Abstract
Two images of the same scene are related by what is called the epipolar equation. It is specified by a matrix called the fundamental matrix. By computing the fundamental matrix between two images, one can analyze the 3D structure of the scene, which we discuss in Chaps. 4 and 5. This chapter describes the principle and typical computational procedures for accurately computing the fundamental matrix by considering the statistical properties of the noise involved in correspondence detection. As in ellipse fitting, the methods are classified into algebraic and geometric approaches. However, the fundamental matrix has an additional property called the rank constraint: it is required to have determinant 0. Three approaches for enforcing it are introduced here: a posteriori rank correction, hidden variables, and extended FNS. We then describe the procedure of repeatedly using them to compute the geometric distance minimization solution. The RANSAC procedure for removing wrong correspondences is also described.
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Kanatani, K., Sugaya, Y., Kanazawa, Y. (2016). Fundamental Matrix Computation. In: Guide to 3D Vision Computation. Advances in Computer Vision and Pattern Recognition. Springer, Cham. https://doi.org/10.1007/978-3-319-48493-8_3
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DOI: https://doi.org/10.1007/978-3-319-48493-8_3
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