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Contents.m
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% Multifractal analysis
%
% license: European Union Public License
%
% Main functions :
% reduced_msm - Compute the MSM and the chromatically reduced image of a greyscale image.
% unitary - Compute the MSM and the chromatically reduced image of an image with a naive
% unitary gradient instead of the true one.
% source - Compute the source of an image, starting from the estimation of the MSM and
% of the derivatives of the reconstructed image.
% reconstruction - Compute the reconstruction of an image.
%
% Analysis and reconstruction with the micro-wavelet:
% fourier_cross - Cross Fourier Transform or Inverse Cross Fourier Transform with a micro-wavelet.
% init_cross - Initialise the micro-wavelet for analysis-reconstruction.
% convolution_cross - Convolution with the micro-wavelet.
% propagation - Reconstruction of a signal suing the essential density and the universal propagator.
% propagation_cross - Reconstruction of a local patch with the micro-wavelet.
% derive_spectral - Compute derivatives of an image by considering the frequency domain and by use of
% the micro-wavelet.
% derive_msm - Transform the Hausdorff measure of the MSM in the frequency space.
% derive_msm_unitary - Compute the reduced_from_msm unitary essential vectorial field.
% mask_gradient - Apply the mask of MSM on the gradient images.
% mask_gradient_msm - Compute an orientated MSM (or not, depending on the orientation of the gradient
% over MSM) and an orientated gradient vectors.
% filter_spectral - Transformation in the frequency domain: computes the value of a matrice after
% having processed a scalar product with the norm of the frequency vector in the
% frequency domain.
%
% Estimation of the singularity exponents and the MSM:
% msm - Compute the MSM.
% upm - Compute the MSM and the density of the MSM in the image according to some
% adjusting parameters.
% distribution_UPM - Compute the values and the distribution of singularity exponents.
% quantile_threshold - Compute the adaptative threshold giving the value of the singularity exponents of
% the pixels of the MSM, according to the desired density.
% msm_from_sing - Compute the MSM and its density according to the distribution of the singularity
% exponents.
%
% Computation of unitary and essential gradients:
% dummy - Compute the reconstruction of the image starting from the reduced_from_msm unitary
% essential vectorial field.
% reduced_unitary - Compute the chromatically reduced_from_msm image reconstructed using an unitary
% gradient instead of the original one.
% gradient_essential - Compute the essential gradient field
% given the chromatically reduced_from_msm image.
%
% Extraction and representation of the source:
% represent_source - Represent the vectorial field of source by its norm and its orientation.
% source_angle - Compute the orientation of a vectorial field. Used for the representation of
% the source.
% source_norm - Compute the norm of a vectorial field (eventually log-representation).
%
% Routines :
% duplicate - Duplicate the image edges so that it is periodic in both directions.
% bits - Return the nearest upper powers of 2.
% clique - Extract a patch from an image.
% psnr - Compute the PSNR ratio between an image and its approximation.
% vec_normalise - Normalise an image by its module (pixel by pixel).
% vec_divide - Compute the complex division of two vectorial fields in the complex domain.
% vec_multiply - Compute the complex multiplication of two vectorial fields in the complex domain.
%
% Exemple of use : launch :
% 1) reduced_msm or unitary
% 2) source
% 3) reconstruction