Estimação não-linear da matriz fundamental com apenas cinco parâmetros desconhecidos (Nonlinear Estimation of the Fundamental Matrix with Only Five Unknowns)

José Alexandre de França (jaf@jaf.eng.br)1, Marcelo Ricardo Stemmer (marcelo@das.ufsc.br)2, Maria Bernadete de Morais França (mbmorais@uel.br)1


1Universidade Estadual de Londrina
2Universidade Federal de Santa Catarina

This paper appears in: Revista IEEE América Latina

Publication Date: June 2014
Volume: 12,   Issue: 4 
ISSN: 1548-0992


Abstract:
Two images captured by an uncalibrated binocular vision system are related by the epipolar geometry. This geometry is completely characterized by a $3 \times 3$ matrix, called the fundamental matrix, which can be obtained from a set of point correspondences. This paper presents a new nonlinear method to calculate the fundamental matrix. To impose the rank two restriction, the method uses a quite simple parametrization. It has the advantage of having a reduced search space, with only five unknowns. Experimental tests demonstrated that the new method obtain accurate results for a large set of point correspondences. In this case, the quality of the estimated matrix is as good as the obtained with other nonlinear methods. However, the results are obtained at a low computational cost and with rapid convergence.

Index Terms:
Epipolar Geometry, Stereo Vision, Virtual Parallax   


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