An Improved Method for Computation of Fundamental Matrix

In augmented reality, the real surgical scene information is required for three-dimensional reconstruction in order to merge real and virtual information. The estimation of the fundamental matrix is one of the key steps. Both the linear method and iterative least squares didn´t impose the constraint that the rank of the fundamental matrix is two and the estimation results weren´t accurate enough and nonlinear method needs an appropriate initial value. The MAPSAC algorithm was robust, but the Sampson errors of the results were still large. In this paper we proposed a MAPSACNL algorithm which integrates the MAPSAC algorithm and nonlinear method by using the results of MAPSAC as the initial value of the fundamental matrix and then optimizing it by Levenberg-Marquardt method. We compared the results of our methods and the results of linear method and the iterative least squares, which showed MAPSACNL method estimating the fundamental matrix was more robust and had less Sampson errors for the variance of the iterative numbers, the corner points numbers and the zeta value.