A robust algorithm to estimate the fundamental matrix

A new method, the biepipole constraint algorithm, is developed to estimate the fundamental matrix (F-matrix) based on an 8-parameter model and the geometrical analysis. First, through the analysis of the new constraints, the four parameters of the F-matrix can be estimated by solving a nonlinear unconstraint optimization problem. The objective function of the optimization problem is an equation of degree six in four unknowns. Then, the four other parameters of the F-matrix can be evaluated by using the SVD method. Particular novelties of the algorithm are the obvious geometrical meanings of the parameters, fewer matching point pairs and higher accuracy. Results are presented for synthetic and real image pairs, which show that our algorithm performs very well in terms of robustness to outliers and noises, so that excellent results can be obtained. Ó 2000 Elsevier Science B.V. All rights reserved.