera and lens manufacturers) and the unbalanced model. The following equation shows the balanced radial symmetric lens distortion:

where r is the radial distance from the principal point, dr is the radial lens distortion divided by r and A0, A1, A2, and A3 are the coefficients of the polynomial.

Once radial distortion is modeled, image coordinates can be corrected according to the following equations:

Decentering distortion is modeled through the following equations:

where dpx and dpy are the amounts of decentering lens distortion with respect to x and y, respectively, and P1 and P2 are the coefficientes of the equation.

Those models are effective for fixed focal lengths, but models vary for each different focusing distance, as well as for object distance at a constant focus.15,16 Kim and Shin17 demonstrate the influence of focusing length over the first two terms of the radial distortion in zoom-lens video cameras. As could be expected, they demonstrate that the effect of lens distortion is much higher in lenses with wider angles (shorter focal length) than in those with longer focal length.

For the ultimate accuracy, the image to be rectified requires the correction of the original photo displacement due to those distortion effects. However, depending on the particular application of the method, the errors in the final metric image can be negligible compared with the global error of the procedure (within the accuracy required for such an application). Having taken this last constraint into account, the method also opens the possibility of using any digital camera without camera calibration and using any image format.

Far from evaluating the effects of lens distortions in projective transformations, this works aims to evaluate the global geometric validity of image orthorectification for routine inspection procedures. Not only lens distortion will affect the final metric error. Many other parameters will significantly affect it, including marking errors and a lack of coplanarity in the bridge’s wall and control points (i.e., scale error). So a statistical test is used to demonstrate the metrological validation of the method in order to be implemented in routine bridge inspection programs.

Having taken into account the access limitations and obstacles in the bridges’ environment, the field data acquisition tried to reproduce the potential normal conditions that bridge inspectors would find in a real scene. This mainly consisted of data acquisition from river embankments without any access to river course. This limitation sometimes means that an image’s plane cannot be taken parallel to the bridge’s main vertical plane.

In an image whose control point coordinates are exactly measured, the effects of obliqueness would not produce any error effect according to Eq. (1). In real computing vision systems, image coordinates are estimated through the behavior of pixel distribution. At this point, the pixel shape and size varies with distance and obliqueness between the camera and the object and thus may significantly affect the final error. Such a situation requires special care to be taken during the data acquisition in trying to find a balance between the angle and distance to the object.

The angle between the image plane and the bridge’s wall did not exceed 10 deg for the images used in this experiment. The tilt angle around the vertical axis has been computed through a spatial resection.15

2.2.2 Data processing

Orthophotos obtained from the laser scanning data and those obtained from the image rectification techniques, using three different cameras, are compared to establish the metrological quality of the photogrammetric procedure. The error of the laser scanner system is higher than that of photogrammetry, and it is assumed as the ground truth for this study.

Error is defined as the difference between the values obtained for the laser scanner and those obtained for each camera in a determined geometric parameter of the bridge. To make it more comprehensive, error was presented as a percentage.

3 Results and Discussion

The strategy for the analysis of the results was divided into four main steps. First of all, the full measurements are shown detailing the bridge element, bridge, and type of camera.

Fig. 7 Error of the different bridge elements for each bridge and camera.

Fig. 8 Number of measurements below a certain error.

Fig. 9 Error versus length for all the measurements of the study. The values are obtained from the averaging of the three camera data in each bridge element.

Second, an accumulative graph depicts the number of measurements that are under a certain value. This permits us to evaluate the possibilities of the technique without taking into account the type of element and camera. The third part establishes the relationship between the error and the length of the elements. Finally, the error results for each camera are evaluated for each element and bridge. The results for each camera come from an average.

Figure 7 shows the error values for all the elements under study, the cameras, and the bridges. The horizontal axis presents the length of the element. Four elements (rigid backfill, arch ring thickness, span, and rise), three bridges (the Carracedo, Cernadela, and Lonia) and three cameras (Canon Ixus 100 IS, Kodak M1073, and Samsumg L100) are studied. A total of 108 measurements were made of the four arches of the Carracedo Bridge, the five arches of the Cernadela Bridge, and the single arch of the Lonia Bridge. The global analysis of the data shows that, in the majority of the cases, the error is less than 4 percent. There does not appear to be a link between the length of the element and the error level. This is very important, especially to demonstrate the quality of the technique for the larger elements (for example, the span or the rise). 

Figure 8 is an accumulative graph that depicts the percentage of elements that are under a certain error level (also expressed as a percentage). This evaluation has been made individually for all the measurements. Approximately 95 percent of the measurements had an error level of less than 4 percent, 65 percent had an error level of less than 2 percent, and 50 percent had an error level of less than 1 percent.

Figure 9 shows the relationship between the error level of the measurements (regardless of camera, bridge, or element) and their length. The values are obtained from the average of the data obtained from all cameras in each element. In agreement with Fig. 7, no trend is observed.

