Generalized Two Dimensional Brushlet Packet Transform

DESCRIPTION:

Computes a generalized two dimensional bruhslet packet transform. This function is defunct.

USAGE:

gbpt.2d(x, partition, taper = "poly2", n.taper=8, boundary="zero")
igbpt.2d(x)

REQUIRED ARGUMENTS:

x
an image or a matrix or, for igbpt.2d only, an object of class gbpt.2d.
partition
a list or a vector specifying the partition of the input x. The bruhslet packets are computed for each specified partition. If a vector is specified, the same parition is useed for x and y cordinates; if a list is specified, the first vector in the list is used as the x partition and the second vector used as a y-partition. The end of points of each partition vector are 0 and nrow(x) and 0 and ncol(x) and need not be specified. See below for details.

OPTIONAL ARGUMENTS:

taper
a character string, indicating the taper function: "boxcar", "poly1", "poly2", "poly3", "poly4", "poly5", or "trig". See the function bp.table for details.
n.taper
a non-negative integer. The length of the taper will be 2*n.taper.
boundary
a character string, available boundary rules: "reflect", "periodic" and "zero". See the function bp.table for details.

VALUE:

an object of class gbpt.2d.

DETAILS:

This algorithm is a generalized version of the Bruhslet Packet Transform (See bpt ). Whereas in bpt.2d the only kinds of partitions that can be defined are dyadic partitions (partitions corresponding to powers of 2), in this function any kind of partition (not neccesarily dyadic) can be defined. In case the partitions are dyadic, the resulting transform will be identical to the Bruhslet Packet Transform. The algorithms for the taper functions are given in the S+WAVELETS User's Manual, in the section "Cosine Packet Algorithms". They are discussed in greater depth in Wickerhauser (1994). The default optional arguments taper, boundary can be reset using function wavelet.options, see wavelet.options for details.

REFERENCES:

Meyer, F.G. and Coifman, R.R. (1997), Brushlets: A tool for directional image analysis and image compression Applied and Computational Harmonic Analysis, Academic Press Publishers.

Wickerhauser, M. V. (1994). Adapted Wavelet Analysis from Theory to Software. A. K. Peters Ltd, Wellesley, MA.

SEE ALSO:

EXAMPLES:

## compute the generalized bruhslet packet transform for a dyadic partition

brain.gbpt <- gbpt.2d(brain, partition=c(256, 512, 768), n.taper=8)

## the above transform is the same as obtained by the following bpt.2d function

brain.bpt  <- bpt.2d(brain, n.levels=2, n.taper=8, dct.type=4)

## to reconstruct the image apply the igbpt.2d function

recon <- igbpt.2d(brain.gbpt)

## we can also compute the gbpt for a non-dyadic partition

brain.gbpt <- gbpt(brain, partition=list(c(25, 47, 100, 717, 930),c(50,78,100)), n.taper=8)