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Variational Texture Synthesis with Sparsity and Spectrum Constraints

Tartavel, Guillaume; Gousseau, Yann; Peyré, Gabriel (2015), Variational Texture Synthesis with Sparsity and Spectrum Constraints, Journal of Mathematical Imaging and Vision, 52, 1, p. 124-144. http://dx.doi.org/10.1007/s10851-014-0547-7

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Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00881847
Date
2015
Journal name
Journal of Mathematical Imaging and Vision
Volume
52
Number
1
Publisher
Springer
Pages
124-144
Publication identifier
http://dx.doi.org/10.1007/s10851-014-0547-7
Metadata
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Author(s)
Tartavel, Guillaume

Gousseau, Yann

Peyré, Gabriel
Abstract (EN)
This paper introduces a new approach for texture synthesis. We propose a unified framework that both imposes first order statistical constraints on the use of atoms from an adaptive dictionary, as well as second order constraints on pixel values. This is achieved thanks to a variational approach, the minimization of which yields local extrema, each one being a possible texture synthesis. On the one hand, the adaptive dictionary is created using a sparse image representation rationale, and a global constraint is imposed on the maximal number of use of each atom from this dictionary. On the other hand, a constraint on second order pixel statistics is achieved through the power spectrum of images. In a sense, this method reconciles the first and second theory proposed by B. Julesz for texture discrimination. An advantage of the proposed method is its ability to truly synthesize textures, without verbatim copy of small pieces from the exemplar. In an extensive experimental section, we show that the resulting synthesis achieves state of the art results, both for structured and small scale textures.
Subjects / Keywords
Exemplar-based synthesis; Non-convex optimization; Statistical image modeling; Sparse decomposition; Dictionary learning; Random phase textures; Gaussian random fields

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