Improving the efficiency of a least median of squares schema for the estimation of the fundamental matrix
A robust and efficient approach to estimate the fundamental matrix is proposed. The main goal is to reduce the computational cost involved in the estimation when robust schemas are applied. The backbone of the proposed technique is the conventional Least Median of Squares (LMedS) technique. It is well known that the LMedS is one of the most robust regressors for highly contaminated data and unstable models. Unfortunately, its computational complexity renders it useless for practical applications. To overcome this problem, a small number of low-dimensionality least-square problems are solved using well-selected subsets from the input data. The results of this initial approach are fed into the LMedS schema, which is applied to recover the final estimation of the Fundamental matrix. The complexity is substantially reduced by applying a selection process based on an effective statistical analysis of the inherent correlation of the input data. This analysis is used to define a suitable clustering of the data and to drive the subset selection aiming at the reduction of the search space in the LMedS schema. It is shown that avoiding redundancies better estimates can be obtained while keeping the computational cost low. Selected results of computer experiments were conducted to assess the performance of the proposed technique.
least median of squares fundamental matrix epipolar geometry semivariogram function k-means clustering