Internal EPT Functions

Description

The chooseindex2d is internal EPT functions.

Details

These are not to be called by the user.

Length of Day Data

Description

The length-of-day was produced by Gross (2001) from 20 January 1962 to 6 January 2001. The length-of-day (LOD) data was analyzed in Huang et al. (2003).

Usage

data(LOD)

Format

A list of LOD, YEAR, MONTH and DATE

References

Gross, R. S. (2001) Combinations of Earth orientation measurements: SPACE2000, COMB2000, and POLE2000. JPL Publication 01-2. Jet Propulsion Laboratory, Pasadena, CA.

Huang, N. E., Wu, M. C., Long, S. R., Shen, S., Qu, W., Gloerson, P. and Fan, K. L. (2003) A confidence limit for the empirical mode decomposition and Hilbert spectral analysis. Proceedings of the Royal Society London A., 459, 2317–2345.

Examples

data(LOD)
names(LOD)

xt <- LOD$LOD[LOD$YEAR >= 1981 & LOD$YEAR <= 2000] # From 1981/1/1 to 2000/12/31
xt <- xt/10^4 # measured in millisecond

# EP transform for LOD
outLOD <- eptransf(signal=xt, tau=15, process=c("envelope", "average"), boundary="none")

# outLOD$EpM : candidate of remaining component 
eptplot(outLOD)

op <- par(mfcol=c(3,1), mar=c(2,2,2,1))
plot(xt, type='l', main="LOD", xlab="", ylab="", ylim=range(xt))
plot(xt - outLOD$EpM, type='l', main="candidate of frequency component 
    with half month period", xlab="", ylab=""); abline(h=0, lty=3)
plot(outLOD$EpM, type='l', main="candidate of remaining component", 
    xlab="", ylab="", ylim=range(xt))


# sifting
LODdecom1 <- eptdecomp(signal=xt, tau=15, process=c("envelope", "average"),  
    boundary="none", tol=sd(xt)*0.1^3, maxiter = 30)

# extraction of frequency component with half month period 
plot(xt, type='l', main="LOD", xlab="", ylab="", ylim=range(xt))
plot(LODdecom1$FC, type='l', main="frequency component 
    with half month period", xlab="", ylab=""); abline(h=0, lty=3)
plot(LODdecom1$residue, type='l', main="remaining component", 
    xlab="", ylab="", ylim=range(xt))

# EP transform for remaining signal from LODdecom1
outLOD2 <- eptransf(signal=LODdecom1$residue, tau=30, process=c("envelope", "average"),
    boundary="none")

# outLOD2$EpM : candidate of remaining component for residue signal from LODdecom1
plot(LODdecom1$residue, type='l', main="remaining component from LODdecom1", 
    xlab="", ylab="", ylim=range(xt))
plot(LODdecom1$residue - outLOD2$EpM, type='l', main="candidate of frequency component
    with one month period", xlab="", ylab=""); abline(h=0, lty=3)
plot(outLOD2$EpM, type='l', main="candidate of remaining component", 
    xlab="", ylab="", ylim=range(xt))

# sifting
LODdecom2 <- eptdecomp(signal=LODdecom1$residue, tau=30, process=c("envelope", "average"),
    boundary="none", tol=sd(xt)*0.1^3, maxiter = 50)

# extraction of frequency component with one month period 
plot(LODdecom1$residue, type='l', main="remaining component from LODdecom1", 
    xlab="", ylab="", ylim=range(xt))
plot(LODdecom2$FC, type='l', main="frequency component with one month period", 
    xlab="", ylab=""); abline(h=0, lty=3)
plot(LODdecom2$residue, type='l', main="remaining component", xlab="", ylab="",
    ylim=range(xt))

