Two-dimensional structure functions for direction-dependent multiscale analysis of textures.
The nth order structure function of a two-dimensional field can be defined as:
where denotes a spatial position,
and
are the separation distances along each dimension of the field,
is the expected value operator and
is called the increment. So:
-
The variance of the increment is the second order structure function
.
-
The skewness of the increment is the ratio
-
The kurtosis of the increment is
and so on.
A change of coordinates from cartesian to polar allows for analysis with respect to direction: .
This repository contains four main functions contained in the Structure_functions.py file:
- Incrs_anisotropic_generator2d: takes as input a two-dimensional field
and two scales
and
and generates the process
which is the spatial increment of the two-dimensional field.
- compute_moments_2D: computes the
order moment of a given n-dimensional field introduced as input.
- field_2D_polar: returns the cartesian field used as input in polar coordinates.
- polar_axis: returns 2 numpy arrays characterizing the polar coordinates of the output field of the function field_2D_polar
These functions can be combined to perform a multiscale direction-dependent analysis of images based on structure functions, see Script.ipynb.
Carlos Granero-Belinchon, Stephane G. Roux, Nicolas B. Garnier, Pierre Tandeo, Bertrand Chapron and Alexis Mouche, Two-dimensional structure functions to characterize convective rolls in the marine atmospheric boundary layer from Sentinel-1 SAR images, preprint https://hal.archives-ouvertes.fr/hal-03576400
Carlos Granero-Belinchon
Mathematical and Electrical Engineering Department
IMT Atlantique
Brest, France
e: carlos.granero-belinchon [at] imt-atlantique.fr
w: https://cgranerob.github.io/
w: https://www.imt-atlantique.fr/en/person/carlos-granero-belinchon