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We present a novel approach for RANSAC-based computation of the fundamental matrix based on epipolar homography decomposition. We analyze the geometrical meaning of the decomposition-based representation and show that it directly induces a consecutive sampling strategy of two independent sets of correspondences. We show that our method guarantees a minimal number of evaluated hypotheses with respect to current minimal approaches, on the condition that there are four correspondences on an image line. We validate our approach on real-world image pairs, providing fast and accurate results.

We address the problem of epipolar geometry using the motion of silhouettes. Such methods match epipolar lines or frontier points across views, which are then used as the set of putative correspondences. We introduce an approach that improves by two orders of magnitude the performance over state-of-the-art methods, by significantly reducing the number of outliers in the putative matching. We model the frontier points' correspondence problem as constrained flow optimization, requiring small differences between their coordinates over consecutive frames. Our approach is formulated as a Linear Integer Program and we show that due to the nature of our problem, it can be solved efficiently in an iterative manner. Our method was validated on four standard datasets providing accurate calibrations across very different viewpoints.

Computing the epipolar geometry between cameras with very different viewpoints is often problematic as matching points are hard to find. In these cases, it has been proposed to use information from dynamic objects in the scene for suggesting point and line correspondences. We propose a speed up of about two orders of magnitude, as well as an increase in robustness and accuracy, to methods computing epipolar geometry from dynamic silhouettes. This improvement is based on a new temporal signature: motion barcode for lines. Motion barcode is a binary temporal sequence for lines, indicating for each frame the existence of at least one foreground pixel on that line. The motion barcodes of two corresponding epipolar lines are very similar, so the search for corresponding epipolar lines can be limited only to lines having similar barcodes. The use of motion barcodes leads to increased speed, accuracy, and robustness in computing the epipolar geometry., Comment: Update metadata

Videos recorded by wearable egocentric cameras can suffer from quality degradations that cannot always be fixed by current methods. When several wearable video cameras are viewing the same scene, each having highly variable quality, it is possible to combine them into a single high-quality video. Current techniques select for each point in time the highest quality video stream, but the highest quality video may not be relevant. E.g. the best quality video can come from a person that happen to look sideways from the main attraction. We propose the curation of a single video stream from multiple egocentric videos by requiring that the selected video will also view the most interesting region in the scene. Importance of a region is determined by the "wisdom of the crowd", i.e. the number of cameras looking at a region. The resulting video is more interesting and of higher quality than any individual video streams can possibly obtain. Several examples are presented demonstrating the effectiveness of this technique.

The paper does three things. First invariant distributions play an important role in a variety of problems in systems theory (cf. [I]). We show that such invariant distributions correspond to a Riccati type partial differential equations. These concrete PDE's appear to be a useful way for analysis and computation in specific problems. Secondly, we use this to prove that invariant distributions are rare and to classify them in some cases. Thirdly we study "minimal" factorizations of systems. We show that minimal factorizations are nongeneric, indicate a consequence for control, and compute them explicitly for a class of special problems, thereby obtaining a generalization and strengthening of a theorem of Boyd and Chua.