Rejection of mismatched correspondences along the affine epipolar line

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Identifying the correspondences of points between images is an important task. It finds applications in depth recovery, motion recovery, photogrammetry, and robotics. Commonly, one uses the epipolar geometry to constrain the problem from a two-dimensional to a one-dimensional search. However, the estimation of the epipolar parameters itself depends on finding a sufficiently accurate set of initial point correspondences. Mismatched correspondences present themselves as outliers in this parameter estimation. Even if the epipolar geometry is perfectly found, it is still not sufficient to disambiguate false matches whose points lie along the epipolar line. This paper attempts to identify (and thereby reject) such mismatched correspondences, within the framework of an affine projection model and the use of three images. The robust Least Median of Squares (LMedS) approach is utilized in two stages. First, it is used to estimate the epipolar parameters and reject those point-correspondences whose orthogonal distance to the epipolar lines are significant. Second, points are resolved along their epipolar lines and the LMedS is used to solve for a consistent rotation for all points using three images.