{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T14:42:51Z","timestamp":1761057771982},"reference-count":22,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Patt. Recogn. Artif. Intell."],"published-print":{"date-parts":[[1998,9]]},"abstract":"<jats:p> This paper addresses the problem of computing the fundamental matrix which describes a geometric relationship between a pair of stereo images: the epipolar geometry. In the uncalibrated case, epipolar geometry captures all the 3D information available from the scene. It is of central importance for problems such as 3D reconstruction, self-calibration and feature tracking. Hence, the computation of the fundamental matrix is of great interest. The existing classical methods<jats:sup>14<\/jats:sup> use two steps: a linear step followed by a nonlinear one. However, in some cases, the linear step does not yield a close form solution for the fundamental matrix, resulting in more iterations for the nonlinear step which is not guaranteed to converge to the correct solution. In this paper, a novel method based on virtual parallax is proposed. The problem is formulated differently; instead of computing directly the 3 \u00d7 3 fundamental matrix, we compute a homography with one epipole position, and show that this is equivalent to computing the fundamental matrix. Simple equations are derived by reducing the number of parameters to estimate. As a consequence, we obtain an accurate fundamental matrix with a stable linear computation. Experiments with simulated and real images validate our method and clearly show the improvement over the classical 8-point method. <\/jats:p>","DOI":"10.1142\/s0218001498000452","type":"journal-article","created":{"date-parts":[[2003,7,17]],"date-time":"2003-07-17T12:25:53Z","timestamp":1058444753000},"page":"817-840","source":"Crossref","is-referenced-by-count":10,"title":["A Stable and Accurate Algorithm for Computing Epipolar Geometry"],"prefix":"10.1142","volume":"12","author":[{"given":"Boubakeur S.","family":"Boufama","sequence":"first","affiliation":[{"name":"Department of Math and Computer Science, University of Prince Edward Island, 550 University Avenue, Charlottetown, PE Canada C1A 4P3, Canada"}]},{"given":"Roger","family":"Mohr","sequence":"additional","affiliation":[{"name":"INRIA, 38330 Montbonnot, France"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"p_2","first-page":"563","author":"Faugeras O.","year":"1992","journal-title":"G. 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