### Decomposition Result
ttt <- paste(LOD$YEAR, LOD$MONTH, LOD$DATE, sep="/")
ttt <- ttt[LOD$YEAR >= 1981 & LOD$YEAR <= 2000]
ttt <- as.Date(ttt)

att <- as.Date(c("1981/1/1", "1982/1/1", "1983/1/1", "1984/1/1", "1985/1/1", "1986/1/1",
                 "1987/1/1", "1988/1/1", "1989/1/1", "1990/1/1", "1991/1/1", "1992/1/1", 
                 "1993/1/1", "1994/1/1", "1995/1/1", "1996/1/1", "1997/1/1", "1998/1/1", 
                 "1999/1/1", "2000/1/1", "2001/1/1"))

plot(ttt, xt, type='l', main="LOD", xlab="", ylab="", xaxt = "n")
axis(1, at=att, labels=seq(1981, 2001)) 

plot(ttt, LODdecom1$FC, type="l", main="component with half month period by EPT", 
    xlab="", ylab="", xaxt = "n")
axis(1, at=att, labels=seq(1981, 2001)); abline(h=0, lty=3)

plot(ttt, LODdecom2$FC, type="l", main="component with one month period by EPT", 
    xlab="", ylab="", xaxt = "n")
axis(1, at=att, labels=seq(1981, 2001)); abline(h=0, lty=3)

par(op)

Solar Radiation

Description

The solar radiations were hourly observed at Seoul, Daegu, and Busan in South Korea from September 1, 2003 to September 29, 2003. The data are available from Korea Meteorological Administration (https://data.kma.go.kr). Daegu and Busan, located in the southeast of the Korean Peninsula, are close to each other geographically, whereas Seoul is located in the middle of the Peninsula. In addition, note that Daegu and Busan were severely damaged by a typhoon named “MAEMI" at that time, while Seoul was hardly affected by the typhoon. It is expected that the climatic characteristics of Daegu and Busan are similar, and the pattern of Seoul seems to be different from the other two cities.

Usage

data(SolarRadiation)

Format

A daraframe of Date, Seoul, Daegu and Busan.

Examples

data(SolarRadiation)
names(SolarRadiation)

# ensemble patch transform
SolarRadiationEpU <- SolarRadiationEpL <- NULL

for(j in 1:3) {
    tmp <- eptransf(signal=SolarRadiation[,j+1], tau=24, process=c("envelope", "average"), 
        pquantile=c(0, 1), gamma=0)
    SolarRadiationEpU <- cbind(SolarRadiationEpU, tmp$EpU)
    SolarRadiationEpL <- cbind(SolarRadiationEpL, tmp$EpL)
}

# Correlation of the solar radiations at Seoul, Daegu, and Busan
cor(SolarRadiation[, 2:4])

# Correlation of ensemble average of upper envelope
cor(SolarRadiationEpU)

op <- par(mfrow=c(3,1), mar=c(2,2,2,2))
plot(SolarRadiation[,2], type='l', main="(a) solar-radiation in Seoul and upper envelope",
    ylim=c(0, 3.3), xaxt="n"); axis(1, at=seq(1, 30*24, by=24), labels=seq(1, 30, by=1)) 
lines(SolarRadiationEpU[,1], lty=2); lines(SolarRadiationEpL[,1], lty=2)
plot(SolarRadiation[,3], type='l', main="(b) solar-radiation in Daegu and upper envelope",
    ylim=c(0, 3.3), xaxt="n"); axis(1, at=seq(1, 30*24, by=24), labels=seq(1, 30, by=1)) 
lines(SolarRadiationEpU[,2], lty=2); lines(SolarRadiationEpL[,2], lty=2)
plot(SolarRadiation[,4], type='l', main="(c) solar-radiation in Busan and upper envelope",
    ylim=c(0, 3.3), xaxt="n"); axis(1, at=seq(1, 30*24, by=24), labels=seq(1, 30, by=1)) 
lines(SolarRadiationEpU[,3], lty=2); lines(SolarRadiationEpL[,3], lty=2)
par(op)

Decomposition of a signal by Ensemble Patch Transform

Description

This function decomposes a signal into frequency component and residue of ensemble patch transform by sifting process.

Usage

eptdecomp(tindex = NULL, signal, type = "rectangle", tau, 
    process = c("average", "average"), pquantile = c(0, 1), equantile = c(0, 1), 
    gamma = 1, boundary = "symmetric", stoprule = "type1", 
    tol = sd(signal, na.rm = TRUE) * 0.1^2, maxiter = 10, check = FALSE) 

Arguments

Details

This function decomposes a signal into frequency component and residue of ensemble patch transform by sifting process for a size parameter.

