Using Spatial Order to Boost the Elimination of Incorrect Feature Matches

Correctly matching feature points in a pair of images is an important preprocessing step for many computer vision applications. In this paper we propose an efficient method for estimating the number of correct matches without explicitly computing them. In addition, our method estimates the region of overlap between the images. To this end, we propose to analyze the set of matches using the spatial order of the features, as projected to the x-axis of the image. The set of features in each image is thus represented by a sequence. This reduces the analysis of the matching problem to the analysis of the permutation between the sequences. Using the Kendall distance metric between permutations and natural assumptions on the distribution of the correct and incorrect matches, we show how to estimate the abovementioned values. We demonstrate the usefulness of our method in two applications: (i) a new halting condition for RANSAC based epipolar geometry estimation methods that considerably reduce the running time, and (ii) discarding spatially unrelated image pairs in the Structure-from-Motion pipeline. Furthermore, our analysis can be used to compute the probability that a given match is correct based on the estimated number of correct matches and the rank of the features within the sequences. Our experiments on a large number of synthetic and real data demonstrate the effectiveness of our method. For example, the running time of the image matching stage in the Structure-from-Motion pipeline may be reduced by about 99% while preserving about 80% of the correctly matched feature points.