Stationarity testing for locally stationary wavelet fields

Description

This package contains functions for testing for stationarity within images, specifically locally stationary wavelet (LS2W) fields. In addition the package contains functions for implementing quadtree image decompositions, as well as code for simulating LS2W processes for a given spectral structure.

Author(s)

Sarah L. Taylor and Matt Nunes

Maintainer: Matthew Nunes <nunesrpackages@gmail.com>

References

For details on testing LS2W fields for stationarity, see

Taylor, S.L., Eckley, I.A., and Nunes, M.A. (2014) A Test of Stationarity for Textured Images. Technometrics, 56 (3), 291-301.

For further information on LS2W processes, see

Eckley, I.A., Nason, G.P., and Treloar, R.L. (2010) Locally stationary wavelet fields with application to the modelling and analysis of image texture Journal of the Royal Statistical Society Series C, 59, 595-616.

Perform bootstrap stationarity test for images.

Description

For a given image this function performs bootstrapping to test the hypothesis that the image is stationary.

Usage

TOS2D(image, detrend = FALSE, nsamples = 100, theTS = avespecvar, verbose = TRUE,...)

Arguments

Details

This function first of all crops the image (if necessary) to have dyadic dimensions. The test statistic (theTS), which should be based upon the local wavelet spectrum, is calculated for this original image and the local wavelet spectrum under the null hypothesis is calculated, so as to be able to simulate realisations under the null hypothesis. nsamples images are simulated and test statistic is found for each. The function returns all the test statistic values which may be passed to getpval in order to find a p-value for the test. For full details on this testing procedure see Taylor et al. (2014).

Value

A list with the following components:

Author(s)

Sarah L. Taylor

References

Taylor, S.L., Eckley, I.A., and Nunes, M.A. (2014) A Test of Stationarity for Textured Images. Technometrics, 56 (3), 291-301.

See Also

avespecvar, getpval

Examples

# Generate a stationary image
# 
testimage <- matrix(rnorm(64*64), nrow=64, ncol=64)
#
#Run test of stationarity

## Not run: TestofStat<-TOS2D(testimage)

A test statistic for spatial stationarity.

Description

Calculates a test statistic for a test of stationarity based on the local wavelet spectrum.

Usage

avespecvar(spectrum)

Arguments

Details

The test statistic given by Taylor et al. (2014) for a test for stationarity is computed for use in the boostrap testing procedure (TOS2D).

Value

Author(s)

Sarah L. Taylor

References

Taylor, S.L., Eckley, I.A., and Nunes, M.A. (2014) A Test of Stationarity for Textured Images. Technometrics, 56 (3), 291-301.

See Also

TOS2D

Examples

#Generate a cddews object
#
X <- Haar2MA.diag(64)

testspec<-cddews(X,smooth=FALSE)

#Find the value of the test statistic
#
avespecvar(testspec)
#

Assesses whether two textured images are the same texture.

Description

The function combines two images together, and then tests the montage for stationarity.

Usage

compareImages(Im1, Im2, testsize = min(nrow(Im1), nrow(Im2)), alpha=0.05,...)

Arguments

Details

An image montage of two images is created, and the homogeneity measure TOS2D is used in combination with getpval to assess stationarity of the montage. If the image is assessed as stationary, the two images are considered as the same texture.

Value

Author(s)

Sarah L. Taylor and Matt Nunes

References

Taylor, S.L., Eckley, I.A., and Nunes, M.A. (2014) A Test of Stationarity for Textured Images. Technometrics, 56 (3), 291-301.

See Also

TOS2D, countTextures

Examples

# create two images to be compared:
X1<-simTexture(32,K=1,imtype="S1")[[1]]
X2<-simTexture(32,K=1,imtype="S1", sd=1.6)[[1]]
                             
# use the test to compare them:

test<-compareImages(X1,X2,nsamples=100, smooth=FALSE)

countTextures

Description

Groups a list of (stationary) images into texture classes.

