Gradient pattern analysis

Gradient pattern analysis (GPA) is a geometric computing method for characterizing geometrical bilateral <a href="/facts/Symmetry_breaking/q3yqVlNQ">symmetry breaking</a> of an ensemble of symmetric vectors regularly distributed in a square lattice. Usually, the lattice of vectors represent the first-order <a href="/facts/Gradient/TsR7uukj">gradient</a> of a scalar field, here an M x M square amplitude <a href="/facts/Matrix_(mathematics)/qa8FI4ko">matrix</a>. 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 
 
 
 
 
 N
 
 V
 
 
 =
 
 M
 
 2
 
 
 
 
 {\displaystyle N_{V}=M^{2}}
 
 asymmetric vectors. As each vector can be characterized by its norm and phase, variations in the 
 
 
 
 
 M
 
 2
 
 
 
 
 {\displaystyle M^{2}}
 
 amplitudes can modify the respective 
 
 
 
 
 M
 
 2
 
 
 
 
 {\displaystyle M^{2}}
 
 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.

Gradient pattern analysis open-in-new

Gradient pattern analysis