共查询到10条相似文献,搜索用时 353 毫秒
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A wavelet-based method for multifractal image analysis. I. Methodology and test applications on isotropic and anisotropic random rough surfaces 总被引:3,自引:0,他引:3
A. Arnéodo N. Decoster S.G. Roux 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,15(3):567-600
We generalize the so-called wavelet transform modulus maxima (WTMM) method to multifractal image analysis. We show that the
implementation of this method provides very efficient numerical techniques to characterize statistically the roughness fluctuations
of fractal surfaces. We emphasize the wide range of potential applications of this wavelet-based image processing method in
fundamental as well as applied sciences. This paper is the first one of a series of three articles. It is mainly devoted to
the methodology and to test applications on random self-affine surfaces (e.g., isotropic fractional Brownian surfaces and anisotropic monofractal rough surfaces). Besides its ability to characterize
point-wise regularity, the WTMM method is definitely a multiscale edge detection method which can be equally used for pattern
recognition, detection of contours and image denoising. Paper II (N. Decoster, S.G. Roux, A. Arnéodo, to be published in Eur.
Phys. J. B 15 (2000)) will be devoted to some applications of the WTMM method to synthetic multifractal rough surfaces. In paper III (S.G.
Roux, A. Arnéodo, N. Decoster, to be published in Eur. Phys. J. 15 (2000)), we will report the results of a comparative experimental analysis of high-resolution satellite images of cloudy
scenes.
Received 8 July 1999 相似文献
3.
We generalize the wavelet transform modulus maxima (WTMM) method to multifractal analysis of 3D random fields. This method is calibrated on synthetic 3D monofractal fractional Brownian fields and on 3D multifractal singular cascade measures as well as their random function counterpart obtained by fractional integration. Then we apply the 3D WTMM method to the dissipation field issued from 3D isotropic turbulence simulations. We comment on the need to revisit previous box-counting analyses which have failed to estimate correctly the corresponding multifractal spectra because of their intrinsic inability to master nonconservative singular cascade measures. 相似文献
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Chaos game representation (CGR) is proposed as a
scale-independent representation for DNA sequences and provides
information about the statistical distribution of oligonucleotides
in a DNA sequence. CGR images of DNA sequences represent some kinds of
fractal patterns, but the common multifractal analysis based on the
box counting method cannot deal with CGR images perfectly. Here, the
wavelet transform modulus maxima (WTMM) method is applied to the
multifractal analysis of CGR images. The results show that the
scale-invariance range of CGR edge images can be extended to three
orders of magnitude, and complete singularity spectra can be
calculated. Spectrum parameters such as the singularity spectrum
span are extracted to describe the statistical character of DNA
sequences. Compared with the singularity spectrum span, exon
sequences with a minimal spectrum span have the most uniform
fractal structure. Also, the singularity spectrum parameters are
related to oligonucleotide length, sequence component and species,
thereby providing a method of studying the length polymorphism of
repeat oligonucleotides. 相似文献
6.
S. Roux J.F. Muzy A. Arneodo 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,8(2):301-322
Swirling turbulent flows display intermittent pressure drops associated with intense vorticity filaments. Using the wavelet
transform modulus maxima representation of pressure fluctuations, we propose a method of characterizing these pressure drop
events from their time-scale properties. This method allows us to discriminate fluctuations induced by just formed (young)
as well as by burst (old) filaments from background pressure fluctuations. The statistical characteristics of these filaments
(core size, waiting time) are analyzed in details and compared with previously reported experimental and numerical findings.
Their intermittent occurrence is found to be governed by a pure Poisson's law, the hallmark of independent events. Then we
apply the wavelet transform modulus maxima (WTMM) method to the background pressure fluctuations. This study reveals that,
once removed all the filaments, the “multifractal” nature of pressure fluctuations still persists. This is a clear indication
that the statistical contribution of the filaments is not important enough to account for the intermittency phenomenon in
turbulents flows.
Received 27 July 1998 and Received in final form 23 November 1998 相似文献
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A. Bershadskii T. Nakano D. Fukayama T. Gotoh 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,18(1):95-101
Using results of a direct numerical simulation (DNS) of 3D turbulence we show that the observed generalized scaling (i.e. scaling moments versus moments of different orders) is consistent with a lognormal-like distribution of turbulent energy dissipation fluctuations
with moderate amplitudes for all space scales available in this DNS (beginning from the molecular viscosity scale up to largest ones). Local multifractal thermodynamics has been developed to interpret the data obtained using the generalized scaling, and a new interval
of space scales with inverse cascade of generalized energy has been found between dissipative and inertial intervals of scales
for sufficiently large values of the Reynolds number.
Received 21 July 2000 相似文献
9.
U. Tırnaklı C. Tsallis M. L. Lyra 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,11(2):309-315
Dissipative one-dimensional maps may exhibit special points (e.g., chaos threshold) at which the Lyapunov exponent vanishes. Consistently, the sensitivity to the initial conditions has a
power-law time dependence, instead of the usual exponential one. The associated exponent can be identified with 1/(1-q), where q characterizes the nonextensivity of a generalized entropic form currently used to extend standard, Boltzmann-Gibbs statistical
mechanics in order to cover a variety of anomalous situations. It has been recently proposed (Lyra and Tsallis, Phys. Rev.
Lett. 80, 53 (1998)) for such maps the scaling law , where and are the extreme values appearing in the multifractal function. We generalize herein the usual circular map by considering inflexions of arbitrary power z, and verify that the scaling law holds for a large range of z. Since, for this family of maps, the Hausdorff dimension df equals unity for all z in contrast with q which does depend on z, it becomes clear that df plays no major role in the sensitivity to the initial conditions.
Received 5 February 1999 相似文献
10.
Gregory L. Eyink 《Journal of statistical physics》1995,78(1-2):353-375
Parisi and Frisch proposed some time ago an explanation for multiscaling of turbulent velocity structure functions in terms of a multifractal hypothesis, i.e., they conjecture that the velocity field has local Hölder exponents in a range [h
min,h
max], with exponents <h occurring on a setS(h) with a fractal dimensionD(h). Heuristic reasoning led them to an expression for the scaling exponentz
p
ofpth order as the Legendre transform of the codimensiond-D(h). We show here that a part of the multifractal hypothesis is correct under even weaker assumptions: namely, if the velocity field hasL
p
-mean Hölder indexs, i.e., if it lies in the Besov spaceB
p
s,
, then local Hölder regularity is satisfied. Ifs<d/p, then the hypothesis is true in a generalized sense of Hölder space with negative exponents and we discuss the proper definition of local Hölder classes of negative index. Finally, if a certain box-counting dimension exists, then the Legendre transform of its codimension gives the scaling exponentz
p
, and, more generally, the maximal Besov index of order,p, ass
p
=z
p
/p. Our method of proof is derived from a recent paper of S. Jaffard using compactly-supported, orthonormal wavelet bases and gives an extension of his results. We discuss implications of the theorems for ensemble-average scaling and fluid turbulence. 相似文献