Page - 166 - in Proceedings of the OAGM&ARW Joint Workshop - Vision, Automation and Robotics

whereXjc is the original reference 3Dpoint and ∥∥Xj−Xjc∥∥ corresponds to the deviation from this reference during calibration and α is a free parameter. Note that here each structure point has its own lifting variable wj, it is also possible to represent the target accuracy with just one global scalar w. The system is solved using a standard non-linear least squares solver [1]. III. INDUSTRIAL APPLICATIONS The presented calibration formulation has been used in different industrial applications for single- and multi-camera calibration and long term calibration maintenance using commercially printed (low cost) targets that are affected by printing inaccuracies. A handheld stereo system calibration has been kept by non-expert users under 0.06 pixel RMS reprojection error for over a year. Because non-expert users are involved, strong and robust convergence properties are essential. Figure 1 shows rectified images of this device with and without the proposed structure adjustment. The whole system performs volumetric simultaneous localization and mapping (SLAM) without opportunities for loop closing. A 3D model of the volumetric fusion can be seen in Figure 2. For the accuracy evaluation ground truth data of the floor plan of the scene is available. Rectification errors are accumulated through the volumetric fusion, leading to a de- tectable influence of slight rectification errors. A rectification error like in Figure 1a leads to drift in height of about 5cm, the shown scene is 4 meters long. (a) Weak calibration, 0.15px rectification deviation from zero mean. (b) Rectification with proposed method, nearly perfectly cen- tered optical flow check. Fig. 1: The top row shows a histogram of rectification deviations. They are obtained by computing a histogram of the vertical component of unconstrained optical flow initialized with the stereo result. The histogram range is ±2 pixel. The bottom row shows the image pairs with example epipolar lines. Figure 3 shows a stereo based inspection application for corrosionmonitoring inhot steel components, ladlesandpro- cess chambers that can cope with up to 1.600◦C. The main goal of the system is the detection of thinning of material i.e. volumetric changes in registered consecutively measured models.The typicaldistance to the target liesbetween60and 200cm. To cope with the varying distance range focusable liquid lenses were used (Varioptic Caspian). The lenses are focusable from 7cm to infinity and are newly calibrated Fig. 2: A resulting 3D model obtained with a SLAM system calibrated by the presented method. Rectification errors of 0.2px are clearly noticeable in this application and lead to insufficient model accuracy. Fig. 3: Stereo system with active speckle projection for the inspection of red hot steel components, ladles and cham- bers with up to 1.600◦C. ©Materials Processing Institute supported by Dr BG Crutchley of i3D robotics Ltd. after focus change and prior to each measurement campaign. The calibration of the liquid lenses together with the high temperature environment poses the greatest challenge in this application. REFERENCES [1] S. Agarwal, K. Mierle, and Others, “Ceres solver,” http://ceres- solver.org. [2] A. Albarelli, E. Rodola`, and A. Torsello, “Robust camera calibration using inaccurate targets,” Trans. Pattern Anal. Mach. Intell, vol. 31, no. 2, pp. 376–383, 2009. [3] M. J. Black and A. Rangarajan, “On the unification of line processes, outlier rejection, and robust statistics with applications in early vision,” International Journal of Computer Vision, vol. 19, no. 1, pp. 57–91, 1996. [4] K. H. Strobl and G. Hirzinger, “More accurate pinhole camera cali- bration with imperfect planar target,” in Computer Vision Workshops (ICCVWorkshops), 2011 IEEE International Conference on. IEEE, 2011, pp. 1068–1075. [5] M. Vo, Z. Wang, L. Luu, and J. Ma, “Advanced geometric camera calibration for machine vision,” Optical Engineering, vol. 50, no. 11, pp. 110503–110503, 2011. [6] C. Zach, “Robust bundle adjustment revisited,” inEuropeanConference on Computer Vision. Springer, 2014, pp. 772–787. [7] M. Zollho¨fer, M. Nießner, S. Izadi, et al., “Real-time non-rigid re- construction using an rgb-d camera,” ACM Transactions on Graphics (TOG), vol. 33, no. 4, p. 156, 2014. 166