XIA, Gui-Song; FERRADANS, Sira; PEYRÉ, Gabriel; AUJOL, Jean-François

doi:10.1137/130918010

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XIA, Gui-Song
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]

FERRADANS, Sira
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]

PEYRÉ, Gabriel
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]

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Ce document a été publié dans

SIAM Journal on Imaging Sciences. 2014, vol. 7, n° 1, p. 476-508

Society for Industrial and Applied Mathematics

Résumé en anglais

This paper addresses the problem of modeling textures with Gaussian processes, focusing on color stationary textures that can be either static or dynamic. We detail two classes of Gaussian processes parameterized by a small number of compactly supported linear filters, the so-called textons. The first class extends the spot noise (SN) texture model to the dynamical setting. We estimate the space-time texton to fit a translation-invariant covariance from an input exemplar. The second class is a specialization of the auto-regressive (AR) dynamic texture method to the setting of space and time stationary textures. This allows one to parameterize the covariance with only a few spatial textons. The simplicity of these models allows us to tackle a more complex problem, texture mixing which, in our case, amounts to interpolate between Gaussian models. We use optimal transport to derive geodesic paths and barycenters between the models learned from an input data set. This allows the user to navigate inside the set of texture models and perform texture synthesis from each new interpolated model. Numerical results on a library of exemplars show the ability of our method to generate arbitrary interpolations among unstructured natural textures. Moreover, experiments on a database of stationary textures show that the methods, despite their simplicity, provide state of the art results on stationary dynamical texture synthesis and mixing.< Réduire

Mots clés en anglais

optimal transport

dynamic textures

Gaussian process

texture mixing

Texture analysis

texture synthesis

URI

https://oskar-bordeaux.fr/handle/20.500.12278/189515

DOI

http://dx.doi.org/10.1137/130918010

Projet Européen

Sparsity, Image and Geometry to Model Adaptively Visual Processings

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Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251