emd2d: Bidimenasional Empirical Mode Decomposition

In EMD: Empirical Mode Decomposition and Hilbert Spectral Analysis

Description

This function performs the bidimenasional empirical mode decomposition utilizing extrema detection based on the equivalence relation between neighboring pixels.

Usage

emd2d(z, x = NULL, y = NULL, tol = sd(c(z)) * 0.1^2, max.sift = 20, 
    boundary = "reflexive", boundperc = 0.3, max.imf = 5, sm = "none", 
    smlevels = 1, spar = NULL, weight = NULL, plot.imf = FALSE) 

Arguments

z	matrix of an image observed at (x, y)
x, y	locations of regular grid at which the values in z are measured
tol	tolerance for stopping rule of sifting
max.sift	the maximum number of sifting
boundary	specifies boundary condition from “none", “symmetric" or “reflexive".
boundperc	expand an image by adding specified percentage of image at the boundary when boundary condition is 'symmetric' or 'reflexive'.
max.imf	the maximum number of IMF's
sm	specifies whether envelop is constructed by interpolation, thin-plate smoothing, Kriging, local polynomial smoothing, or loess. Use “none" for interpolation, “Tps" for thin-plate smoothing, “mKrig" for Kriging, “locfit" for local polynomial smoothing, or “loess" for loess. See Kim et al. (2012) for detalis.
smlevels	specifies which level of the IMF is obtained by smoothing other than interpolation.
spar	specifies user-supplied smoothing parameter of thin-plate smoothing, Kriging, local polynomial smoothing, or loess.
weight	deprecated.
plot.imf	specifies whether each IMF is displayed. If plot.imf=TRUE, click the plotting area to start the next step.

Details

This function performs the bidimenasional empirical mode decomposition utilizing extrema detection based on the equivalence relation between neighboring pixels. See Kim et al. (2012) for detalis.

Value

imf	two dimensional IMF's
residue	residue image after extracting the IMF's
maxindex	index of maxima
minindex	index of minima
nimf	number of IMF's

References

Huang, N. E., Shen, Z., Long, S. R., Wu, M. L. Shih, H. H., Zheng, Q., Yen, N. C., Tung, C. C. and Liu, H. H. (1998) The empirical mode decomposition and Hilbert spectrum for nonlinear and nonstationary time series analysis. Proceedings of the Royal Society London A, 454, 903–995.

Kim, D., Park, M. and Oh, H.-S. (2012) Bidimensional Statistical Empirical Mode Decomposition. IEEE Signal Processing Letters, 19, 191–194, doi: 10.1109/LSP.2012.2186566.

See Also

extrema2dC, extractimf2d.

Examples

data(lena)
z <- lena[seq(1, 512, by=4), seq(1, 512, by=4)]
image(z, main="Lena", xlab="", ylab="", col=gray(0:100/100), axes=FALSE)

## Not run: 
lenadecom <- emd2d(z, max.imf = 4)
imageEMD(z=z, emdz=lenadecom, extrema=TRUE, col=gray(0:100/100))
## End(Not run)

### Test Image
ndata <- 128

x <- y <- seq(0, 9, length=ndata)
meanf1 <- outer(sin(2 * pi * x), sin(2 * pi * y))
meanf2 <- outer(sin(0.5 * pi * x), sin(0.5 * pi * y))
meanf <- meanf1 + meanf2

snr <- 2
set.seed(77)
zn <- meanf + matrix(rnorm(ndata^2, 0, sd(c(meanf))/snr), ncol=ndata)

rangezn <- range(c(meanf1, meanf2, meanf, zn))
par(mfrow=c(2,2), mar=0.1 + c(0, 0.25, 3, 0.25))
image(meanf1, main="high frequency component", xlab="", ylab="", zlim=rangezn, 
    col=gray(100:0/100), axes=FALSE)
image(meanf2, main="low frequency component", xlab="", ylab="", zlim=rangezn, 
    col=gray(100:0/100), axes=FALSE)
image(meanf, main="test image", xlab="", ylab="", zlim=rangezn, col=gray(100:0/100), axes=FALSE)
image(zn, main="noisy image", xlab="", ylab="", zlim=rangezn, col=gray(100:0/100), axes=FALSE)

## Not run: 
out <- emd2d(zn, max.imf=3, sm="locfit", smlevels=1, spar=0.004125)
par(mfcol=c(3,1), mar=0.1 + c(0, 0.25, 0.25, 0.25)) 
image(out$imf[[1]], main="", xlab="", ylab="", col=gray(100:0/100), zlim=rangezn, axes=FALSE)
image(out$imf[[2]], main="", xlab="", ylab="", col=gray(100:0/100), zlim=rangezn, axes=FALSE)
image(out$imf[[3]], main="", xlab="", ylab="", col=gray(100:0/100), zlim=rangezn, axes=FALSE)
## End(Not run)

EMD documentation built on Jan. 4, 2022, 1:08 a.m.