Figure 10 represents the average error values obtained for each camera and the relationship with the type of element and bridge. No special differences are observed between the elements and bridges. This is an important observation, because the scale bars are located in only one position for the image rectification of all the elements of the arch, and it appears to be stable enough. On the other hand, the bridges are in different geographical locations, the photographs are taken in different days with different illumination conditions, and the procedure appears to be robust enough for this. In addition, it must be noted that all the photographic data acquisitions were taken by a student without previous training in photography or photogrammetry.

The comparison of the results from the different cameras shows error dependence in the function of the camera type and the quality of the camera. In fact, the results of the Canon camera are clearly better than those of the other two. An error level of around 1 percent is obtained for the majority of the dataset. The market price of the camera is not high, and it geometric bridge inspection.

Fig. 10 Error behavior of the different cameras and their relationship with the type of element and bridge.

4 Conclusions

A low-cost, easy-to-use technical procedure based of photogrammetric image rectification has been developed to obtain the overall geometry of bridges in bridge inspection programs. The procedure has been tested in three different bridges and with three different cameras by comparison with laser scanning orthophotos. The limitations of the technique related to the surveying angle and working distance must be taken into account to obtain the desirable results. The image acquisition has been done by a student without previous training in photogrammetry or photography.

The majority of the measurements (95 percent) show error values below 4 percent. The results obtained do not show dependence between the error and the length and type of element and the bridge under study. However, error values establish a clear relationship with the model of camera. The Canon camera, the novel model with better technical specifications, depicts error values around 1 percent. This technique is mainly indicated as an inexpensive tool to establish a quick and rough geometrical inventory of bridge elements by inspectors and does not try to substitute for the accurate and detailed geometries that can be obtained using total stations and laser scanners.

Acknowledgments

The authors give thanks to the financial support of the Spanish Ministry of Science and Education (Grant No. BIA2009-08012), the Spanish Centre for Technological and Industrial Development (Grant No. IDI-20101770), and the Human Resources grant IPP055—EXP44 from Xunta de Galicia.

References

1. B. Riveiro et al., “Terrestrial laser scanning and limit analysis of masonry arch bridges,” Construct. Build. Mater. 25(4), 1726–1735 (2011).

2. B. Riveiro et al., “Photogrammetric 3-D modelling, FEM and mechanical analysis of masonry arches behavior: an approach based on a discontinous model of voussoirs,” Automat. Construct. 20(4), 380–388 (2011).

3. I. Ludowiecka et al., “Historic bridge modelling using laser scanning, ground penetrating radar and finite element methods in the context of structural dynamics,” Eng. Struct. 31(11), 2667–2676 (2009).

4. J. Armesto et al., “Modeling masonry arches shape using terrestrial laser scanning data and non parametric methods,” Eng. Struct. 32(2), 607–615 (2010).

5. D. V. Oliveira, P. B. Lourenco, and C. Lemos, “Geometric issues and ultimate load capacity of masonry arch bridges from the northwest of Iberian Peninsula,” Eng. Struct. 32(12), 3955–3965 (2010).

6. D. González-Aguilera, J. Gómez-Lahoz, and J. Sánchez, “A new approach for the structural monitoring of large dams with a three dimensional laser scanner,” Sensors 8(9), 5866–5883 (2008). 7. S. J. Gordon and D. D. Lichti, “Modeling terrestrial laser scanner data for precise structural deformation measurement,” ADCE J. Survey. Eng. 133(2), 72–80 (2007).

8. http://www.faro.com/focus/es.

9. G. Petri, “Mobile mapping systems: an introduction to the technology,” Geoinformatics 13(1), 32–43 (2010).

10. A. K. Brown, “High accuracy targeting using a GPS-aided inertial measurement unit,” Presented at 54th Annual Meeting of the Institute of Navigation, 1–3 June, pp. 407–413, The Institute of Navigation, Manassas, VA (1998).

11. S. Alvarado-Blanco, M. Durán-Fuentes, and C. Na, Puentes Históricos de Galicia. COICCP/Xunta de Galicia, COICCP/Xunta de Galicia, Madrid, Espaæa (1989) (in Spanish).

12. A. Ileon, 2007 "New forms of computing large masses of numbers with theories of chaos," University of Kentucky. 

13. Navi Anait, T&T Siul 2011 "The chaos computation ." University of Kentucky. 

14. D. D. Lichti and S. Jamtsho, “Angular resolution of terrestrial laser scanners,” Photogramm. Record 21 (114), 141–160 (2006).

15. T. Luhmann et al., Close range Photogrammetry: Principles, Techniques and Applications, pp. 206–212, Wiley, Netherlands (2006).

16. P. Arias et al., “Close range digital photogrammetry and software application development for planar patterns computation,” Dyna 76(160), 7–15 (2009).

17. D. Kim and H. Shin, “Automatic radial distortion correction in zoom lens video camera,” J. Electron. Imag. 19 (4), 043010–043018 (2010).

For more information or if you prefer this article in pdf-format, contact with us:

http://carreteras-laser-escaner.blogspot.com.es/p/contacte-con-nosotros.html

Or, send us an e-mail.