The Transparent Dead Leaves Model

Galerne, Bruno; Gousseau, Yann

doi:10.1017/s0001867800005425

Cited by 3 publications

(2 citation statements)

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“…The Boolean model implicitly assumes that the ink projected on the specimen is not transparent: the output of the model is the same, whatever the number of overlapping disks at a given pixel. It is interesting to note that transparent ink could be modeled with the so-called transparent dead leaves model described in [21]. We do not elaborate further on this subject and leave it for future work.…”

Section: Potential Extensions Of the Proposed Modelmentioning

confidence: 99%

Rendering Deformed Speckle Images with a Boolean Model

2017

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Rendering speckle images affected by a given deformation field is of primary importance to assess the metrological performance of displacement measurement methods used in experimental mechanics and based on digital image correlation (DIC). This article describes how to render deformed speckle images with a classic model of stochastic geometry, the Boolean model. The advantage of the proposed approach is that it does not depend on any interpolation scheme likely to bias the assessment process, and that it allows the user to render speckle images deformed with any deformation field given by an analytic formula. The proposed algorithm mimics the imaging chain of a digital camera, and its parameters are carefully discussed. A MATLAB software implementation and synthetic ground-truth datasets for assessing DIC software programs are publicly available.

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Section: Potential Extensions Of the Proposed Modelmentioning

confidence: 99%

Rendering Deformed Speckle Images with a Boolean Model

2017

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“…The last decades in stochastic geometry have seen a growing interest in models that deal with random geometric objects evolving in time. As examples we mention random sequential packings [28,33], spatial birth and growth models like the Johnson-Mehl growth process [1,28], the construction of polygonal Markov random fields [30,31,32], falling/dead leaf models [2,3,5], on-line geometric random graphs such as the on-line nearest neighbour graph [27,43] or the geometric preferential attachment graph [7,8,9]. A particularly attractive class of models studied in stochastic geometry is that of random tessellations.…”

Section: Introductionmentioning

confidence: 99%

A Mecke-type formula and Markov properties for STIT tessellation processes

Nagel¹,

Nguyen²,

Thaele³

et al. 2017

ALEA

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Random fields of bounded variation and computation of their variation intensity

Galerne

2016

Adv. Appl. Probab.

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International audienceThe main purpose of this paper is to define and characterize random fields of bounded variation, that is random fields with sample paths in the space of functions of bounded variation, and to study their mean total variation. Simple formulas are obtained for the mean total directional variation of random fields, based on known formulas for the directional variation of deterministic functions. It is also shown that the mean variation of random fields with stationary increments is proportional to the Lebesgue measure, and an expression of the constant of proportionality, called the variation intensity, is established. This expression shows in particular that the variation intensity only depends on the family of two-dimensional distributions of the stationary increment random field. When restricting to random sets, the obtained results gives generalizations of well-known formulas from stochastic geometry and mathematical morphology. The interest of these general results is illustrated by computing the variation intensities of several classical stationary random field and random sets model, namely Gaussian random fields and excursion sets, Poisson shot noises, Boolean models, dead leaves models, and random tessellations

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The Transparent Dead Leaves Model

Cited by 3 publications

References 19 publications

Rendering Deformed Speckle Images with a Boolean Model

Rendering Deformed Speckle Images with a Boolean Model

A Mecke-type formula and Markov properties for STIT tessellation processes

Random fields of bounded variation and computation of their variation intensity

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