Guided sampling via weak motion models and outlier sample generation for epipolar geometry estimation

The problem of automatic robust estimation of the epipolar geometry in cases where the correspondences are contaminated with a high percentage of outliers is addressed. This situation often occurs when the images have undergone a significant deformation, either due to large rotation or wide baseline of the cameras. An accelerated algorithm for the identification of the false matches between the views is presented. The algorithm generates a set of weak motion models (WMMs). Each WMM roughly approximates the motion of correspondences from one image to the other. The algorithm represents the distribution of the median of the geometric distances of a correspondence to the WMMs as a mixture model of outlier correspondences and inlier correspondences. The algorithm generates an outlier correspondence sample from the data. This sample is used to estimate the outlier rate and to estimate the outlier pdf. Using these two pdfs the probability that each correspondence is an inlier is estimated. These probabilities enable to guide the sampling. In the RANSAC process this guided sampling accelerates the search process. The resulting algorithm when tested on real images achieves a speedup of between one or two orders of magnitude!