Usage

	countTextures(Imgs, medpol = TRUE, ...)

Arguments

Details

The procedure recursively uses the function compareImages to decide whether two images are of the same texture or not. More specifically, the first image is sequentially tested with all others in the list, assigning the images the label "1" if assessed as the same texture as the first image. All other (unclassified) images are then similarly compared with candidates from different texture classes, until all images have been assigned a group label. Testing recursively in this way, there are at most choose(length(Imgs),2) comparisons performed, but in reality the number could be a lot fewer.

Value

Author(s)

Sarah L. Taylor and Matt Nunes

References

Taylor, S.L., Eckley, I.A., and Nunes, M.A. (2014) A Test of Stationarity for Textured Images. Technometrics, 56 (3), 291-301.

See Also

compareImages

Examples

## Not run: 
 X1<-simTexture(128,K=1,imtype="S1")[[1]]
 X2<-simTexture(128,K=1,imtype="S1")[[1]]
 X3<-simTexture(128,K=1,imtype="S1",sd=1.6)[[1]]

 Xlist<-list(X1,X2,X3)

 Xlist.class<-countTextures(Xlist, bs=100)

## End(Not run)

Crops a rectangular image to a specified (square) dimension

Description

If the input image is not of dimension 2^n \times 2^n, for some n, then the image is cropped to an optionally specified size.

Usage

cropimage(image, newsize = NULL, pos = "e")

Arguments

Details

As we often wish to work with images whose dimensions are some power of 2, this function will determine whether the image is of an appropriate size and if not it will crop the image so that it is. The optional pos argument specifies the position of the cropped subimage to be returned; for example pos="e" specifies the central region. See mix2images for more details on the positioning argument.

Value

Author(s)

Matt Nunes

See Also

mix2images

Examples

#
#Create an image with dimensions not a power of two
#
testimage <- matrix(rnorm(300^2),nrow=300,ncol=300)
#
#Crop the image
#
Newimage <- cropimage(testimage)
#
# Check new dimension size.
#
dim(Newimage)
#        

Computes a p-value for the output of the test for stationarity.

Description

Computes and returns a p-value from the output of the bootstrap test for stationarity.

Usage

getpval(statvec, verbose = TRUE)

Arguments

Value

Author(s)

Sarah L. Taylor

References

Taylor, S.L., Eckley, I.A., and Nunes, M.A. (2014) A Test of Stationarity for Textured Images. Technometrics, 56 (3), 291-301.

See Also

TOS2D

Examples

#Generate a stationary image

testimage <- matrix(rnorm(64*64), nrow=64, ncol=64)

# Run test of stationarity

## Not run: TestofStat<-TOS2D(testimage)

# Obtain p-value

getpval(TestofStat$samples)

## End(Not run)

Performs an image quadtree decomposition.

Description

The quadtree decomposition is achieved by recursively splitting subimages into regions of stationarity.

Usage

imageQT(image, test = TOS2D, minsize = 64,alpha=0.05, ...)

Arguments

Details

This function works by assessing an image for homogeneity. If it is not homogeneous, the image is split into its four subquadrants. Each of these is then tested for homogeneity. The heterogeneous subimages are then again subdivided and tested again. This procedure is repeated until either all subimages are deemed stationary or the minimum testing size minsize is reached.

Value

An object of class imageQT with the following components:

Author(s)

Sarah L. Taylor and Matt Nunes

References

Sonka, M., Boyle, R., and Hlavic, V. (1999) Image processing, analysis and machine vision. 2nd Edition, PWS Publishing.
Taylor, S.L., Eckley, I.A., and Nunes, M.A. (2014) A Test of Stationarity for Textured Images. Technometrics, 56 (3), 291-301.

See Also

plot.imageQT, TOS2D

Examples

# generate an image:
X<-simTexture(128,K=1,imtype="NS1", sd = 3)[[1]]

## Not run: XQT<-imageQT(X,binfun=TOS2D.bin)

A linear function between two constant values.

