ON THE ESTIMATION OF THE FUNDAMENTAL MATRIX: A CONVEX APPROACH TO CONSTRAINED LEAST-SQUARES
G. Chesi, A. Garulli , A. Vicino , R. Cipolla
In this paper we consider the problem of estimating the fundamental matrix from point correspondences. It is well known that the most accurate estimates of this matrix are obtained by criteria minimizing geometric errors when the data are affected by noise. It is also well known that these criteria amount to solving non-convex optimization problems and, hence, their solution is affected by the optimization starting point. Generally, the starting point is chosen as the fundamental matrix estimated by a linear criterion but this estimate can be very inaccurate and, therefore, inadequate to initialize methods with other error criteria.
Here we present a method for obtaining a more accurate estimate of the fundamental matrix with respect to the linear criterion. It consists of the minimization of the algebraic error taking into account the rank 2 constraint of the matrix. Our aim is twofold. First, we show how this non-convex optimization problem can be solved avoiding local minima using recently developed convexification techniques. Second, we show that the estimate of the fundamental matrix obtained using our method is more accurate than the one obtained from the linear criterion, where the rank constraint of the matrix is imposed after its computation by setting the smallest singular value to zero. This suggests that our estimate can be used to initialize non-linear criteria such as the distance to epipolar lines and the gradient criterion, in order to obtain a more accurate estimate of the fundamental matrix. As a measure of the accuracy, the obtained estimates of the epipolar geometry are compared in experiments with synthetic and real data.
If you have difficulty viewing files that end
which are gzip compressed, then you may be able to find
tools to uncompress them at the gzip
If you have difficulty viewing files that are in PostScript, (ending
'.ps.gz'), then you may be able to
find tools to view them at
We have attempted to provide automatically generated PDF copies of documents for which only PostScript versions have previously been available. These are clearly marked in the database - due to the nature of the automatic conversion process, they are likely to be badly aliased when viewed at default resolution on screen by acroread.