leader: Calculating the wavelet leaders decomposition of a square matrix

Description

This function calculates the wavelet decomposition leaders of a square matrix . Concretely , the output function returns a 'Leader' class object that allows calculations hmin , c1 and c2 . These indicators can then be used to discriminate, classify, study the image.

Usage

leader(image, wf="d6",frac = 0, full = T, energy=F)

Arguments

image

a square matrix representing the image in gray level to analyze

name of the wavelet filter to use in the decomposition. By default, "d6" is used . "d6" has 3 vanishing moments which implies that it is orthogonal to polynomials of degree 2. Only "d4", "d6" and "d8" are available.

frac

Index of fractional integration

full

boolean indicating whether the analysis is complete , or if it is limited to the wavelet decomposition. The full analysis (TRUE) enables the estimation of hmin , c1 and c2. The limited analysis (FALSE ) estimates hmin and determines the index of fractional integration.

energy

boolean indicating whether the indicators t1 and t2 are calculated. t1 is the logarithm of the sum of wavelet coefficients, t2 is the logarithm of the sum of wavelet coefficients. t2 is related to energy.

Value

dwtn: The wavelet decomposition . This decomposition preserves only the maximum absolute value for the detailed breakdown HL , LH and HH for each pixel
leader: wavelet leaders decomposition
J: The number of scale of the wavelet decomposition. This number is equal to the number of significant scales.
frac: Index of fractional integration
full: boolean indicating whether the analysis is complete or limited
full: boolean indicating whether the analysis is complete or limited
df.mf: Data frame containing the indicators by scales of analysis allowing calculation of hmin , c1 and c2

References

Herwig Wendt, Stephane Roux, Stephane Jaffard, Patrice Abry. Wavelet leaders and bootstrap for multifractal analysis of images. Signal Processing, Elsevier, 2009, 6 (89), pp.1100-1114.

Examples

Run this code

library(wmlf)
data(bocage)
l_b=leader(bocage,full=FALSE)
plotfit(l_b) 

l_b=leader(bocage,frac=1,full=TRUE)
plotfit(l_b)
fit(l_b,2:5)