Gradient pattern analysis: Difference between revisions

Revision as of 12:38, 25 March 2009

Revision as of 12:45, 25 March 2009

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The original ideas on GPA was introduced by Rosa, Sharma and Valdivia, 1999 \cite{Rosa99}. Usually GPA is applied for spatio-temporal pattern analysis in physics and environmental sciences operating on time-series and images.

{\bf== Contents} ==

{\bf [[Calculation}]]

{\bf [[Relation to other methods}]]

{\bf [[References}]]

{\bf [[External Links}]]

\itemize== Calculation ==

\itemize Relation to other methods

\itemize References

\itemize External Links

By connecting all vectors using a Delaunay triangulation criterium it is possible to characterize gradient asymetries computing the so-called \textit{''gradient asymmetry coefficient}'', that has been defined as:

{\bf Calculation}

By connecting all vectors using a Delaunay triangulation criterium it is possible to characterize gradient asymetries computing the so-called \textit{gradient asymmetry coefficient}, that has been defined as:

\begin{equation}

G_A=\frac{|N_C-N_V|}{N_V},

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For a complex extended pattern (matrix of amplitudes of a spatio-temporal pattern) composed by locally asymmetric fluctuations, $

G_{A}$ is nonzero, defining different classes of irregular fluctuation patterns (1/f noise, chaotic, reactive-diffusive, etc).

Besides $G_{A}$ other measurements (called {\it ''gradient moments}'') can be calculated form the gradient lattice \cite{rosa03}. 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).

{\bf Relation to other methods}

When GPA is conjugated with wavelet analysis, then the method is called {\it Gradient Spectral Analysis}, usually applied to short time series analysis \cite{rosa08})

\itemize== Relation to other methods ==

When GPA is conjugated with wavelet analysis, then the method is called {\it ''Gradient Spectral Analysis}'', usually applied to short time series analysis \cite{rosa08})

{\bf References}

\itemize== References ==

\bibitem{rosa99} R. R. Rosa, A. S. Sharma and J. Valdivia, {\em Int. J. Mod. Phys. C \/} {\bf 10}, 147 (1999).

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\bibitem{rosa08} R.R.Rosa et al., {\em Advances in Space Research} {\bf 42}, 844 (2008), doi:10.1016/j.asr.2007.08.015.

{\bf External Links}

\itemize== External Links ==

Lab for Computing and Applied Mathematics

(MATLAB code for Gradient Spectral Analysis).