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
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00881847
Journal nameJournal of Mathematical Imaging and Vision
MetadataShow full item record
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 / KeywordsExemplar-based synthesis; Non-convex optimization; Statistical image modeling; Sparse decomposition; Dictionary learning; Random phase textures; Gaussian random fields
Showing items related by title and author.