Anisotropic texture modeling and applications to medical image analysis

Biermé, Hermine; Richard, Frédéric; Rachidi, M.; Benhamou, Claude-Laurent

doi:10.1051/proc/2009008

Cited by 10 publications

(6 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In future works, we plan to use TBM simulations of AFBF to evaluate the estimators we constructed using quadratic variations [7,36]. We also intend to use those simulations to rene the adequacy between models and radiographic images we analyze for the characterization of osteoporosis and breast cancer [5,8,36]. We will use the following lemma.…”

Section: The Use Of Elementary Elds Our Evaluation Was Focused On Elmentioning

confidence: 99%

A Turning-Band Method for the Simulation of Anisotropic Fractional Brownian Fields

Biermé¹,

Moisan²,

Richard³

2015

Journal of Computational and Graphical Statistics

Self Cite

View full text Add to dashboard Cite

Abstract. In this paper, we propose a method for simulating realizations of twodimensional anisotropic fractional Brownian elds (AFBF) introduced by Bonami and Estrade (2003). The method is adapted from a generic simulation method called the turning-band method (TBM) due to Matheron (1973). The TBM reduces the problem of simulating a eld in two dimensions by combining independent processes simulated on oriented bands. In the AFBF context, the simulation elds are constructed by solving an integral equation arising from the application of the TBM to non-stationary anisotropic elds. This garantees the convergence of simulations as their precision is increased. The construction is followed by a theoretical study of the convergence rate. Another key feature of this work is the simulation of band processes. Using self-similarity properties, processes are simulated exactly on bands with a circulant embedding method, so that simulation errors are exclusively due to the eld approximation. Moreover, we design a Dynamic Programming algorithm that selects band orientations achieving the optimal trade-o between computational cost and precision. Finally, we conduct a numerical study showing that the approximation error does not signicantly depend on the regularity of the elds to be simulated, nor on their degree of anisotropy. Experiments also suggest that simulations preserve eld statistical properties. IntroductionIn this paper, we address the issue of simulating realizations of a generic class of Gaussian elds, known as Anisotropic Fractional Brownian Fields (AFBF) and introduced in [9]. Date: October 9, 2012. 1991 Mathematics Subject Classication. 60G60; 60G22; 60-04.

show abstract

Section: The Use Of Elementary Elds Our Evaluation Was Focused On Elmentioning

confidence: 99%

A Turning-Band Method for the Simulation of Anisotropic Fractional Brownian Fields

Biermé¹,

Moisan²,

Richard³

2015

Journal of Computational and Graphical Statistics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Most operator-scaling random fields, as their one-dimensional counterparts, exhibit long-range dependence. Gaussian random fields with long-range dependence are known to have applications in medical image processing [7,19] and hydrology [1,20]. Econometric interpretation for aggregated models has also been discussed in the literature [17].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Operator-scaling Gaussian random fields via aggregation

Shen¹,

Wang²

2020

Bernoulli

View full text Add to dashboard Cite

We propose an aggregated random-field model, and investigate the scaling limits of the aggregated partial-sum random fields. In this model, each copy in the aggregation is a ±1-valued random field built from two correlated one-dimensional random walks, the law of each determined by a random persistence parameter. A flexible joint distribution of the two parameters is introduced, and given the parameters the two correlated random walks are conditionally independent. For the aggregated random field, when the persistence parameters are independent, the scaling limit is a fractional Brownian sheet. When the persistence parameters are tail-dependent, characterized in the framework of multivariate regular variation, the scaling limit is more delicate, and in particular depends on the growth rates of the underlying rectangular region along two directions: at different rates different operator-scaling Gaussian random fields appear as the region area tends to infinity. In particular, at the so-called critical speed, a large family of Gaussian random fields with long-range dependence arise in the limit. We also identify four different regimes at non-critical speed where fractional Brownian sheets arise in the limit.

show abstract

“…For the simulation of random fields, the library PyAFBF relies upon the turning-band method developed in (Biermé et al, 2015). This method was historically designed to facilitate research on the anisotropic fractional Brownian field (AFBF) (Bonami & Estrade, 2003) and related models (Benassi et al, 1997;Guyon & Perrin, 2000;Peltier & Levy Vehel, 1996;Polisano et al, 2014;Vu & Richard, The library is of interest for researchers in image processing where random fields can serve as texture or noise models for medical images (Biermé et al, 2009;Biermé & Richard, 2011;Richard, 2015Richard, , 2016aRichard & Biermé, 2010) or photographic films (Richard, 2017). It could also be interesting for machine learning researchers who could include the random field simulation in the design or the learning of image generative models such as Generative Adversarial Networks.…”

Section: Statement Of Needmentioning

confidence: 99%

PyAFBF: a Python library for sampling image textures from the anisotropic fractional Brownian field.

Richard¹

2022

JOSS

View full text Add to dashboard Cite

The Python library PyAFBF is devoted to the simulation of anisotropic textures of image. These textures are sampled from a mathematical model called the anisotropic fractional Brownian field (AFBF) (Bonami & Estrade, 2003); see Figure 1 for an illustration. The library offers several features. Users can generate a wide variety of textures by setting the simulated model manually or randomly either manually or randomly. It also includes tools to compute model features (regularity, anisotropy,…) which may serve as attributes to describe generated textures. The library further offers the possibility to sample heterogeneous textures from random field models related to the AFBF.

show abstract

Anisotropic texture modeling and applications to medical image analysis

Cited by 10 publications

References 23 publications

A Turning-Band Method for the Simulation of Anisotropic Fractional Brownian Fields

A Turning-Band Method for the Simulation of Anisotropic Fractional Brownian Fields

Operator-scaling Gaussian random fields via aggregation

PyAFBF: a Python library for sampling image textures from the anisotropic fractional Brownian field.

Contact Info

Product

Resources

About