A Method for Determination of the Extrinsic Camera Parameters from a Pair of Images with the Use of Dual Quaternions

Abstract

Real-world problems associated with the use of the moving vehicles present a problem for estimation of the unknown motion parameters on the basis of the data obtained from a static camera set on the surface of those vehicles. The initial data (in absence of information about the vehicle motion) are the images obtained from different viewpoints. The traditional approach to estimation of the rotation and translation parameters, which consists in determination of the so-called fundamental matrix and the subsequent calculation of the required matrices has several drawbacks. In particular, if the largest portion of the predefined points in the images is located on the same plane, the fundamental matrix estimation involves serious errors, which, in turn, lead to errors in estimation of the camera parameters. Unlike in the traditional approach, in this paper the corresponding points are used to estimate not the fundamental matrix, but the internal and external camera parameters directly. Besides, this paper presents a multiple view geometry model, based on three-dimensional images and camera parameters in the form of dual quaternions. The proposed approach to the problem is a new method of estimation of the unknown camera parameters, which is more accurate and reliable compared with the traditional one. This method was implemented as a program in C + +. Using the developed program, the authors carried out an experiment to establish a correlation between the errors in the input data (points of coordinates on the planes of the camera) and the errors in the estimated rotation and translation parameters. As the result, it was confirmed that the accuracy of the parameters' estimation in most cases surpasses the quality of the results obtained by using the fundamental matrix.