Description Usage Arguments Details Value See Also Examples
This function performs twodimensional ensemble patch transform of an image for a size parameter.
1 2 3 4 
x, y 
locations of regular grid at which the values in image 
z 
matrix of an image observed at location 
type 
patch type of 
tau 
a size parameter for twodimensional ensemble patch transform: 
theta 
a degree of clockwise rotation of a patch. 
process 
specifies transform types for patch and ensemble processes:

pquantile 
quantiles for lower and upper envelopes of patch transform. When it is 
equantile 
quantiles for lower and upper envelopes of ensemble patch transform. 
gamma 
controls the amount of envelope magnitude. 
boundary 
specifies boundary condition from 
This function performs twodimensional ensemble patch transform of an image for a size parameter tau
, and
produces statistics and envelopes for twodimensional 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
.
x, y 
locations of regular grid at which the values in image 
z 
matrix of an image observed at location 
pstat 
centrality of patch transform for size parameter 
Epstat 
centrality of ensemble patch transform for size parameter 
psd 
standard deviation of patch transform for size parameter 
Epsd 
standard deviation of ensemble patch transform for size parameter 
pL 
lower envelope of patch transform for size parameter 
pU 
upper envelope of patch transform for size parameter 
pM 
mean envelope, 
pR 
distance between lower and upper envelopes, 
EpL 
lower envelope of ensemble patch transform for size parameter 
EpU 
upper envelope of ensemble patch transform for size parameter 
EpM 
mean envelope, 
EpR 
distance between lower and upper envelopes, 
parameters 
a list of input parameters of 
nlevel 
the number of size parameter 
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38  #### 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="highfrequency component")
image(coscomp2, xlab="", ylab="", col=gray(0:100/100), axes=FALSE, main="lowfrequency 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)

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