NPG Nonlinear Processes in Geophysics NPG Nonlin. Processes Geophys. 1607-7946 Copernicus Publications Göttingen, Germany 10.5194/npg-14-293-2007 Multifractal imaging filtering and decomposition methods in space, Fourier frequency, and eigen domains Cheng Qiuming 1 2 State Key Laboratory of Geological Processes and Mineral Resources, China University of Geosciences, Wuhan 430074, Beijing 100083, China Department of Earth and Space Science and Engineering, Department of Geography, York University, Toronto M3J1P3, Canada 18 06 2007 14 3 293 303 Copyright: © 2007 Qiuming Cheng 2007 This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Generic License. To view a copy of this licence, visit https://creativecommons.org/licenses/by-nc-sa/2.5/ This article is available from https://npg.copernicus.org/articles/14/293/2007/npg-14-293-2007.html The full text article is available as a PDF file from https://npg.copernicus.org/articles/14/293/2007/npg-14-293-2007.pdf

The patterns shown on two-dimensional images (fields) used in geosciences reflect the end products of geo-processes that occurred on the surface and in the subsurface of the Earth. Anisotropy of these types of patterns can provide information useful for interpretation of geo-processes and identification of features in the mapped area. Quantification of the anisotropy property is therefore essential for image processing and interpretation. This paper introduces several techniques newly developed on the basis of multifractal modeling in space, Fourier frequency, and eigen domains, respectively. A singularity analysis method implemented in the space domain can be used to quantify the intensity and anisotropy of local singularities. The second method, called S-A, characterizes the generalized scale invariance property of a field in the Fourier frequency domain. The third method characterizes the field using a power-law model on the basis of eigenvalues and eigenvectors of the field. The applications of these methods are demonstrated with a case study of Environment Scan Electric Microscope (ESEM) microimages for identification of sphalerite (ZnS) ore minerals from the Jinding Pb/Zn/Ag mineral deposit in Shangjiang District, Yunnan Province, China.

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