eptransf2d: 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

x, y

locations of regular grid at which the values in image z are measured. When those are NULL, the image is supposed to be equally spaced.

matrix of an image observed at location (x, y).

type

patch type of "rectangle" or "oval".

tau

a size parameter for two-dimensional ensemble patch transform: tau[1] for horizontal size and tau[2] for vertical size of a two-dimensional patch. When length(tau) is 1, the horizontal and vertical size are the same.

theta

a degree of clockwise rotation of a patch.

process

specifies transform types for patch and ensemble processes: process[1] for patch process and process[2] for ensemble process. Each process has options of "average", "median", or "envelope". Note that when process[1] is "average" or "median", process[2] must be "average" or "median". When process[1] is "envelope", lower and upper envelopes are obtained by \(\code{pquantile[1]} \times 100 \%\)-quantile and \(\code{pquantile[2]} \times 100 \%\)-quantile of patches, respectively. When process[2] is "envelope", ensemble lower and upper envelopes are obtained as \(\code{equantile[1]} \times 100 \%\)-quantile and \(\code{equantile[2]} \times 100 \%\)-quantile of lower and upper envelopes of shifted patches, respectively.

pquantile

quantiles for lower and upper envelopes of patch transform. When it is c(0, 1), minimum and maximum of a patch are used for lower and upper envelopes, respectively.

equantile

quantiles for lower and upper envelopes of ensemble patch transform.

gamma

controls the amount of envelope magnitude.

boundary

specifies boundary condition from "reflexive", "periodic" or "none".

Value

x, y

locations of regular grid at which the values in image z are measured. When it is NULL, the image is supposed to be equally spaced.

matrix of an image observed at location (x, y).

pstat

centrality of patch transform for size parameter tau.

Epstat

centrality of ensemble patch transform for size parameter tau.

psd

standard deviation of patch transform for size parameter tau.

Epsd

standard deviation of ensemble patch transform for size parameter tau.

lower envelope of patch transform for size parameter tau.

upper envelope of patch transform for size parameter tau.

mean envelope, (pL + pU) / 2, of patch transform for size parameter tau.

distance between lower and upper envelopes, (pU - pL), of patch transform for size parameter tau.

EpL

lower envelope of ensemble patch transform for size parameter tau.

EpU

upper envelope of ensemble patch transform for size parameter tau.

EpM

mean envelope, (EpL + EpU) / 2, of ensemble patch transform for size parameter tau.

EpR

distance between lower and upper envelopes, (EpU - EpL), of ensemble patch transform for size parameter tau.

parameters

a list of input parameters of type, tau, theta, process, pquantile, equantile, gamma, and boundary.

nlevel

the number of size parameter tau. For eptransf2d(), nlevel is 1.

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.

Examples

Run this code

# NOT RUN {
#### 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")

# }
# NOT RUN {
#### 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")
# }
# NOT RUN {
par(op)
# }