Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 14 3 2007 10.5194/npg-14-293-2007 http://www.nonlin-processes-geophys.net/14/293/2007/ http://www.nonlin-processes-geophys.net/14/293/2007/npg-14-293-2007.html http://www.nonlin-processes-geophys.net/14/293/2007/npg-14-293-2007.pdf 293 303 2007-06-18 Multifractal imaging filtering and decomposition methods in space, Fourier frequency, and eigen domains Qiuming Cheng qiuming@yorku.ca 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 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. 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