Description

A function with which to generate nonstationary covariance structure.

Usage

lincurve(x, start = 1, end = 2, a = 0.25)

Arguments

Value

Author(s)

Matt Nunes

See Also

scurve, simTexture

Examples

x<-seq(0,1,length=128)

y<-lincurve(x,start=1,end=2,a=.25)

plot(x,y,type="l")

Insert one image into another.

Description

Image A is re-sized to a specified proportion of Image B, then inserted into Image B at a given position.

Usage

mix2images(imageA, imageB, prop = 0.25, pos = "e")

Arguments

Details

This function first of all crops Image A to be a given proportion of Image B and then inserts it into image B at the specified location. If image B is too small for the size of image A required then the whole of image A is placed in image B. Both must be dyadic in length and square images.

Value

Author(s)

Sarah L. Taylor

References

Taylor, S.L., Eckley, I.A., and Nunes, M.A. (2014) A Test of Stationarity for Textured Images. Technometrics, 56 (3), 291-301.

Examples

# Generate 2 images.
#
ImageA <- matrix(rnorm(256^2), nrow=256, ncol=256)
ImageB <- matrix(rnorm(256^2, sd=2.8), nrow=256, ncol=256)
#
# Insert Image A into Image B at a proportion of 0.25
#
MixImaImb <- mix2images(ImageA, ImageB, prop=0.25, pos="e")
#

A plot function for quadtree decompositions.

Description

A plot function for quadtree decompositions.

Usage

## S3 method for class 'imageQT'
plot(x, cires, unclassval = 0, class = FALSE, QT = TRUE, 
		return = FALSE, qtl = 1, ...)

Arguments

Details

The function plots the chosen quadtree decomposition, and optionally the textured region classification output from countTextures. If the classification output is plotted (class=TRUE), each textured region is uniquely coloured according to its texture group.

Value

Author(s)

Sarah L. Taylor and Matt Nunes

See Also

imageQT, countTextures

Examples

## Not run: 

X<-simTexture(256,K=1,imtype="NS2")[[1]]

XQT<-imageQT(X, bs=100, smooth=FALSE)

XCI <- Tex(XQT$imS, bs=100, smooth=FALSE)

plot(XQT, XCI, QT=T, class=T)

## End(Not run)

Image manipulation

Description

A function which rearranges image content for nice plotting.

Usage

plotmtx(m)

Arguments

Details

Due to the input and plotting output of the R base function image, this function reorders the pixels within an image such that, when used, the image function produces a plot of a image (matrix) "as is".

Value

Author(s)

Matt Nunes

See Also

image

Examples

Im<-simTexture(n=256,type="NS4",K=1)[[1]]

image(plotmtx(Im))

Print out information about a TOS2D object in readable form.

Description

This function prints out information about a TOS2D object in a nice human-readable form.

Usage

## S3 method for class 'TOS2D'
print(x, ...)
## S3 method for class 'TOS2D'
summary(object, ...)

Arguments

Author(s)

Matt Nunes

See Also

TOS2D

Examples

## Not run: 
#
# Generate a TOS2D object for a HaarMontage realisation 
#
X<-simTexture(n=256,K=1,imtype="S1")[[1]]

Xres <- TOS2D(X)

summary(Xres)

## End(Not run)

Print out information about a imageQT object in readable form.

Description

This function prints out information about a imageQT object in a nice human-readable form.

Usage

## S3 method for class 'imageQT'
print(x, ...)

Arguments

Author(s)

Matt Nunes

See Also

imageQT

Examples

## Not run: 
#
# Generate a imageQT object for a HaarMontage realisation 
#
X<-simTexture(n=256,K=1,imtype="S1")[[1]]

Xres <- imageQT(X)

print(Xres)

## End(Not run)

An S curve function between two constant values.

Description

A function with which to generate nonstationary covariance structure.

