IJMLC 2012 Vol.2(3): 244-247 ISSN: 2010-3700

Flaws in the Computer Algorithm for Reconstructing a Scene from Two Projections

Tayeb Basta

Abstract—In 1981 Longuet-Higgins represented the world point by two vectors in the two camera reference frames and developed the essential matrix. Such a matrix is a relation between the corresponding image points on the two images of a world point on a rigid scene. The essential matrix is independent of the position and orientation of the cameras used to capture the two views. The calculation of the essential matrix requires the knowledge of at least five accurate pairs of corresponding points. The unavailability of a procedure that fulfills such a requirement led researchers to focus their attention on developing estimation methods of the essential matrix without questioning the mathematical correctness of its derivation. In this paper, we identify and expose flaws in Longuet-Higgins’ derivation of the essential matrix. These flaws are the result of mixing up between the scalar product of vectors in a single reference frame and the transformation of vectors from one reference frame to another.

Index Terms—Dot product, essential matrix, epipolar geometry, Stereo vision.

T. Basta is with Al Ghurair University, Dubai, UAE (e-mail: tayebasta@ gmail.com).

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Cite: Tayeb Basta, "Flaws in the Computer Algorithm for Reconstructing a Scene from Two Projections," International Journal of Machine Learning and Computing vol. 2, no. 3, pp. 244-247, 2012.