  Complexity measures are essential to understand complex systems and there are
numerous definitions to analyze one-dimensional data. However, extensions of
these approaches to two or higher-dimensional data, such as images, are much
less common. Here, we reduce this gap by applying the ideas of the permutation
entropy combined with a relative entropic index. We build up a numerical
procedure that can be easily implemented to evaluate the complexity of two or
higher-dimensional patterns. We work out this method in different scenarios
where numerical experiments and empirical data were taken into account.
Specifically, we have applied the method to i) fractal landscapes generated
numerically where we compare our measures with the Hurst exponent; ii) liquid
crystal textures where nematic-isotropic-nematic phase transitions were
properly identified; iii) 12 characteristic textures of liquid crystals where
the different values show that the method can distinguish different phases; iv)
and Ising surfaces where our method identified the critical temperature and
also proved to be stable.