Usage

scurve(x, a = 1, start = 1, end = 2)

Arguments

Value

Author(s)

Matt Nunes

See Also

lincurve, simTexture

Examples

x<-seq(0,1,length=100)

y<-scurve(x,.4,1,2)

plot(x,y,type="l")

simTextureulation function for LS2W processes.

Description

This function will generate images of a specified type

Usage

simTexture(n = 256, sd = 1, K = 150, imtype = "S1", ...)

Arguments

Details

Several different processes can be generated with the simTexture function. The stationary processes are: a random normal process of specified standard deviation, sd (S1); a spatial moving average process with parameter rho (S2); an isotropic random field with a Matern covariance with shape parameter nu (S3) and a diagonal Haar moving average process of a specified order order and standard deviation sd (S4) (see the Haar2MA.diag function in the LS2W package for more details).
The nonstationary processes are: a random field with unit standard deviation on the first half-plane, concatenated with a random normal half-plane of standard deviation sd (NS1); a white noise half-plane concatenated with a Matern stationary process (NS2); a Haar Montage of specified standard deviation sd (NS3) (see the LS2W HaarMontage function for more details); a process with a slowly-varying covariance structure (NS4); a white noise process with a central subregion of random Normal deviates with non-unit standard deviation sd (NS5); a white noise process with a subregion of random Normal deviates with non-unit standard deviation in the middle section of the top left quadrant sd (NS6); the final process is similar to NS5, except that there is an additional texture in a subregion of the image. In other words, the image is a montage of three two-dimensional Normal processes with differing standard deviations. The base texture is again of unit variance, whereas the other two textures have standard deviations sd and sd2 (NS7).

The other optional arguments for simTexture are as follows:
type - the type of neighbourhood dependence for the random field, either "queen" or "rook" (see the cell2nb function documentation in the spdep package for more details).
rho - moving average parameter for the process S2.
nu - shape parameter for the Matern covariance for process S3.
order - Haar moving average order for S4.
fn - scurve or lincurve for NS4.
start - start value for NS4 (passed into scurve or lincurve).
end - end value for NS4 (passed into scurve or lincurve).
a - "gradient" for NS4 (passed into scurve or lincurve).
prop - proportion of inserted subimage for NS5, NS6 and the first subimage (NS7).
sd2 - standard deviation of second inserted subimage for NS7.
prop2 - proportion of second inserted subimage for NS7.
pos1 - position of first inserted subimage for NS7.
pos2 - position of second inserted subimage for NS7.

Value

Warning

Generating lots of images of high dimension may take a long time!
Note that as of version 2.1-4 (2022-05-09), textures S3 and NS2 have been temporarily removed (commented out) from the functionality of this function, due to a broken package (RandomFields).

Author(s)

Sarah L. Taylor and Matt Nunes

References

Matern, B. (1960) Spatial variation. Stochastic models and their application to some problems in forest surveys and other sampling investigations Meddleanden fran statens Skogsforskningsinstitut 49 (5).
Eckley, I.A., Nason, G.P., and Treloar, R.L. (2010) Locally stationary wavelet fields with application to the modelling and analysis of image texture Journal of the Royal Statistical Society Series C, 59, 595-616.
Taylor, S.L., Eckley, I.A., and Nunes, M.A. (2014) A Test of Stationarity for Textured Images. Technometrics, 56 (3), 291-301.

See Also

HaarMontage

Examples

X1 <- simTexture(128,K=1,imtype="S4",order=3)
X2 <- simTexture(128,K=1,imtype="NS4",fn=lincurve,a=.25,start=1,end=2)
X3 <- simTexture(128,K=1,imtype="NS5",sd=1.6,prop=.25)
X4 <- simTexture(128,K=1,imtype="NS7",sd=1.6,prop=.25,sd2=2.8, prop2=0.25, 
pos1=c(10,10),pos2="e")
        
# try plotting the images:

## Not run: image(plotmtx(X1[[1]]))