Skip to Main content Skip to Navigation
Journal articles

Multifractal Analysis of Multivariate Images Using Gamma Markov Random Field Priors

Abstract : Texture characterization of natural images using the mathematical framework of multifractal analysis (MFA) enables the study of the fluctuations in the regularity of image intensity. Although successfully applied in various contexts, the use of MFA has so far been limited to the independent analysis of a single image, while the data available in applications are increasingly multivariate. This paper addresses this limitation and proposes a joint Bayesian model and associated estimation procedure for multifractal parameters of multivariate images. It builds on a recently introduced generic statistical model that enabled the Bayesian estimation of multifractal parameters for a single image and relies on the following original key contributions: First, we develop a novel Fourier domain statistical model for a single image that permits the use of a likelihood that is separable in the multifractal parameters via data augmentation. Second, a joint Bayesian model for multivariate images is formulated in which prior models based on gamma Markov random fields encode the assumption of the smooth evolution of multifractal parameters between the image components. The design of the likelihood and of conjugate prior models is such that exploitation of the conjugacy between the likelihood and prior models enables an efficient estimation procedure that can handle a large number of data components. Numerical simulations conducted using sequences of multifractal images demonstrate that the proposed procedure significantly outperforms previous univariate benchmark formulations at a competitive computational cost.
Document type :
Journal articles
Complete list of metadatas

Cited literature [62 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01925387
Contributor : Open Archive Toulouse Archive Ouverte (oatao) <>
Submitted on : Friday, November 16, 2018 - 4:18:12 PM
Last modification on : Tuesday, September 8, 2020 - 10:52:07 AM
Long-term archiving on: : Sunday, February 17, 2019 - 2:54:11 PM

File

Wendt_20427.pdf
Publisher files allowed on an open archive

Identifiers

Citation

Herwig Wendt, Sébastien Combrexelle, Yoann Altmann, Jean-Yves Tourneret, Stephen Mclaughlin, et al.. Multifractal Analysis of Multivariate Images Using Gamma Markov Random Field Priors. SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2018, 11 (2), pp.1294-1316. ⟨10.1137/17M1151304⟩. ⟨hal-01925387⟩

Share

Metrics

Record views

281

Files downloads

773