Estimating the focus of expansion in a video sequence using the trajectories of interest points *

• Development of an algorithm for the estimation of the focus of expansion
• Algorithm based on the cross ratio property applied to interest point trajectories
• The algorithm gives accurate focus of expansion localization even for low textured scenes.

In this paper, we present a new algorithm for the computation of the focus of expansion in a video sequence. Although several algorithms have been proposed in the literature for its computation, almost all of them are based on the optical flow vectors between a pair of consecutive frames, so being very sensitive to noise, optical flow errors and camera vibrations. Our algorithm is based on the computation of the vanishing point of point trajectories, thus integrating information for more than two consecutive frames. It can improve performance in the presence of erroneous correspondences and occlusions in the field of view of the camera.The algorithm has been tested with virtual sequences generated with Blender, as well as some real sequences from both, the public KITTI benchmark, and a number of challenging video sequences also proposed in this paper. For comparison purposes, some algorithms from the literature have also been implemented. The results show that the algorithm has proven to be very robust, outperforming the compared algorithms, specially in outdoor scenes, where the lack of texture can make optical flow algorithms yield inaccurate results. Timing evaluation proves that the proposed algorithm can reach up to 15fps, showing its suitability for real-time applications.

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