A Flexible Method for Zoom Lens Calibration and Modeling Using a Planar Checkerboard

This paper presents a fl exible method for zoom lens calibration and modeling using a planar checkerboard. The method includes the following four steps. First, the principal point of the zoom-lens camera is determined by a focus-of-expansion approach. Second, the infl uences of focus changes on the principal distance are modeled by a scale parameter. Third, checkerboard images taken at varying object distances with convergent image geometry are used for camera calibration. Finally, the variations of the calibration parameters with respect to the various zoom and focus settings are modeled using polynomials. Three different types of lens are examined in this study. Experimental analyses show that high precision calibration results can be expected from the developed approach. The relative measurement accuracy (accuracy normalized with object distance) using the calibrated zoom-lens camera model ranges from 1:5 000 to 1:25 000. The developed method is of signifi cance to facilitate the use of zoom-lens camera systems in various applications such as robotic exploration, hazard monitoring, traffi c monitoring, and security surveillance. Introduction One focus in the fi elds of close-range photogrammetry and computer vision research and applications is increasingly on zoom-lens cameras (Willson, 1994; Li and Lavest, 1996; Ahmed and Farag, 2000; Fraser and Al-Ajlouni, 2006; Ergun, 2010; Stamatopoulos and Fraser, 2011; Sanz-Ablanedo et al., 2012). Zoom-lenses, due to their fl exibility and controllability, have inherent advantages in the expansion of the imaging capabilities of fi xed lens cameras (Willson, 1994; Li and Lavest, 1996). In the past, fi xed lens cameras have been more commonly used for photogrammetric tasks than those with zoom lenses, mainly due to diffi culties in metric modeling and calibration of zoom-lens cameras (Ahmed and Farag, 2000). Bo Wu is with the Department of Land Surveying & GeoInformatics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong ([email protected]). Han Hu is with the Department of Land Surveying & GeoInformatics, The Hong Kong Polytechnic University, and the State Key Laboratory of Information Engineering in Surveying Mapping and Remote Sensing, Wuhan University, P.R. China. Qing Zhu is with the Faculty of Geosciences and Environmental Engineering of Southwest Jiaotong University, Chengdu, P.R. China. Yeting Zhang is with the State Key Laboratory of Information Engineering in Surveying Mapping and Remote Sensing, Wuhan University, P.R. China. Photogrammetric Engineering & Remote Sensing Vol. 79, No. 6, June 2013, pp. 555–571. 0099-1112/13/7906–555/$3.00/0 © 2013 American Society for Photogrammetry and Remote Sensing Camera calibration is the process of determining a camera’s intrinsic parameters including principal distance, principal point offset, and lens distortions (Tsai, 1987). The principal distance and principal point offset are known as camera interior orientation (IO) parameters. They, together with the exterior orientation (EO) parameters, enable the derivation of 3D metric information in object space. Selfcalibration approaches have been studied and used intensively in the photogrammetry community (Brown, 1971; Faig, 1975; Remondino and Fraser, 2006). This particular approach incorporates the intrinsic parameters of a camera into a photogrammetric bundle adjustment process so that all can be solved together and simultaneously with other unknowns. However, determinability of all parameters is not assured from self-calibration, which requires strong geometric confi gurations of the image networks for bundle adjustment to be achieved. In circumstances of applications using zoom-lens cameras such as 3D measurements and reconstruction of relatively long-range targets in areas not easily approachable to humans, monitoring of extremely hazardous situations such as mud-rock fl ows and landslides, automatic traffi c monitoring and urban security surveillance, image networks with strong geometric confi gurations are diffi cult or sometimes impossible to obtain for all the lens settings. Therefore, zoomlens camera calibration, as a stand-alone step, is preferred for these applications. Previous zoom-lens calibration methods usually employ a special control fi eld with precisely measured targets as ground truth. For example, Fraser and Al-Ajlouni (2006) employed a 3D control fi eld for zoom-lens calibration comprised of a 140 object point array covering an area of approximately 5 m × 3 m. Ergun (2010) used a 3D calibration fi eld to calibrate a zoom lens. The fi eld contains 112 circular coded targets across different depth ranges. In close-range photogrammetric applications using zoom-lens cameras such as those mentioned above, the lens settings are subject to frequent changes, and accordingly, the zoom lens needs to be calibrated frequently to ensure ideal metric accuracies. However, frequent calibration of the in-use zoom-lens camera system in a specifi c control fi eld is inconvenient or sometimes not feasible. In addition, calibration of zoom lens normally involves plenty of zoom and focus settings. Particularly, at large focused distance with zoom lens, the camera may need to be posed dozens of meters away from the calibration targets to capture sharp images. In this case, an in-door control fi eld