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Extrinsic Self Calibration of a Camera and a 3D Laser Range Finder from Natural Scenes Davide Scaramuzza , Ahad Harati , and Roland Siegwar IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS, 2007 . Presenter: Van-Dung Hoang hvzung@islab.ulsan.ac.kr
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Extrinsic Self Calibration of a Camera and a 3D Laser Range Finder from Natural ScenesDavideScaramuzza, AhadHarati, and Roland SiegwarIEEE/RSJ International Conference on Intelligent Robots and Systems, IROS, 2007 Presenter: Van-Dung Hoang hvzung@islab.ulsan.ac.kr October 12, 2013
Content • Introduction • Camera and LRF model • Bearing angle images • Extrinsic laser-camera calibration • Experiments • Conclusions
Introduction • Proposed new method for determining the position and direction of 3D LRF with respect to camera. • This approach does not require and calibration object (e.g. chessboard). • Laser range will be visualize in 3D range and highlighted edge of object. • Correspondence features of camera image and laser image will be manually selected. • Extrinsic parameters will be discovered by using PnP method.
Camera model • The camera system consists of perspective camera, catadioptric mirror, which has a single center of projection. • Image point- 3D point estimate (u,v) is point in image. [x, y, z] is a ray from center of camera to point in world. is scalar value. F is a project function, it depend on the camera used.
LRF model • 3D laser system construct from 2D Laser SICK LMS200. • Combining the rotation of the mirror inside the 2D scanner with the external rotation of the scanner itself. • Impossible to adjust the two centers of rotation exactly on the same point. • These offset values have to be estimated by calibrating the 3D sensor by considering its observation model (other work). • This paper focuses extracting the extrinsic calibration of a 3D laser scanner with a camera is general (does not depend on the sensor model).
LRF model • The sensor model can be written: • where ρijis the j-thmeasured distance with orientation θj in the i-th scan line, and angle j (external rotation) with the horizontal plane. • (dx, dz) is offset of the external rotation axis from the center of the laser mirror.
Bearing angle images • Highlight depth discontinuities and direction changes in range image so that the user can easily find the corresponding points of the camera image points. • Creation depth image from laser range (a) • Edge detection (b) use Sobel • Only consider the depth between two adjacent points significantly changes. • This work don’t consider the surface direction (normal vectors) • Highlight details of surface along some specific direction (vertical, horizontal,…)
Bearing angle images • Bearing Angle (BA) the angle between the laser beam and the segment joining two consecutive measurement points (a) Where ρi is the i- thdepth value in the selected trace of the depth matrix and dis the corresponding angle increment. • Constructing BA image.
Bearing angle images Pi Pi-1 pi pi-1
Extrinsic laser-camera calibration • Data process: • Collecting data and image. • Computing BA images • Manually select correspondence points between BA image and intensity image. • Store correspondence points where θC and θL are unit norm orientation vectors of camera and laser pointsdL is the point distances in laser frame.
Extrinsic laser-camera calibration • Extrinsic calibration • Finding rotation R and translation T between Camera-LRF + To minimize error function where (R, T, pi) is the reprojection onto the image plane of the laser pointpi, miis correspondence image point with pi. + Due to camera resolution is not uniform, another criteria is used. where θCLis the unit norm orientation vector of (R, T, pi)
Extrinsic laser-camera calibration • Algorithm for discovering: rotation and translation parameters. • The extrinsic parameters of transformation between the camera and LRF are determined from known corresponding 3D points. It is solved by using the P3P method
Extrinsic calibration extraction • The rotation matrix R =Xif det(X)=1, otherwise for failure solution. • Step 4: Translation:
Experimental results • Setup the system: • Camera SONY XCD-SX910-CR • Mirror: KAIDAN 360 One VR hyperbolic • Laser SICK LMS 200. • FOV 180O,resolution 0.5O • Rotating scanner. • FOV 360O, resolution 1O
Experimental results Estimation of the rotation (roll, pitch, and yaw angles) versus the number of selected points (the x-axis ranges from 4 to 10). Estimation of the translation (meters) versus the number of selected points.
Experimental results • Re-projection laser point onto intensity image
Experimental results • Construction 3D point cloud from laser points and vision points.
Conclusions • The method uses only a few correspondent points that manually selected by the user from natural scene. • No calibration patterns are required, nor more than one single laser- camera acquisition necessary. • The proposed method relies on a novel technique to visualize the range information obtained from a 3D laser scanner. • The BA images and the application of the method to an omni camera were the two main contributions of the paper. • Proposed approach requires no special equipment and allows the user to calibrate quickly the system.
Project function • This paper the camera coordinate system coincides with the single effective viewpoint. • The x-y plane is orthogonal to the mirror axis. The distance d between focal points of conic and the latus rectum l.