Two and three view geometry based on noisy data: An experimental evaluation

摘要

It is well known that, based on known multi view geometry, and given a single point in one image, its corresponding point in a second image can be determined up to a one dimensional ambiguity; and that, given a pair of corresponding points in two images, their corresponding point in the third image can be uniquely determined. These relationships have been widely used in computer vision community for the applications such as correspondences, stereo, motion analysis, etc. However, in the real world, images are noisy. How to apply accurate mathematical relationships of multi view geometry to noisy data and the various numerical algorithms available for doing so stably and accurately is an active topic of research. In this paper, some major methods currently available for the computation of two and three view geometries for both calibrated and un-calibrated cameras are analysed, a novel method of calculating the trifocal tensor for the calibrated camera is deduced, and a quantitative evaluation of the influences of the noise at different levels, corresponding to different methods of computing two and three view geometries, is performed through the experiments on synthetic data. Based on the experiment results, several novel algorithms are introduced which improve the performance of searching for correspondences in real images across two or three views.