Abstract
A major challenge in 3D reconstruction is the computation of the fundamental matrix. Automatic computation from uncalibrated image pairs is performed from point correspondences. Due to imprecision and wrong correspondences, only an approximation of the true fundamental matrix can be computed. The quality of the fundamental matrix strongly depends on the location and number of point correspondences.Furthermore, the fundamental matrix is the only geometric constraint between two uncalibrated views, and hence it can be used for the detection of wrong point correspondences. This property is used by current algorithms like RANSAC, which computes the fundamental matrix from a restricted set of point correspondences. In most cases, not only wrong correspondences are disregarded, but also correct ones, which is due to the criterion used to eliminate outliers. In this context, a new criterion preserving a maximum of correct correspondences would be useful.In this paper we introduce a novel criterion for outlier elimination based on a probabilistic approach. The enhanced set of correspondences may be important for further computation towards a 3D reconstruction of the scene.
Highlights
Modern point matching algorithms like SIFT, provide a large number of point matches, even in stereo image pairs with large changes in scale, translation and rotation between the images
We knew from the epipolar geometry and its uncertainty that its correspondence x¢ would be located within this region with a given probability a, which was derived from the Mahalanobis distance k
The results presented here were obtained using RANSAC for an estimation of the fundamental matrix
Summary
Modern point matching algorithms like SIFT (see [4, 5]), provide a large number of point matches, even in stereo image pairs with large changes in scale, translation and rotation between the images. Algorithms for computing the fundamental matrix can be classified into algorithms sensitive to wrong matches and algorithms detecting and ignoring so-called outliers like RANSAC or Least Median of Squares. In [3] and [7] algorithms of both categories are described and compared. Algorithms of the first category should only be used after preliminary outlier removal. Based on [3], we used RANSAC combined with the normalized 8-point algorithm to compute a first estimation of the fundamental matrix in order to perform outlier removal. As a consequence we have developed a new criterion to evaluate correspondences between two images, considering the estimation of the fundamental matrix and its uncertainty. We show how the criterion can be used in an effective way for outlier removal, and we compare our results with those using a conventional criterion.
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