Generalised Epipolar Constraints |
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Authors: | Åström Kalle Cipolla Roberto Giblin Peter |
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Affiliation: | (1) Department of Mathematics, Lund University, Lund, Sweden;(2) Department of Engineering, University of Cambridge, Cambridge, UK;(3) Department of Pure Mathematics, University of Liverpool, Liverpool, UK |
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Abstract: | In this paper we will discuss structure and motion problems for curved surfaces. These will be studied using the silhouettes or apparent contours in the images. The problem of determining camera motion from the apparent contours of curved three-dimensional surfaces, is studied. It will be shown how special points, called epipolar tangency points or frontier points, can be used to solve this problem. A generalised epipolar constraint is introduced, which applies to points, curves, as well as to apparent contours of surfaces. The theory is developed for both continuous and discrete motion, known and unknown orientation, calibrated and uncalibrated, perspective, weak perspective and orthographic cameras. Results of an iterative scheme to recover the epipolar line structure from real image sequences using only the outlines of curved surfaces, is presented. A statistical evaluation is performed to estimate the stability of the solution. It is also shown how the motion of the camera from a sequence of images can be obtained from the relative motion between image pairs. |
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Keywords: | curved surface epipolar geometry frontier point uncalibrated camera apparent contour silhouette motion extraction |
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