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Comparison with a recent relaxation method

Recently a features matching method has been presented by Zhang's et al. in [ 14 ] which is based on maximizing the sum of a measure of support over the possible feature pairings. The method (as it can be tried out on their on-line demo) manages to disentangle itself in quite difficult situations and produces matches good enough to allow an easy recovery of the epipolar geometry.

We have adventured in re-implementing Zhang's et al. method and have performed some qualitative comparisons. Amazingly the performances of the methods is remarkably similar both in the good and bad cases.

The explanation is simple. Their method relies upon a pairwise correspondence strength that uses a local measure of support weighing the straight correlation between candidate matches with a measure of ``distortion'' of distances to neighboring matches; the underlying principle is that the relative distance between neighboring sets of features should not change under a local affine approximation of the transformation. The relaxation stage does nothing but selecting matches with mutual maximal strength that also have little ambiguity with other competing matches.

As explained in Section 4 , these criteria are implicitly implemented in the method proposed here, albeit in a decisively global fashion. The globality of the proposed algorithm - as opposed to the relative local-ness of Zhang's - gives it a relative speed disadvantage. However, although not mentioned in [ 14 ], a close look at the algorithm reveals that its complexity is , where n is the number of features in one image, M is the average number of candidates in the other image and K is the average number of neighbors (within a given radius) of a features. As a matter of fact, M and (to some extent) K both grow linearly with the number of overall features and so one should watch out before declaring it O ( n ) (as it can be discovered experimentally!).

One last thing to be said is that Zhang's method performs well when there are many features sprinkled uniformly in the images in order to give support to candidate matches. The method proposed here performs extremely well also in sparse situations , which might be a clear advantage in multistage approaches where just a few good features can be matched well in order to compute the epipolar geometry.