Finite-Element Approach to Camera Modelling and Calibration

Abstract

This paper is focused on the finite-element (FE) method of camera calibration. The FE method enables the modelling of systematic error effects, including those which cannot be recovered by standard modelling procedures, e.g., those based on Brown’s distortion model. The FE approach to camera modelling has been previously published a number of times; however, some important aspects were not sufficiently addressed in this earlier research work. In addition, the computing power was too low to test the finite-element method with high-resolution FE grid. The proposed FE implementation is fully independent of any polynomial model and includes correction of the distance-dependent distortion effect. Besides modelling the effects such as lens distortion and sensor unflatness, the approach also accommodates the calibration of non-perspective lenses such as fisheye lenses. In addition to introducing the proposed FE calibration method, this paper addresses the related issues of sufficient target density, correction pattern smoothness and FE grid size. It also reports on experimental testing of the new FE implementation using the acceptance test procedure of the German VDI guideline 2634. Two different cameras were calibrated within the acceptance tests to analyse the impacts of the sensor size and field of view of the lens. For comparison with the FE method, both data sets were also processed using standard photogrammetric software (AICON 3D Studio). The results have proven the ability of the proposed FE modification to recover any systematic effects and to model ultra-wide field-of-view lenses, while achieving highly accurate measurements. The method is able to model the distance-dependent distortion effect, but requires a very large number of observations, which may be expensive and difficult to establish in practise. The proposed method, which can be characterised by utilising a high-resolution grid, is mostly intended for laboratory calibration of highly stable camera systems and not for on-the-job type calibration, where the target density would likely not be sufficiently large.