emd2d {EMD}

Bidimenasional Empirical Mode Decomposition

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)