Value

See Also

eptransf, meptransf.

Examples

#### example : composite of two components having different frequencies
ndata <- 1000 
tindex <- seq(0, 1, length=ndata)
comp1 <- cos(90*pi*tindex)
comp2 <- cos(10*pi*tindex)
f <- comp1 + comp2 

op <- par(mfrow=c(3,1), mar=c(2,2,2,1))
plot(tindex, f, main="a signal", xlab="", ylab="", type='l')
abline(h=0, lty=3)
plot(tindex, comp1, main="high-frequency component", xlab="", ylab="", type='l')
abline(h=0, lty=3)
plot(tindex, comp2, main="low-frequency component", xlab="", ylab="", type='l')
abline(h=0, lty=3)

#### Decomposition by Ensemble Patch Transform  
outdecom <- eptdecomp(signal=f, tau=21, process=c("envelope", "average"), pquantile=c(0, 1))

#### Decomposition result
plot(tindex, f, main="a signal", xlab="", ylab="", type='l'); abline(h=0, lty=3)
plot(outdecom$FC, type='l', main="", xlab="", ylab=""); abline(h=0, lty=3)
title(paste0("high-frequency component, tau=", 21))
lines(comp1, col="red", lty=2, lwd=0.5)
plot(outdecom$residue, type="l", main="", xlab="", ylab=""); abline(h=0, lty=3)
title(paste0("low-frequency component, tau=", 21))
lines(comp2, col="red", lty=2, lwd=0.5)
par(op)

Decomposition of an Image by Two-dimensional Ensemble Patch Transform

Description

This function decomposes an image into frequency component and residue of two-dimensional ensemble patch transform by sifting process.

Usage

eptdecomp2d(x = NULL, y = NULL, z, type = "rectangle", tau, theta = 0, 
    process = c("average", "average"), pquantile = c(0, 1), equantile = c(0, 1), 
    gamma = 1, boundary = "reflexive", 
    stoprule = "type2", tol = 0.1^2, maxiter = 10, check = FALSE) 

Arguments

Details

This function decomposes an image into frequency component and residue of two-dimensional ensemble patch transform by sifting process for a size parameter.

Value

See Also

eptransf2d, meptransf2d.

Examples

#### example : composite of two components having different frequencies
nr <- nc <- 128; x <- seq(0, 1, length=nr); y <- seq(0, 1, length=nc)

coscomp1 <- outer(cos(20 * pi * x), cos(20 * pi * y))
coscomp2 <- outer(cos(5* pi * x), cos(5 * pi * y))
cosmeanf <- coscomp1 + coscomp2

op <- par(mfcol=c(3,1), mar=c(0,0.5,2,0.5))
image(cosmeanf, xlab="", ylab="", col=gray(0:100/100), axes=FALSE, main="a composite image")
image(coscomp1, xlab="", ylab="", col=gray(0:100/100), axes=FALSE, main="high-frequency component")
image(coscomp2, xlab="", ylab="", col=gray(0:100/100), axes=FALSE, main="low-frequency component")


#### Decomposition by Ensemble Patch Transform  
outcossift <- eptdecomp2d(z=cosmeanf, tau=8)

#### Decomposition Result
op <- par(mfrow=c(2,2), mar=c(2,2,2,1))
image(outcossift$FC, xlab="", ylab="", col=gray(0:100/100), axes=FALSE, main="Decomposed HF")
persp(outcossift$FC, theta = -30, phi = 45, col = "white", xlab="X", ylab="Y", main="Decomposed HF")
image(outcossift$residue, xlab="", ylab="", col=gray(0:100/100), axes=FALSE, main="Residue")
persp(outcossift$residue, theta = -30, phi = 45, col = "white", xlab="X", ylab="Y", main="Residue")

par(op)

Multiscale Visualization of Ensemble Patch Transform of a Signal

Description

This function displays time-scale representation of ensemble patch transform of a signal for a sequence of size parameters.

