Recovery of Epipolar Geometry from Line Segments or Straight Lines

Abstract

Essentially, two types of geometric primitives have been used in solving motion and structure problem, namely points and straight lines. When points are used, two perspective views are sufficient to recover the motion and structure of the scene, as was described in the last chapter. When straight lines are used, three perspective views are necessary. Closed-form solutions are available either for point correspondences [90, 162] (and see the last chapter for uncalibrated images) or for line correspondences [147, 89, 58]. Algorithms using both points and lines are also available [146, 59]. However, another important type of geometric primitives, namely that of line segments, has been since long ignored in motion and structure from motion^l, although the importance of line segments in computer vision has never been underestimated (as a matter of a fact, straight lines are merely the geometric abstraction of line segments by ignoring their endpoints). The overlook of line segments in the domain of motion and structure from motion is probably due to the lack of mathematical elegance in representing line segments.