qccwavliftinganalysisint.3

spiht for linux this is used to decod and encode vedio i wich all enjoy

.TH QCCWAVLIFTINGANALYSISINT 3 "QCCPACK" ""
.SH NAME
QccWAVLiftingAnalysisInt, QccWAVLiftingSynthesisInt \- 
perform integer-valued lifting analysis/synthesis of a signal
.SH SYNOPSISINT
.B #include "libQccPack.h"
.sp
.BI "int QccWAVLiftingAnalysisInt(QccVectorInt " signal ", int " signal_length ", int " phase ", const QccWAVLiftingScheme *" lifting_scheme ", int " boundary );
.br
.BI "int QccWAVLiftingSynthesisInt(QccVectorInt " signal ", int " signal_length ", int " phase ", const QccWAVLiftingScheme *" lifting_scheme ", int " boundary );
.SH DESCRIPTION
.B QccWAVLiftingAnalysisInt()
performs one level of an
integer-valued wavelet decomposition,
which maps integer signal values into integer-valued wavelet coefficients
(see "INTEGER-TO-INTEGER WAVELET TRANSFORMS" below).
Specifically,
lifting analysis is employed to produce a lowpass subband
and a highpass subband of
.IR signal .
The lowpass subband is returned as the
first half of
.IR signal ;
the highpass subband is returned as the last half of
.IR signal .
.I signal_length
gives the length of
.I signal
and may be even or odd.
.LP
If
.I phase
is
.BR QCCWAVWAVELET_PHASE_EVEN ,
then
.I signal
is assumed to start with a even-indexed sample.
Otherwise, if
.I phase
is
.BR QCCWAVWAVELET_PHASE_ODD ,
it indicates that
.I signal
starts with an odd-indexed sample.
.I phase
is passed to
.BR QccWAVWaveletLWTInt (3),
the lazy wavelet transform,
the first step of lifting analysis, to indicate the
signal origin.
.LP
In the case that
.I signal_length
is even, both the odd and even subbands of produced by lifting analysis
are the same length.  On the other hand, if
.I signal_length
is odd, one of the two subbands will be one sample longer
than the other. Which subband will be longer will depend on
the value of
.IR phase .
Specifically, if
.IR phase
is
.BR QCCWAVWAVELET_PHASE_EVEN ,
then the lowpass subband is one sample longer than the highpass
subband. If
.IR phase
is
.BR QCCWAVWAVELET_PHASE_ODD ,
the the highpass subband is one sample longer than the lowpass
subband.
.LP
.I lifting_scheme
gives the particular lifting scheme to employ,
which must be an integer-valued lifting scheme.
Lifting implementations of
wavelet analysis and synthesis are "hard-coded" into the QccPack library
for purposes of execution speed and ease of implementation.
As a consequence, only a limited number of wavelets
are current supported, and this list cannot be extended by the user
(without modifying the QccPack source code, or course).
The currently supported integer-valued lifting schemes and their corresponding
.B LFT
files (see
.BR QccWAVLiftingScheme (3))
are
.RS