Usage

eptmap(eptransf, taus = eptransf$parameters$tau, maptype = c("C", "D", "DC", "DD"), 
    stat = c("pstat", "Epstat", "pM", "EpM", "psd", "Epsd"),
    der = c("time", "tau"), ncolor = 100, ...) 

Arguments

Details

This function performs multiscale visualization of ensemble patch transform of a signal for a sequence of size parameters. This function creates images with heat.colors(ncolor) colors.

Value

image

See Also

eptransf, meptransf, eptplot.

Examples

# a doppler signal
n <- 1000
tindex <- seq(0, 1, length=n)
j <- 5
f <- 10 * sqrt(tindex*(1-tindex)) * sin((2*pi*(1+2^((9-4*j)/5))) / (tindex+2^((9-4*j)/5)))

set.seed(7)
fnoise <- f + 0.4 * rnorm(n)

op <- par(mar=c(2,2,2,1))
plot(f, type="l", , xlab="", ylab="", ylim=range(fnoise))
points(fnoise, cex=0.3)


taus <- seq(4, 64, by=4)

# try1 : Multiscale EPT by average patch transform and average ensemble transform 
try1 <- meptransf(tindex=tindex, signal=fnoise, taus=taus, process=c("average", "average"))

par(mfrow=c(2,2))
eptmap(try1, maptype="C", stat="pstat", main="centrality of patch transform")
eptmap(try1, maptype="D", stat="psd", main="standard deviation of patch transform")
eptmap(try1, maptype="C", stat="Epstat", main="centrality of ensemble patch transform")
eptmap(try1, maptype="D", stat="Epsd", main="standard deviation of ensemble patch transform")

eptmap(try1, maptype="DC", stat="Epstat", der="time", 
    main="derivative of centrality w.r.t time")
eptmap(try1, maptype="DC", stat="Epstat", der="tau", 
    main="derivative of centrality w.r.t tau")
eptmap(try1, maptype="DD", stat="Epsd", der="time", 
    main="derivative of standard deviation w.r.t time")
eptmap(try1, maptype="DD", stat="Epsd", der="tau", 
    main="derivative of standard deviation w.r.t tau", ncolor=70)

# try2 : Multiscale EPT by envelope patch transform and average ensemble transform 
try2 <- meptransf(tindex=tindex, signal=fnoise, taus=taus, process=c("envelope", "average"),
    pquantile=c(0, 1))

eptmap(try2, maptype="C", stat="pM", main="mean envelope of patch transform")
eptmap(try2, maptype="C", stat="EpM", main="mean envelope of ensemble patch transform")
eptmap(try2, maptype="DC", stat="EpM", der="time", 
    main="derivative of mean envelope w.r.t time")
eptmap(try2, maptype="DC", stat="EpM", der="tau", 
    main="derivative of mean envelope w.r.t time")

par(op)

Plot of Components by Ensemble Patch Transform of a Signal

Description

This function plots ensemble patch transform of a signal for a sequence of size parameters tau's.

Usage

eptplot(eptransf, taus = eptransf$parameters$tau)

Arguments

Details

This function plots ensemble patch transform of a signal for a sequence of size parameters taus.

Value

plot

See Also

eptransf, meptransf, eptmap.

Examples

n <- 500                                                                      
set.seed(1)
x <- c(rnorm(n), arima.sim(list(order = c(1,0,0), ar = 0.9), n = n, sd=sqrt(1-0.9^2)))

taus <- seq(10, 100, by=10)

# eptr1 : Multiscale EPT by average patch transform and average ensemble transform 
eptr1 <- meptransf(tindex=1:(2*n), signal=x, taus=taus, process=c("average", "average"), 
    boundary="none")
names(eptr1)

op <- par(mfcol=c(4,1), mar=c(4,2,2,0.1))
plot(x, xlab="", type="l", main="signal")

eptplot(eptr1)
eptplot(eptr1, taus=20)
eptplot(eptr1, taus=c(20, 30))
lines(eptr1$Epstat[, 2], col="blue")
lines(eptr1$Epstat[, 3], col="red")

