D2autoplot {LS2W}

Plots a two-dimensional autocorrelation wavelet.

Description

Plots a 2-D autocorrelation wavelet for a given wavelet ata specific scale and decomposition direction.

Usage

D2autoplot(J, filter.number = 1, family = "DaubExPhase", direction = 3,
main = "2-D Autocorrelation Wavelet", OPLENGTH = 10000, scaling = "other", box="TRUE")

Arguments

J

A negative integer representing the order of the autocorrelation wavelet to be displayed.

filter.number

The index of the wavelet to be used.

family

The wavelet family employed.

direction

This variable dictates which of the three possible wavelets at a given level is being displayed. Recall from the work of Daubechies, that one way of constructing 2-D wavelets results in three wavelets. One corresponds to the vertical components of an image, another refers to the horizontal components whilst the final wavelet deals with the diagonal. Thus, keeping this construction in mind, it is easy to see that there are three autocorrelation wavelets when we are in two dimensions. This argument simply allows the user to specify which decomposition direction is to be displayed. Direction 1 corresponds to the Vertical direction, Direction 2 to the Horizontal direction whilst specifying direction=3 means that we wish the Diagonal ACW to be displayed.

main

Allows the user to specify a common title for each of the various spectral plots generated

OPLENGTH

This integer variable defines some workspace of length OPLENGTH which is used by the code. If the workspace is not long enough, then the routine will stop and tell you what OPLENGTH should be set to.

scaling

Allows the user to scale the x and y-axes (of minimal use!). There are currently two options. The first is Haar, which scales the x and y axes so that their entries are those of the actual Haar 2-D ACW. The second is other - which basically allows S-plus to do its ow

box

Allows the user to specify whether the resulting plotted is boxed.

Value

None.

Side Effects

Produces an image corresponding to the 2-D discrete autocorrelation wavelet of a given wavelet at a specific scale and decomposition direction.

Author(s)

Idris Eckley

References

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.

Eckley, I.A. and Nason, G.P. (2011). LS2W: Implementing the Locally Stationary 2D Wavelet Process Approach in R, Journal of Statistical Software, 43(3), 1-23. URL http://www.jstatsoft.org/v43/i03/.

Examples

#
# To produce the Haar 2-D discrete autocorrelation wavelet at level -6 
# in the diagonal horizontal direction type
#
 D2ACW(J=-6, filter.number=1, family="DaubExPhase")
#
#Now let's look at the actual autocorrelation wavelet at that level
#

 D2autoplot(J=-6, filter.number=1, family="DaubExPhase", scaling="Haar")