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.
Image morphing has proved to be a powerful tool for generating compelling and pleasing visual effects and has been widely used in entertainment industry. However, traditional image morphing methods suffer from a number of drawbacks: feature specification between images is tedious and the reliance on 2D information ignores the possible advantages to be gained from 3D knowledge. In this paper, we utilize recent advantages of computer vision technologies to diminish these drawbacks. By analyzing multi view geometry theories, we propose a processing pipeline based on three reference images. We first seek a few seed correspondences using robust methods and then recover multi view geometries using the seeds, through bundle adjustment. Guided by the recovered two and three view geometries, a novel line matching algorithm across three views is then deduced, through edge growth, line fitting and two and three view geometry constraints. Corresponding lines on a novel image is then obtained by an image transfer method and finally matched lines are fed into the traditional morphing methods and novel images are generated. Novel images generated by this pipeline have advantages over traditional morphing methods: they have an inherent 3D foundation and are therefore physically close to real scenes; not only images located between the baseline connecting two reference image centers, but also extrapolated images away from the baseline are possible; and the whole processing can be either wholly automatic, or at least the tedious task of feature specification in traditional morphing methods can be greatly relieved.
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