Calculation
By connecting all vectors using a Delaunay triangulation criterion it is possible to characterize gradient asymmetries computing the so-called gradient asymmetry coefficient, that has been defined as:, where is the total number of asymmetric vectors, is the number of Delaunay connections among them and the property is valid for any gradient square lattice.
As the asymmetry coefficient is very sensitive to small changes in the phase and modulus of each gradient vector, it can distinguish complex variability patterns even when they are very similar but consist of a very fine structural difference. Note that, unlike most of the statistical tools, the GPA does not rely on the statistical properties of the data but depends solely on the local symmetry properties of the correspondent gradient pattern.
For a complex extended pattern (matrix of amplitudes of a spatio-temporal pattern) composed by locally asymmetric fluctuations, is nonzero, defining different classes of irregular fluctuation patterns (1/f noise, chaotic, reactive-diffusive, etc.).
Besides other measurements (called gradient moments) can be calculated from the gradient lattice. Considering the sets of local norms and phases as discrete compact groups, spatially distributed in a square lattice, the gradient moments have the basic property of being globally invariant (for rotation and modulation).
The primary research on gradient lattices applied to characterize weak turbulence from X-ray images of solar active regions was developed in the Department of Astronomy at University of Maryland, College Park, USA. A key line of research on GPA's algorithms and applications has been developed at Lab for Computing and Applied Mathematics (LAC) at National Institute for Space Research (INPE) in Brazil.
Read more about this topic: Gradient Pattern Analysis
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