A versatile entropic measure of grey level inhomogeneity

Piasecki, R.

doi:10.1016/j.physa.2009.02.031

Cited by 12 publications

(12 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By recourse to the sliding cell-sampling (SCS) approach a striking effect was detected. Multiple intersecting curves (MIC) of the measure were encountered for paired simulated patterns differing, for instance, in the grey contrasting of sub-domains which were similar in size or symmetry properties [1,4]. This fact indicates a non-trivial dependence of the GLI on the length scale and suggests that the measure includes some features that may be useful for a multiscale variability analysis of complex patterns.…”

Section: Introductionmentioning

confidence: 98%

Entropic descriptor of a complex behaviour

Piasecki

Plastino

2010

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

A B S T R A C TWe propose a new type of entropic descriptor that is able to quantify the statistical complexity (a measure of complex behaviour) by taking simultaneously into account the average departures of a system's entropy S from both its maximum possible value S max and its minimum possible value S min . When these two departures are similar to each other, the statistical complexity is maximal. We apply the new concept to the variability, over a range of length scales, of spatial or grey-level pattern arrangements in simple models. The pertinent results confirm the fact that a highly nontrivial, length-scale dependence of the entropic descriptor makes it an adequate complexitymeasure, able to distinguish between structurally distinct configurational macrostates with the same degree of disorder.

show abstract

Section: Introductionmentioning

confidence: 98%

Entropic descriptor of a complex behaviour

Piasecki

Plastino

2010

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

show abstract

“…Intriguingly, one can obtain the so-called phase entropic descriptors, which determine the spatial inhomogeneity attributed to each phase component, making use of the decomposable multi-phase entropic descriptor [54]. More details with reference to binary patterns are given in the Appendix A while those for gray-level patterns can be found in [24,55].…”

Section: Reconstruction Using Entropic Descriptors-stage Twomentioning

confidence: 99%

“…Of course, we can use similar ideas to obtain gray-level equivalents of the above ED, which can be useful for multi-phase materials [21,24,55].…”

Section: Supplementary Materialsmentioning

confidence: 99%

See 1 more Smart Citation

A Two-Stage Reconstruction of Microstructures with Arbitrarily Shaped Inclusions

et al. 2020

Self Cite

View full text Add to dashboard Cite

The main goal of our research is to develop an effective method with a wide range of applications for the statistical reconstruction of heterogeneous microstructures with compact inclusions of any shape, such as highly irregular grains. The devised approach uses multi-scale extended entropic descriptors (ED) that quantify the degree of spatial non-uniformity of configurations of finite-sized objects. This technique is an innovative development of previously elaborated entropy methods for statistical reconstruction. Here, we discuss the two-dimensional case, but this method can be generalized into three dimensions. At the first stage, the developed procedure creates a set of black synthetic clusters that serve as surrogate inclusions. The clusters have the same individual areas and interfaces as their target counterparts, but random shapes. Then, from a given number of easy-to-generate synthetic cluster configurations, we choose the one with the lowest value of the cost function defined by us using extended ED. At the second stage, we make a significant change in the standard technique of simulated annealing (SA). Instead of swapping pixels of different phases, we randomly move each of the selected synthetic clusters. To demonstrate the accuracy of the method, we reconstruct and analyze two-phase microstructures with irregular inclusions of silica in rubber matrix as well as stones in cement paste. The results show that the two-stage reconstruction (TSR) method provides convincing realizations for these complex microstructures. The advantages of TSR include the ease of obtaining synthetic microstructures, very low computational costs, and satisfactory mapping in the statistical context of inclusion shapes. Finally, its simplicity should greatly facilitate independent applications.

show abstract

“…The basic definition of the EDs is given below in (3.2) and (3.3). In particular, the ED S (C , S ) quantifies the spatial inhomogeneity (statistical complexity) [15,16], while G (C , G ) describes the compositional inhomogeneity (statistical complexity), respectively [16,17]. We recall that a binary pattern can be encoded in two ways: (a) standard one instead of letters and previously used in [10,15], now we make use of exclusively.…”

Section: Hybrid Approach To Microstructure Reconstructionmentioning

confidence: 99%

Speeding up of microstructure reconstruction: I. Application to labyrinth patterns

Piasecki¹,

Olchawa²

2012

Modelling Simul. Mater. Sci. Eng.

View full text Add to dashboard Cite

Recently, entropic descriptors based the Monte Carlo hybrid reconstruction of the microstructure of a binary/greyscale pattern has been proposed (Piasecki 2011 Proc. R. Soc. A 467 806). We try to speed up this method applied in this instance to the reconstruction of a binary labyrinth target. Instead of a random configuration, we propose to start with a suitable synthetic pattern created by cellular automaton. The occurrence of the characteristic attributes of the target is the key factor for reducing the computational cost that can be measured by the total number of MC steps required. For the same set of basic parameters, we investigated the following simulation scenarios: the biased/random alternately mixed #2m approach, the strictly biased #2b and the random/partially biased #2rp one. The series of 25 runs were performed for each scenario. To maintain comparable accuracy of the reconstructions, during the final stages the only selection procedure we used was the biased one. This allowed us to make the consistent comparison of the first three scenarios. The purely random #2r approach of low efficiency was included only for completeness of the approaches. Finally, for the conditions established, the best single reconstruction and the best average tolerance value among all the scenarios were given by the mixed #2m method, which was also the fastest one. The slightly slower the alternative #2b and #2rp variants provided comparable but less satisfactory results.

show abstract

A versatile entropic measure of grey level inhomogeneity

Cited by 12 publications

References 17 publications

Entropic descriptor of a complex behaviour

Entropic descriptor of a complex behaviour

A Two-Stage Reconstruction of Microstructures with Arbitrarily Shaped Inclusions

Speeding up of microstructure reconstruction: I. Application to labyrinth patterns

Contact Info

Product

Resources

About