Seite - 79 - in Proceedings - OAGM & ARW Joint Workshop 2016 on "Computer Vision and Robotics“

Figure2: Left: Thesetupof theDSLRandlaser rangefinderonthecarbonpanel. Right: Theschemat- icsof thecameraand laser rangefinder setup and the ideabehindcalibration. 3. CameraSetupandCalibration Our hardware setup consists of a standard DSLR mounted onto a rigid carbon panel next to a 1D LRF (see Fig. 2), which we control remotly via USB and Bluetooth for easy acquisition of images and distance measurements. We perform intrinsic calibration with a modified version of the Bouguet toolbox and a custom target as proposed in [4]. In the remaining part of the paper we expect the camera to be calibrated and the geometric distortions introduced by the camera and lens assembly to be removed from the images. This enables us to infer the real world line of sight lloswith respect to thecenterofprojectionof thecameraof any givenpixel inan imageIi as: llos,i=K −1 · l2D,i,i, (1) whereKdenotes the camera matrix and l2D,i,i= [x,y,1]T is the 2D position of the laser point i inIi inhomogeneouscoordinates. In theory, provided an intrinsic camera calibrationK and a known plane in 3D, the rotationRLRF and translationtLRF of the laser range finder relative to the camera can be estimated using two mea- surements only. Yet, in order to obtain a more robust estimation, we take several measurements M = {di,Ii}N1 of distances di with corresponding images Ii. Since the application is 3D facade reconstructionandweexpect the facademeasurements tobe takennearly fronto-parallel to the image sensor, we restrict the extrinsic calibration sequence to a fronto-parallel movement of the target rela- tive to the camera, ensuring that the position at which the LRF takes its measurement is well within thecalibration target. In a first step, we detect the target position and orientation in 3D relative to the camera’s center of projection,aswellas the targetposition in2Dwithin the image. Wedetect the laserpointasbrightest object on the calibration target using adaptive thresholding and then take its center of mass as the 2D position l2D,i,i = [xi,yi,1]T of the laser point i in Ii. We then calculate the position l3D,i in 3D of a laserpointby intersecting the lineof sight llos,i, on which the laserpoint lies,with the targetplane. When holding the camera positions fixed and moving the calibration target plane relative to it, all points l3D,i, i ∈ {1, . . . ,N} lie on a straight line. This line corresponds to the viewing direction lLRF of the LRF, which we calculate by fitting a line to the measurements using singular value de- compositiononthe3DpointsstackedtoamatrixL3D= [l3D,1, · ·· ,l3D,N]. Theright-singularvectors obtainedbySVDcorrespondtotheorthogonaldirectionsofmaximumvariancewithinthedata. Thus, theright-singularvectorcorrespondingtothelargestsingularvalueofL3D coincideswith theviewing directionof theLRF,provided that theuncertaintyof theestimationof theLRF’sorigin issufficiently smaller than the relativemovementof thecalibration target. 79