Practical ways to calculate camera lens distortion for real-time camera calibration

In this paper, we address practical methods for calculating camera lens distortion for real-time applications. Although the lens distortion problem can be easily ignored for constant-parameter lenses, it becomes important in the "eld of real-time camera calibrations, particularly for zoom lenses. Tsai's camera calibration method, which is adopted in this paper for real-time application, consists of two stages. While some camera parameters can be calculated algebraically in the "rst stage, a nonlinear optimization process is involved in the second stage for calculating other parameters including lens distortion, which requires a large number of calculations. However, if the lens distortion can be calculated independently of the other camera parameters, we can easily calibrate a camera with a linear method without a computational burden. We propose two di!erent methods for calculating lens distortion independently. These methods are so simple and require so few calculations that the lens distortion can be rapidly calculated even in real-time applications. The "rst one uses a look-up-table (LUT) of focal length and lens distortion, which can be constructed in the initialization process. The second one is a feature-based method using the relationship between the feature points found in an image. Experiments were carried out for both methods, results of which show that the proposed methods are favorably comparable in performance with the non-real-time full optimization method. 2001 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.