Determining the Epipolar Geometry and its Uncertainty: A Review
International Journal of Computer Vision
Introductory Techniques for 3-D Computer Vision
Introductory Techniques for 3-D Computer Vision
What can be seen in three dimensions with an uncalibrated stereo rig
ECCV '92 Proceedings of the Second European Conference on Computer Vision
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Extracting 3D structure from two views is a flourishing subject in computer vision literature. In 1981 Longuet-Higgins introduces what it seemed a mathematically founded theory that relates the corresponding points from the two images independently from the extrinsic camera parameters. Since then a number of contributions based on such a theory was emerged. Higgins defined the world point in two different reference frames and derived a formula relating the image points defined in the two frames through a matrix. Trucco presented Longuet-Higgins' solution by formulating the problem as the product of three planar vectors. He then derived an algebraic formula relating the two image points through an algebraic entity called the essential matrix. Such a matrix is independent of the position of cameras used to capture the two views. In this paper I clarify that the reasoning of Longuet-Higgins in its first form is based on an undefined vectors operation. His reasoning presented in Trucco was misled by assuming that the world reference frame is fixed onto the left camera frame. He did not take into account that (1) dividing the coordinates of a world point by its Z-coordinate is a point belonging to a plane parallel to the XY-plane, (2) fixing the world reference frame onto the left camera implies that the coordinates of any projection belong simultaneously to the world reference frame and the left camera frame. The contribution of this paper is to unveil a misconception in the theory of Higgins' algorithm that remains hidden up to date.