A new model for quantifying anisotropic scale invariance and for decomposition of mixing patterns

被引:134
作者
Cheng, QM [1 ]
机构
[1] York Univ, Dept Geog, Dept Earth & Atmospher Sci, N York, ON M3J 1P3, Canada
来源
MATHEMATICAL GEOLOGY | 2004年 / 36卷 / 03期
基金
加拿大自然科学与工程研究理事会;
关键词
multifractal; self-similarity; anisotropic scaling; geophysical and geochemical data processing; Landsat TM image;
D O I
10.1023/B:MATG.0000028441.62108.8a
中图分类号
P [天文学、地球科学];
学科分类号
07 ;
摘要
A new power - law function has been derived to represent the relationship between area of the set consisting of wave numbers with spectral energy density above S ( A(> S)) on the two-dimensional frequency plane and S. The power - law relation holds if the field concerned possessing isotropic scale invariance or generalized scaling invariance involves rotational and ratio-scale changing transforms. The equation is valid for dealing with common exploration geophysical and geochemical fields encountered in mineral exploration and environmental assessment. This power - law function not only provides a new model for characterizing anisotropic scaling invariance for generalized scaling field, for example, estimating the power exponent of power spectrum of generalized scale invariance measure in frequency domain, but also forms a theoretical base for the S - A filtering technique developed for decomposing a mixing field into components on the basis of distinct scaling properties in the frequency domain. It is demonstrated that the method has potential to become a general technique for image processing and pattern recognition.
引用
收藏
页码:345 / 360
页数:16
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