System Calibration THE DESIGN OF THE PROPOSED SYSTEM

Figure 1. The Proposed System’s setup front view, side view In figure 2 the range camera coordinate system is presented. Figure 2. Swiss ranger SR4000 coordinate system The calibration of the system was necessary to provide colour information of the generated point cloud since the range camera lacks of an imaging sensor. To implement the calibration of the system, the exterior orientation and the calibration parameters of the camera should be calculated. 2.1 Camera Calibration For the camera calibration the OpenCV library was used to develop a standalone application that has the ability to process images, depicting the circular targets of a printed calibration field, and calculates the additional camera calibration parameters Balletti, et. al. 2014. A modified Brown camera calibration mathematical model has been used to determine all the appropriate parameters and correct lens deformation appearing on an image Brown, D.C., 1971. The specific model uses odd and even order polynomial coefficients to model the radial and the tangential distortion of the lenses eq. 1, 2, 3 and 4. 1 5 3 4 2 2 1 r k r k r k x dx ra dia l         1 1 5 3 4 2 2 1 r k r k r k y dy ra dia l         2 ] 2 2 [ 2 2 2 1 tan x r p y x p x dx          3 ] 2 2 [ 2 2 2 1 tan y x p y r p y dy          4 The equations 1-4 supply to the generic collinearity equations a model to eliminate systematic errors. The final estimation of the camera position X , Y , Z and attitude ω, φ, κ is calculated if we take into account the mathematical model including the additional camera calibration parameters namely: f: precise focal distance calculated from the self-calibration process x ,y : principal point location projection of the centre of lenses on the camera sensor k 1 , k 2 , k 3 , p 1 , p 2 : coefficients for the modelling of radial and tangential distortion All the above mentioned parameters are estimated before the camera use and are taken into account for the better estimation of the camera pose, however there is way to provide with the help of the camera calibration parameters x , y , k 1 , k 2 , k 3 , p 1 , p 2 another image that is similar to the original created by our camera but it is free of systematic errors. The image is called idealized and all the previous mentioned errors are corrected after the calibration process. The following table presents the camera calibration parameters. Canon 400D dSLR calibration report for 18 mm lens f 18.6883 mm x -0.0526 mm y -0.4113 K 1 4.915 x 10 -4 K 2 -1.213 x 10 -6 K 3 P 1 1.571 x 10 -4 P 2 1.497 x 10 -4 Table 1 Canon EOS 400D calibration results The idealized image is more accurate since there is no visual effect of the barrel distortion which might an obstacle to recognize long linear futures on the images.

2.2 System Calibration

The exterior orientation of the idealized image was then extracted using ground control points coordinates determined automatically on the intensity image of the range camera and the optical image derived by the dSLR camera. For the system calibration a calibration field was constructed. The calibration field had 14 control points circular targets. In figure 3 the optical image captured by the camera and the intensity image captured by the TOF sensor are presented. Figure 3a System Calibration field Canon Image Figure 3b System Calibration field SR4000 Intensity Image The system calibration software uses two jpeg images for the estimation of the calibration parameters. The first image is the one captured with the Canon Camera figure 3a, while the second one is the intensity image caprtured with the SR4000 figure 3b. The intensity image is coupled with a file including the Cartesian coordinates XYZ of the measured points from the range camera. Each pixel i, j is connected to a unique point in the 3D space which is stored in the 3D Cartesian coordinates file. For the accurate detection of the control points in both the optical and intensity images a centre of gravity algorithm was used. The algorithm detects the centre of the elliptical structure of the control points in the images and the 3D Cartesian coordinates of the points. Using these GCP the exterior orientation was calculated by applying a resection adjustment. The following table presents the exterior orientation parameters. X -0.0027 m Y 0.1623 m Z 0.0685 m ω 179.2235 o φ 0.5038 o κ -180.0145 o Table 2 System calibration parameters This contribution has been peer-reviewed. doi:10.5194isprsarchives-XLI-B5-939-2016 940 The system calibration accuracy estimation of the exterior orientation parameters is limited by the spatial resolution of the range camera point cloud acquisition, which is approximately 0.5 centimetres.

2.3 Point cloud colouring