LWT.int.lft - integer-valued Lazy Wavelet transform
.br
CohenDaubechiesFeauveau.9-7.int.lft - integer-valued 9/7 biorthogonal wavelet
.br
CohenDaubechiesFeauveau.5-3.int.lft - integer-valued 5/3 biorthogonal wavelet
.RE
.LP
.B QccWAVLiftingSynthesisInt()
performs one level of wavelet synthesis.  The first half of
.I signal
is assumed to contain the lowpass subband while the second half contains
the highpass subband.
Lifting synthesis is performed
to produce the output signal which is returned in
.IR signal ,
including a call to
.BR QccWAVWaveletInverseLWTInt (3)
to perform an inverse lazy wavelet transform.
As with
.BR QccWAVLiftingAnalysisInt() ,
.I signal_length
may be even or odd.
.I phase
indicates whether the output
.I signal
is to start with an even- or odd-indexed sample.
.LP
.IR boundary
indicates how lifting should be handled at the ends of the signal and
can be one of the following:
.B QCCWAVWAVELET_BOUNDARY_SYMMETRIC_EXTENSION
(symmetric extension, valid only for biorthogonal wavelets), or
.B QCCWAVWAVELET_BOUNDARY_PERIODIC_EXTENSION
(periodic extension, valid for orthogonal and biorthogonal wavelets).
Check the comments at the start of each
.B LFT
file for permitted values for
.I boundary
for particular lifting schemes.
Note that, if periodic extension is used,
.IR signal_length
must be even (this is due to mathematical constraints).
.LP
The case in which
.IR signal_length
is equal to 1 is degenerate. A wavelet transform is technically not well
defined for this situation because it is not clear how to subsample
the signal. For integer-valued lifting in QccPack, the length-one signal is
merely placed in the lowpass subband unchanged (in which
case the highpass subband has zero length) for 
.IR phase
equal to
.BR QCCWAVWAVELET_PHASE_EVEN ,
or placed in the highpass subband unchanged
(in which case the lowpass subband has zero length) for
.IR phase
equal to
.BR QCCWAVWAVELET_PHASE_ODD .
.LP
Note:
In general, you will probably want to use
.BR QccWAVWaveletDWT1DInt (3)
and
.BR QccWAVWaveletInverseDWT1DInt (3)
instead of these routines
for implementing a discrete wavelet transform and its inverse since
.BR QccWAVWaveletDWT1DInt (3)
and
.BR QccWAVWaveletInverseDWT1DInt (3)
allow any number of scales, or levels, of decomposition to be
performed.
.SH "INTEGER-TO-INTEGER WAVELET TRANSFORMS"
Transforms generally provide perfect reconstruction in that the
inverse transform will perfectly invert transform coefficients
into an exact representation of the original signal.
However, when implemented in floating-point arithmetic, the potential
for loss arises due to the limits of finite precision in both the
forward and inverse transforms.
On the other hand,
transforms that map integer-valued signals into integer-valued
transforms coefficients can guarantee perfect reconstruction, provided
an inverse transform can be found.
For this reason, lifting schemes, in which inverse transforms are
trivial, are favored for the
implementation of integer-valued wavelet transforms. Typically,
the general approach proposed by Calderbank
.IR "et al" .
is followed wherein rounding of floating-point values to integers is performed
at each prediction and update step in a lifting scheme.
Integer versions of several popular biorthogonal wavelets were
created in this manner by Calderbank
.IR "et al" .,
as well as by Xiong
.IR "et al" .
.LP
In traditional floating-point lifting, the prediction and update steps
are generally followed by a single application of scaling by a constant
in order to produce the usual unitary normalization.
This scaling step is somewhat problematic for integer-valued lifting
since the scaling constant is usually not an integer.
In applications wherein unitary scaling is not required
(e.g., in some applications that process each subband completely
independently), the scaling step is simply dropped in order
to implement an integer-valued version of the transform.
Alternatively, one can append three additional lifting steps to 
implement the scaling; these additional lifting steps can then be rendered
integer-valued via appropriate rounding (e.g., Xiong
.IR "et al" .)
making the transforms approximately normalized.
This latter approach of scaling via additional lifting steps
is employed in the integer-valued
lifting schemes implemented in QccPack.
.SH "RETURN VALUES"
These routines
return 0 on success and 1 on error.
.SH "SEE ALSO"
.BR QccWAVLiftingScheme (3),
.BR QccWAVWavelet (3),
.BR QccWAVWaveletDWT1DInt (3),
.BR QccWAVWaveletInverseDWT1DInt (3),
.BR QccPackWAV (3),
.BR QccPack (3)
.LP
A. R. Calderbank, I. Daubechies, W. Sweldens, B.-L. Yeo, "Lossless
Image Compression Using Integer to Integer Wavelet Transforms", in
.IR "Proceedings of the International Conference on Image Processing" ,
Lausanne, Switzerland, pp. 596-599, September 1997.

Z. Xiong, X. Wu, S. Cheng, J. Hua, "Lossy-to-Lossless Compression of
Medical Volumetric Data Using Three-Dimensional Integer Wavelet Transforms,"
.IR "IEEE Transactions on Medical Imaging" ,
vol. 22, pp. 459-470, March 2003.

I. Daubechies and W. Sweldens,
"Factoring Wavelet Transforms Into Lifting Steps,"
.IR "J. Fourier Anal. Appl." ,
vol. 4, no. 3, pp. 245-267, 1998.
.SH AUTHOR
Copyright (C) 1997-2009  James E. Fowler
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