# eptr2 : Multiscale EPT by envelope patch transform and average ensemble transform 
eptr2 <- meptransf(tindex=1:(2*n), signal=x, type="oval", taus=taus, 
    process=c("envelope", "average"), pquantile=c(0,1), gamma=0.06, boundary="none")
names(eptr2)

plot(x, xlab="", type="l")
eptplot(eptr2)
eptplot(eptr2, taus=20)
eptplot(eptr2, taus=c(20, 30))
lines(eptr2$EpM[, 2], col="blue")
lines(eptr2$EpM[, 3], col="red")
par(op)

Ensemble Patch Transform of a Signal

Description

This function performs ensemble patch transform of a signal for a size parameter.

Usage

eptransf(tindex = NULL, signal, type = "rectangle", tau,
    process = c("average", "average"), pquantile = c(0, 1), equantile = c(0, 1), 
    gamma = 1, boundary = "symmetric") 

Arguments

Details

This function performs ensemble patch transform of a signal for a size parameter tau, and produces statistics and envelopes for ensemble patch transform. When process[1] is "average" or "median", outputs related to envelopes are defined as NULL. When process[2] is "envelope", outputs, pstat and Epstat, are defined as NULL.

Value

See Also

meptransf, eptdecomp.

Examples

# a doppler signal
n <- 256
tindex <- seq(0, 1, length=n)
j <- 5
f <- 10 * sqrt(tindex*(1-tindex)) * sin((2*pi*(1+2^((9-4*j)/5))) / (tindex+2^((9-4*j)/5)))
fnoise <- f + 0.4 * rnorm(n)
  
#### Ensemble statistics
op <- par(mfrow=c(5,3), mar=c(2,2,2,1))
layout(matrix(c(1, 1, 1, 2:13), 5, 3, byrow = TRUE))

plot(f, main="a doppler signal", xlab="", ylab="", type='l', ylim=range(fnoise))
points(fnoise); abline(h=0, lty=3)

#### Ensemble Patch Transform  
taus <- c(5, 10, 20)

out <- list()
for (i in 1:length(taus)) 
    out[[i]] <- eptransf(signal=fnoise, tau=taus[i], process=c("average", "average"))
    
for (i in 1:length(taus)) {
    plot(out[[i]]$Epstat, type="l", xlab="", ylab="",
        main=paste0("ensemble average of patch mean, tau=", taus[i]))
    abline(h=0, lty=3)   
}

for (i in 1:length(taus)) 
    plot(out[[i]]$Epsd, type='l', xlab="", ylab="", 
         main=paste0("ensemble average of standard deviation, tau=", taus[i]))  

out2 <- list()
for (i in 1:length(taus)) 
    out2[[i]] <- eptransf(signal=fnoise, tau=taus[i], process=c("envelope", "average"))
    
for (i in 1:length(taus)) {
    plot(out2[[i]]$EpM, type="l", col="red", xlab="", ylab="", 
         ylim=range(c(out2[[i]]$EpU,out2[[i]]$EpL)),
         main=paste0("ensemble average of mean envelope, tau=", taus[i]))
    points(fnoise, cex=0.1)
    abline(h=0, lty=3); lines(out2[[i]]$EpU); lines(out2[[i]]$EpL)    
}

for (i in 1:length(taus))
    plot(out2[[i]]$EpR, type='l', xlab="", ylab="",
         main=paste0("ensemble average of envelope distance, tau=", taus[i]))
         
par(op)

Two-dimensional Ensemble Patch Transform of an Image

Description

This function performs two-dimensional ensemble patch transform of an image for a size parameter.

Usage

 
eptransf2d(x = NULL, y = NULL, z, type = "rectangle", tau, theta = 0, 
    process = c("average", "average"), pquantile = c(0, 1), equantile = c(0, 1), 
    gamma = 1, boundary = "reflexive") 

Arguments

Details

This function performs two-dimensional ensemble patch transform of an image for a size parameter tau, and produces statistics and envelopes for two-dimensional ensemble patch transform. When process[1] is "average" or "median", outputs related to envelopes are defined as NULL. When process[2] is "envelope", outputs, pstat and Epstat, are defined as NULL.

