Gradient Pattern Analysis

Gradient pattern analysis (GPA) is a geometric computing method for characterizing symmetry breaking of an ensemble of asymmetric vectors regularly distributed in a square lattice. Usually, the lattice of vectors represent the first-order gradient of a scalar field, here an M x M square amplitude matrix. An important property of the gradient representation is the following: A given M x M matrix where all amplitudes are different results in an M x M gradient lattice containing asymmetric vectors. As each vector can be characterized by its norm and phase, variations in the amplitudes can modify the respective gradient pattern.

The original concept of GPA was introduced by Rosa, Sharma and Valdivia in 1999. Usually GPA is applied for spatio-temporal pattern analysis in physics and environmental sciences operating on time-series and digital images.

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