Abstract: The fundamental matrix (F matrix) relates corresponding points across two different viewpoints and defines the basic relationship between any two images of the same scene. Therefore, the F matrix plays an important role in most computer vision applications. Some important computing methods for the F matrix were introduced and analyzed after describing the epipolar geometry in computer vision. At last, these methods were implemented and their performarr ces were evaluated systematically based on simulated data and practical images. The test results proved that 1) the linear methods will work well on precisely located point-pairs without no mismatch; 2) the iterative nonlinear methods can conquer the Gaussian noise in positions of point pairs, however, have poor performance for mismatched points; 3) the robust methods can resolve the problems brought by noise and mismatching. Furthermore, the results also showed that the cigen-analysis based orthogonal regression methods outperform the conventional least squares methods.

Key words: Computer vision, Epipolar geometry, Fundamental matrix, Robust estimation, Image matching