Value

See Also

meptransf2d, eptdecomp2d.

Examples

#### example : composite of two components having different frequencies
nr <- nc <- 128; x <- seq(0, 1, length=nr); y <- seq(0, 1, length=nc)

coscomp1 <- outer(cos(20 * pi * x), cos(20 * pi * y))
coscomp2 <- outer(cos(5* pi * x), cos(5 * pi * y))
cosmeanf <- coscomp1 + coscomp2

op <- par(mfcol=c(3,1), mar=c(0,0.5,2,0.5))
image(cosmeanf, xlab="", ylab="", col=gray(0:100/100), axes=FALSE, main="a composite image")
image(coscomp1, xlab="", ylab="", col=gray(0:100/100), axes=FALSE, main="high-frequency component")
image(coscomp2, xlab="", ylab="", col=gray(0:100/100), axes=FALSE, main="low-frequency component")


#### Ensemble average of Ensemble Patch Transform
outcos <- eptransf2d(z=cosmeanf, tau=12)
rangez <- range(cosmeanf) 

par(mfrow=c(3,1), mar=c(2,2,2,1))
image(outcos$Epstat, xlab="", ylab="", col=gray(0:100/100), axes=FALSE, zlim=rangez, 
      main="ensemble average of patch mean")
persp(outcos$Epstat, theta = -30, phi = 45, col = "white", xlab="X", ylab="Y", 
      main="ensemble average of patch mean")
image(outcos$Epsd, xlab="", ylab="", col=gray(0:100/100), axes=FALSE, 
      main="ensemble average of standard deviation")

#### Ensemble Envelope of Ensemble Patch Transform
outcos2 <- eptransf2d(z=cosmeanf, tau=12, process = c("envelope", "average"))
par(mfrow=c(2,2), mar=c(2,2,2,1))
image(outcos2$EpL, xlab="", ylab="", col=gray(0:100/100), axes=FALSE, 
      main="ensemble average of lower envelope")
image(outcos2$EpU, xlab="", ylab="", col=gray(0:100/100), axes=FALSE, 
      main="ensemble average of upper envelope")
image(outcos2$EpM, xlab="", ylab="", col=gray(0:100/100), axes=FALSE, 
      main="ensemble average of mean envelope")
image(outcos2$Epsd, xlab="", ylab="", col=gray(0:100/100), axes=FALSE, 
      main="ensemble average of standard deviation")

par(op)

Finding Local Extrema and Zero-crossings of a Signal

Description

This function identifies local extrema and zero-crossings of a signal.

Usage

localextrema(y)

Arguments

Details

This function identifies local extrema and zero-crossings of a signal.

Value

See Also

eptransf, eptdecomp.

Examples

y <- c(0, 1, 2, 1, -1, 1:4, 5, 6, 0, -4, -6, -5:5, -2:2)
#y <- c(0, 0, 0, 1, -1, 1:4, 4, 4, 0, 0, 0, -5:5, -2:2, 2, 2)
#y <- c(0, 0, 0, 1, -1, 1:4, 4, 4, 0, 0, 0, -5:5, -2:2, 0, 0)

plot(y, type = "b"); abline(h = 0)
localextrema(y)

findextrema <- localextrema(y)
points(findextrema$maxindex, y[findextrema$maxindex], pch=16, col="red")
points(findextrema$minindex, y[findextrema$minindex], pch=16, col="blue")

Multiscale Ensemble Patch Transforms of a Signal

Description

This function performs multiscale ensemble patch transforms of a signal for a sequence of size parameters.

Usage

meptransf(tindex = NULL, signal, type = "rectangle", taus, 
    process = c("average", "average"), pquantile = c(0, 1), equantile = c(0, 1), 
    gamma = 1, boundary = "symmetric") 

Arguments

Details

This function performs multiscale ensemble patch transforms of a signal for a sequence of size parameters taus, and produces statistics and envelopes for ensemble patch transform. When process[1] is "average" or "median", outputs related to envelopes are defined as NULL. When process[2] is "envelope", outputs, pstat and Epstat, are defined as NULL.

