On Simulation of Manifold Indexed Fractional Gaussian Fields

Brouste, Alexandre; Istas, Jacques; Lambert-Lacroix, Sophie

doi:10.18637/jss.v036.i04

Cited by 4 publications

(1 citation statement)

References 8 publications

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“…Although many generalizations have been proposed to include anisotropy in Gaussian random fields [37,39], in the following section, we only consider the isotropic version of the fBf.…”

Section: Fractional Brownian Motion and Extensionsmentioning

confidence: 99%

Wavelet-Based Entropy Measures to Characterize Two-Dimensional Fractional Brownian Fields

Nicolis

Mateu

Contreras-Reyes

2020

Entropy

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The aim of this work was to extend the results of Perez et al. (Physica A (2006), 365 (2), 282–288) to the two-dimensional (2D) fractional Brownian field. In particular, we defined Shannon entropy using the wavelet spectrum from which the Hurst exponent is estimated by the regression of the logarithm of the square coefficients over the levels of resolutions. Using the same methodology. we also defined two other entropies in 2D: Tsallis and the Rényi entropies. A simulation study was performed for showing the ability of the method to characterize 2D (in this case, α = 2 ) self-similar processes.

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“…Although many generalizations have been proposed to include anisotropy in Gaussian random fields [37,39], in the following section, we only consider the isotropic version of the fBf.…”

Section: Fractional Brownian Motion and Extensionsmentioning

confidence: 99%

Wavelet-Based Entropy Measures to Characterize Two-Dimensional Fractional Brownian Fields

Nicolis

Mateu

Contreras-Reyes

2020

Entropy

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Manifold indexed fractional fields

Istas¹

2012

ESAIM: PS

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Abstract. (Local) self-similarity is a seminal concept, especially for Euclidean random fields. We study in this paper the extension of these notions to manifold indexed fields. We give conditions on the (local) self-similarity index that ensure the existence of fractional fields. Moreover, we explain how to identify the self-similar index. We describe a way of simulating Gaussian fractional fields.Mathematics Subject Classification. 60G07, 60G15, 60G18.

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Determining the shape of reflectance reference samples for curved surface reflectors

Lanevski

Manoocheri

Vaskuri

et al. 2020

Meas. Sci. Technol.

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Foils made of different materials are often used as reflective insulators. Many manufacturers aim to accurately measure their optical properties to estimate and improve their performance. However, flat reflectance reference samples used in measurements do not correctly represent reflective insulators and cause discrepancies between different measurement techniques. The current work presents a method for modelling surface shape of appropriate reflectance reference samples that could be produced by additive manufacturing. The method is based on studying the reflection distribution of reflective insulators and is described with an example of aluminium foil. The method’s performance is validated using Monte-Carlo simulations.

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On Simulation of Manifold Indexed Fractional Gaussian Fields

Cited by 4 publications

References 8 publications

Wavelet-Based Entropy Measures to Characterize Two-Dimensional Fractional Brownian Fields

Wavelet-Based Entropy Measures to Characterize Two-Dimensional Fractional Brownian Fields

Manifold indexed fractional fields

Determining the shape of reflectance reference samples for curved surface reflectors

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