LECLAIRE, Arthur; RABIN, Julien

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LECLAIRE, Arthur
Institut de Mathématiques de Bordeaux [IMB]

RABIN, Julien
Equipe Image - Laboratoire GREYC - UMR6072

Langue

Communication dans un congrès

Ce document a été publié dans

Seventh International Conference on Scale Space and Variational Methods in Computer Vision, 2019-06-30, Hofgeismar.

Résumé en anglais

The optimal transport (OT) framework has been largely used in inverse imaging and computer vision problems, as an interesting way to incorporate statistical constraints or priors. In recent years, OT has also been used in machine learning, mostly as a metric to compare probability distributions. This work addresses the semi-discrete OT problem where a continuous source distribution is matched to a discrete target distribution. We introduce a fast stochastic algorithm to approximate such a semi-discrete OT problem using a hierarchical multi-layer transport plan. This method allows for tractable computation in high-dimensional case and for large point-clouds, both during training and synthesis time. Experiments demonstrate its numerical advantage over multi-scale (or multi-level) methods. Applications to fast exemplar-based texture synthesis based on patch matching with two layers, also show stunning improvements over previous single layer approaches. This shallow model achieves comparable results with state-of-the-art deep learning methods, while being very compact, faster to train, and using a single image during training instead of a large dataset.< Réduire

URI

https://oskar-bordeaux.fr/handle/20.500.12278/192914

Project ANR

Generalized Optimal Transport Models for Image processing - ANR-16-CE33-0010

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251