Value

See Also

eptransf, eptdecomp.

Examples

#### example : composite of two components having different frequencies
ndata <- 1000 
tindex <- seq(0, 1, length=ndata)
comp1 <- cos(45*pi*tindex)
comp2 <- cos(6*pi*tindex)
f <- comp1 + comp2 

op <- par(mfcol=c(3,1), mar=c(2,2,2,1))
plot(tindex, f, main="a signal", xlab="", ylab="", type='l')
abline(h=0, lty=3)
plot(tindex, comp1, main="high-frequency component", xlab="", ylab="", type='l')
abline(h=0, lty=3)
plot(tindex, comp2, main="low-frequency component", xlab="", ylab="", type='l')
abline(h=0, lty=3)


#### Multiscale Ensemble Patch Transform according to tau's 
taus1 <- seq(20, 60, by=2)
outmulti <- meptransf(signal=f, taus=taus1, process=c("envelope", "average"),
    pquantile=c(0, 1)) 

#### To continue, click the plot in case of "locator(1)".
par(mfrow=c(2,2), mar=c(2,2,2,1))
for (i in 1:length(taus1)) {
  plot(f - outmulti$EpM[,i], type='l', main="", xlab="", ylab=""); abline(h=0, lty=3)
  title(paste0("Remaining component for tau=", taus1[i]))
  lines(comp1, col="red", lty=2, lwd=0.5)
  plot(outmulti$EpM[,i], type="l", main=, xlab="", ylab=""); abline(h=0, lty=3)
  title(paste0("Mean envelope of ensemble patch transform for tau=", taus1[i]))
  lines(comp2, col="red", lty=2, lwd=0.5); locator(1)  
}

par(op)

Multiscale Two-dimensional Ensemble Patch Transforms of an Image

Description

This function performs multiscale two-dimensional ensemble patch transforms of an image for a sequence of size parameters.

Usage

meptransf2d(x = NULL, y = NULL, z, type = "rectangle", taus, theta = 0, 
    process = c("average", "average"), pquantile = c(0, 1), equantile = c(0, 1),
    gamma = 1, boundary = "reflexive") 

Arguments

Details

This function performs multiscale two-dimensional ensemble patch transforms of an image for a sequence of size parameters taus, and produces statistics and envelopes for two-dimensional ensemble patch transform. When process[1] is "average" or "median", outputs related to envelopes are defined as NULL. When process[2] is "envelope", outputs, pstat and Epstat, are defined as NULL.

Value

See Also

eptransf2d, eptdecomp2d.

Examples

#### example : composite of two components having different frequencies
nr <- nc <- 128; x <- seq(0, 1, length=nr); y <- seq(0, 1, length=nc)

coscomp1 <- outer(cos(20 * pi * x), cos(20 * pi * y))
coscomp2 <- outer(cos(5* pi * x), cos(5 * pi * y))
cosmeanf <- coscomp1 + coscomp2

op <- par(mfcol=c(3,1), mar=c(0,0.5,2,0.5))
image(cosmeanf, xlab="", ylab="", col=gray(0:100/100), axes=FALSE, main="a composite image")
image(coscomp1, xlab="", ylab="", col=gray(0:100/100), axes=FALSE, main="high-frequency component")
image(coscomp2, xlab="", ylab="", col=gray(0:100/100), axes=FALSE, main="low-frequency component")


#### Multiscale Ensemble Patch Transform according to tau's 
taus1 <- seq(6, 12, by=2)
outcosmulti <- meptransf2d(z=cosmeanf, taus=taus1)

par(mfrow=c(length(taus1), 2), mar=c(2,2,2,1))
for (i in 1:length(taus1)) {
    estlowfreq <- outcosmulti$Epstat[[i]]
    image(estlowfreq, xlab="", ylab="", col=gray(0:100/100), axes=FALSE, 
        main=paste0("ensemble average of patch mean, tau=", taus1[i]))
    persp(estlowfreq, theta = -30, phi = 45, col = "white", xlab="X", ylab="Y", 
        main=paste0("ensemble average of patch mean, tau=", taus1[i]))
}

par(op)