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Méthodes statistiques pour la mise en correspondance de descripteurs

Olivier Collier 1, 2
1 imagine [Marne-la-Vallée]
LIGM - Laboratoire d'Informatique Gaspard-Monge, CSTB - Centre Scientifique et Technique du Bâtiment, ENPC - École des Ponts ParisTech
Abstract : Many applications, as in computer vision or medicine, aim at identifying the similarities between several images or signals. Thereafter, it is possible to detect objects, to follow them, or to overlap different pictures. In every case, the algorithmic procedures that treat the images use a selection of keypoints that they try to match by pairs. The most popular algorithm nowadays is SIFT, that performs keypoint selection, descriptor calculation, and provides a criterion for global descriptor matching. In the first part, we aimat improving this procedure by changing the original descriptor, that requires to find the argument of the maximum of a histogram: its computation is indeed statistically unstable. So we also have to change the criterion to match two descriptors. This yields a nonparametric hypothesis testing problem, in which both the null and the alternative hypotheses are composite, even nonparametric. We use the generalized likelihood ratio test to get consistent testing procedures, and carry out a minimax study. In the second part, we are interested in the optimality of the procedure of global matching. We give a statistical model in which some descriptors are present in a given order in a first image, and in another order in a second image. Descriptor matching is equivalent in this case to the estimation of a permutation. We give an optimality criterion for the estimators in theminimax sense. In particular, we use the likelihood to find several consistent estimators, which are even optimal under some conditions. Finally, we tackled some practical aspects and showed that our estimators are computable in reasonable time, so that we could then illustrate the hierarchy of our estimators by some simulations.
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https://tel.archives-ouvertes.fr/tel-00904686
Contributor : Olivier Collier <>
Submitted on : Friday, November 15, 2013 - 9:15:49 AM
Last modification on : Wednesday, February 3, 2021 - 7:54:25 AM
Long-term archiving on: : Sunday, February 16, 2014 - 4:29:25 AM

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  • HAL Id : tel-00904686, version 1

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Olivier Collier. Méthodes statistiques pour la mise en correspondance de descripteurs. Statistiques [math.ST]. Université Paris-Est, 2013. Français. ⟨tel-00904686v1⟩

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