# Bidimenasional Empirical Mode Decomposition This function performs the bidimenasional empirical mode decomposition utilizing extrema detection based on the equivalence relation between neighboring pixels. ```r 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. ## Returns - **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 ```r 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) ```

emd2d function