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e Camera Calibration using Iterative Refinement of Control Points

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Accurate Camera Calibration using Iterative Refinement of Control PointsAnkur Datta Jun-Sik KimRobotics InstituteCarnegie Mellon University{ankurd,kimjs,tk}@cs.cmu.eduTakeo KanadeAbstractWe describe a novel camera calibration algorithm forsquare, circle, and ring planar calibration patterns. An it-erative refinement approach is proposed that utilizes the pa-rameters obtained from traditional calibration algorithmsas initialization to perform undistortion and unprojectionof calibration images to a canonical fronto-parallel plane.This canonical plane is then used to localize the calibrationpattern control points and recompute the camera parame-ters in an iterative refinement until convergence. Undistort-ing and unprojecting the calibration pattern to the canoni-cal plane increases the accuracy of control point localiza-tion and consequently of camera calibration. We have con-ducted an extensive set of experiments with real and syn-thetic images for the square, circle and ring pattern, andthe pixel reprojection errors obtained by our method areabout 50% lower than those of the OpenCV Camera Cal-ibration Toolbox. Increased accuracy of camera calibra-tion directly leads to improvements in other applications;we demonstrate recovery of fine object structure for visualhull reconstruction, and recovery of precise epipolar geom-etry for stereo camera calibration.1. IntroductionCamera calibration is an important problem in whicheven small improvements are beneficial for tasks such as3D reconstruction, robot navigation, etc. Algorithms forcalibrating a pinhole camera can be primarily classified intotwo categories; those that require objects with known 3Dgeometry [5], and those that use self-calibration, includingthe use of planar calibration patterns [18, 22, 15, 17]. Dueto their ease of use, calibration algorithms that use planarpatterns have gained widespread acceptance. In addition tothe square planar pattern, circle and ring patterns have alsobeen used [16, 7, 4, 3, 24, 21, 11, 9]. The calibration pro-cedure typically consists of either localizing the calibrationpattern control points (square corners, circle or ring centers)[18, 22, 7, 9] and then solving for the camera parameters, orusing some geometric property of the pattern itself to solvefor the camera parameters directly [4, 3, 24, 21, 11].A major source of error that affects both camera cali-bration approaches; of either localizing the control pointor using geometric properties of the pattern directly, is thatthe input camera calibration images are non-fronto parallelimages that suffer from nonlinear distortion due to cameraoptics. Therefore, precise localization of control points oraccurate determination of geometric properties under suchconditions is a very difficult task, where even small errorsmay lead to imprecise camera calibration. The difficulty oflocalizing square control points in distorted non-fronto par-allel images was noted by Zhang in [23], however, no stepswere presented to rectify it. Heikkila noticed a variant ofthis problem where the center of the projected circle is mis-taken for t he projected center of the circle and proposed arefinement approach for control points that is restricted toonly the circle pattern [7, 8] and does not extend to otherplanar patterns such as the square and the ring pattern.In this paper, we advocate an iterative refinement ap-proach for accurate localization of calibration pattern con-trol points that is applicable to all planar patterns: square,circle and ring. We propose to undistort and unprojectthe input pattern images to canonical fronto-parallel imageswith no distortion; pattern control points are then local-ized in these canonical images. We can localize the con-trol points with high accuracy in the canonical images be-cause they are fronto-parallel and do not suffer from distor-tion effects. Once the control points have been localized,they are then used to recompute the camera calibration pa-rameters. This process is then repeated until convergence.This iterative refinement approach can be bootstrapped us-ing st andard calibration routine like OpenCV [1, 22], whichprovide initial estimates for radial distortion and camera pa-rameters. We have conducted an extensive set of experi-ments with real and synthetic images of square, circle, andring calibration patterns and our results demonstrate recov-ery of calibration parameters with accuracy far exceedingthe traditional approach as employed by OpenCV [1] (seeSection 5). In addition, we also present results on two appli-cations: visual hull reconstruction, where we show that fineobject structure can be recovered from accurate calibrationusing the proposed approach, and stereo camera calibration,where we show that the proposed approach results in preciserecovery of epipolar geometry.Ankur Datta, Junsik Kim and Takeo Kanade, “Accurate Camera Calibration using Iterative Refinement of Control Points,” Workshop on Visual Surveillance (VS) 2009 (held in conjunction with ICCV), October 2009.Figure 1: Top row: Input images of the ring calibration pattern. Bottom row: Input images have been undistorted and unprojected tocanonical fronto-parallel images. Control points can be precisely localized in the canonical images as compared to the input images.2. Related WorkSquare control points were first used in their earliestform by Brown [2] and were made popular by the subse-quent work on camera calibration by Tsai [ 18]. Sturm etal. in [15] use imaged absolute conic to recover camera in-trinsic parameters using linear calibration equations. Zhangintroduced an algorithm that required only a few images ofa planar checkerboard pattern to compute the calibration pa-rameters [22]. The approach consisted of an initial closed-form solution of the camera parameters, followed by a non-linear refinement using Levenberg-Marquardt [14]. Zhang’sapproach to camera calibration has inspired OpenCV [1]and serves as our benchmark to compare progress in cam-era calibration accuracy, consequently we elaborate brieflyon the details of OpenCV in section 3.Circular control points were introduced as an alterna-tive to the square control points for camera calibration[16, 7, 4, 3, 24, 21, 19]. Heikkila in [7] performed aminimization over the weighted sum of squared differ-ences between the observation and the camera model usingLevenberg-Marquardt [14]. Chen et. al. in [3] estimatedthe extrinsic camera parameters and the focal length of thecamera from a single


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