Non-stationary texture synthesis from random field modeling

Atto, Abdourrahmane M.; Tan, Zhangyun; Alata, Olivier; Moreaud, Maxime

doi:10.1109/icip.2014.7025866

Cited by 6 publications

(6 citation statements)

References 9 publications

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“…Finally, note that the above analysis as well as the WLMF are meaningful for homogeneous multifractal functions X, for which the multifractal spectra D(h) of different subsets of t are identical. This excludes the class of multifractional models [8,64], for which the function h(t) is given by a smooth non-stationary evolution. Such models, also of interest in other application contexts, are not considered here, as the focus is on multifractality parameter c 2 which is not relevant to characterize multifractional processes.…”

Section: Wavelet Leader Multifractal Formalismmentioning

confidence: 99%

Bayesian Estimation of the Multifractality Parameter for Image Texture Using a Whittle Approximation

Combrexelle

Wendt

Dobigeon

et al. 2015

IEEE Trans. on Image Process.

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Texture characterization is a central element in many image processing applications. Multifractal analysis is a useful signal and image processing tool, yet, the accurate estimation of multifractal parameters for image texture remains a challenge. This is due in the main to the fact that current estimation procedures consist of performing linear regressions across frequency scales of the 2D dyadic wavelet transform, for which only a few such scales are computable for images. The strongly non-Gaussian nature of multifractal processes, combined with their complicated dependence structure, makes it difficult to develop suitable models for parameter estimation. Here, we propose a Bayesian procedure that addresses the difficulties in the estimation of the multifractality parameter. The originality of the procedure is threefold. The construction of a generic semiparametric statistical model for the logarithm of wavelet leaders; the formulation of Bayesian estimators that are associated with this model and the set of parameter values admitted by multifractal theory; the exploitation of a suitable Whittle approximation within the Bayesian model which enables the otherwise infeasible evaluation of the posterior distribution associated with the model. Performance is assessed numerically for several 2D multifractal processes, for several image sizes and a large range of process parameters. The procedure yields significant benefits over current benchmark estimators in terms of estimation performance and ability to discriminate between the two most commonly used classes of multifractal process models. The gains in performance are particularly pronounced for small image sizes, notably enabling for the first time the analysis of image patches as small as 64 × 64 pixels.

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Section: Wavelet Leader Multifractal Formalismmentioning

confidence: 99%

Bayesian Estimation of the Multifractality Parameter for Image Texture Using a Whittle Approximation

Combrexelle

Wendt

Dobigeon

et al. 2015

IEEE Trans. on Image Process.

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“…In this paper, we have considered one spectral peak for the non-stationary part. In future work, we will extend the ARFBF model to the generalized isotropic fractional fields that can admit several spectral peaks [11]. With such a model, we can address the characterization of an HRTEM image presenting several periodicities with different orientations.…”

Section: Resultsmentioning

confidence: 99%

“…One classical model for describing many stochastic nonstationary natural phenomena is the fractional Brownian motion (fBm) [7,8,9,10,11], noted as ( ). H is called the Hurst parameter.…”

mentioning

confidence: 99%

ARFBF model for non stationary random fields and application in HRTEM images

Tan¹,

Atto²,

Alata

et al. 2015

2015 IEEE International Conference on Image Processing (ICIP)

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This paper presents a new model called Autoregressive Fractional Brownian Field (ARFBF) for analyzing textures which contain stationary and non-stationary components. The paper also proposes two estimation methods for the parameter of an isotropic fractional Brownian field based on Wavelet Packet (WP) spectrum: the Log-Regression on Diagonal WP spectrum (Log-RDWP) and the Log-Regression on Polar representation of WP spectrum (Log-RPWP). The Log-RPWP method provides a better estimation performance for small size images. We show the interest of ARFBF model and Log-RPWP for characterizing High-Resolution Transmission Electron Microscopy (HRTEM) images.

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“…We will use a synthetic database [17] where the concept of true class does not lead to any confusion 6 . This database is composed by Generalized Fractional Brownian Fields (GFBF, [18]). GFBF is a model associated with an arbitrary number of interacting modulated fractional Brownian fields.…”

Section: Performance Validation On Simulated Texture Series and Deep ...mentioning

confidence: 99%

Parametric Rectified Power Sigmoid Units: Learning Nonlinear Neural Transfer Analytical Forms

Atto,

Galichet,

Pastor

et al. 2021

Preprint

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The paper proposes representation functionals in a dual paradigm where learning jointly concerns both linear convolutional weights and parametric forms of nonlinear activation functions. The nonlinear forms proposed for performing the functional representation are associated with a new class of parametric neural transfer functions called rectified power sigmoid units. This class is constructed to integrate both advantages of sigmoid and rectified linear unit functions, in addition with rejecting the drawbacks of these functions. Moreover, the analytic form of this new neural class involves scale, shift and shape parameters so as to obtain a wide range of activation shapes, including the standard rectified linear unit as a limit case. Parameters of this neural transfer class are considered as learnable for the sake of discovering the complex shapes that can contribute in solving machine learning issues. Performance achieved by the joint learning of convolutional and rectified power sigmoid learnable parameters are shown outstanding in both shallow and deep learning frameworks. This class opens new prospects with respect to machine learning in the sense that learnable parameters are not only attached to linear transformations, but also to suitable nonlinear operators.

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Non-stationary texture synthesis from random field modeling

Cited by 6 publications

References 9 publications

Bayesian Estimation of the Multifractality Parameter for Image Texture Using a Whittle Approximation

Bayesian Estimation of the Multifractality Parameter for Image Texture Using a Whittle Approximation

ARFBF model for non stationary random fields and application in HRTEM images

Parametric Rectified Power Sigmoid Units: Learning Nonlinear Neural Transfer Analytical Forms

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