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Enhanced isotropic gradient operator
Author(s) -
Alfaraj Mohammed,
Wang Yuchun,
Luo Yi
Publication year - 2014
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/1365-2478.12106
Subject(s) - operator (biology) , sobel operator , isotropy , fourier transform , harmonic , parameterized complexity , mathematics , mathematical analysis , computer science , harmonic analysis , algorithm , physics , optics , artificial intelligence , biochemistry , chemistry , edge detection , repressor , quantum mechanics , transcription factor , image (mathematics) , gene , image processing
ABSTRACT We present a two‐dimensional (2D) gradient operator that produces more accurate results than known traditional operators such as Ando, Sobel and the so‐called Isotropic operator. We further extend the derivation to three‐dimensional (3D), a powerful feature missing in all conventional operators. We start by constructing a parameterized formula that generically represents all 2D numerical gradient operators. We then solve for the required parameter by equating this numerical gradient with that obtained analytically from a single Fourier harmonic (or, equivalently here, a stationary plane wave). As this parameter is frequency‐ and direction‐dependent (by virtue of the underlying Fourier harmonic), we construe a pragmatic version of it that is independent of these two variables yet capable of significantly reducing the error associated with traditional operators. Extension to 3D is achieved similarly; it requires dealing with two parameters as opposed to only one in the 2D case. Synthetic and real‐data results confirm higher accuracy from this operator than from traditional ones.