qccwavwaveletshapeadaptivedwt1dint.3

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

.TH QCCWAVWAVELETSHAPEADAPTIVEDWT1DINT 3 "QCCPACK" ""
.SH NAME
QccWAVWaveletShapeAdaptiveDWT1DInt, QccWAVWaveletInverseShapeAdaptiveDWT1DInt \- 
integer-valued shape-adaptive discrete wavelet transform and inverse transform for a 1D signal
.SH SYNOPSIS
.B #include "libQccPack.h"
.sp
.BI "int QccWAVWaveletShapeAdaptiveDWT1DInt(QccVectorInt " signal ", QccVectorInt " mask ", int " signal_length ", int " num_scales ", const QccWAVWavelet *" wavelet );
.br
.BI "int QccWAVWaveletInverseShapeAdaptiveDWT1DInt(QccVectorInt " signal ", QccVectorInt " mask ", int " signal_length ", int " num_scales ", const QccWAVWavelet *" wavelet );
.SH DESCRIPTION
.B QccWAVWaveletShapeAdaptiveDWT1DInt()
performs an integer-valued shape-adaptive discrete
wavelet transform (SA-DWT) of a one-dimensional signal.
.I num_scales
gives the number of scales, or levels, of the decomposition.
.BR QccWAVWaveletShapeAdaptiveDWT1DInt()
implements a dyadic decomposition of
.IR signal ;
that is, the lowpass subband is recursively decomposed into lowpass and
highpass bands for each level of decomposition.
The output of the SA-DWT is returned in
.IR signal ,
overwriting the original input signal.
The output subbands reside in 
.I signal
starting with the lowpass subband of the lowest (coarsest) level of
decomposition (i.e., the baseband) with subsequent highpass subbands
of increasing resolution following.
.I wavelet
must indicate an integer-valued lifting scheme (see
.BR QccWAVLiftingSchemeInteger (3)).
.LP
.I mask
indicates where the original input
.I signal
exists. That is, 
.I mask
indicates the intervals of support in the original input
.IR signal .
Where
.I mask
is less than or equal to
.BR QCCALPHA_TRANSPARENT ,
there is no signal, and where
.I mask
is greater than
.BR QCCALPHA_TRANSPARENT ,
the signal exists and is transformed
(see
.BR QccAlpha (3)).
Essentially this shape-adaptive transform is performed by identifying
contiguous non-transparent segments of the input signal, and transforming
these segments individually with a usual 1D DWT 
(via a call to
.BR QccWAVWaveletDWT1DInt (3))
with appropriate
extension at the ends of each segment.
Each segment is transformed so that the global subsampling scheme for
the signal is respected; that is, the starting index for each segment is
determined to be either odd or even based upon its location relative
to the start of
.IR signal ,
and this determines whether odd or even subsampling is used in the
DWT of the segment.
.LP
The transparency mask is transformed (with a Lazy wavelet transform)
alongside the signal so that, at completion of the transform,
.IR mask
indicates where valid coefficients, i.e., coefficients resulting from
non-transparent segments in the input signal,
reside in the output
.IR signal .
The transformed mask is returned in
.IR mask ,
overwriting the original input mask.
.LP
Currently, 
.BR QccWAVWaveletShapeAdaptiveDWT1DInt()
supports only integer-valued biorthogonal wavelets. These may be
used with symmetric extension only.
.LP
Segments within
.I signal
may be of any length, odd or even.
In the case of odd segment length, either the lowpass or highpass
subband at the next coarser scale
will be one sample longer than
the other; which one is longer depends on whether the segment
starts with an even- or odd-indexed sample relative to the
start of
.IR signal .
A segment of length one, i.e., an isolated signal sample,
is somewhat of a degenerate case.
.BR QccWAVWaveletShapeAdaptiveDWT1DInt()
handles a length-1 segment as follows.
If the isolated  sample is even-indexed relative to the start of
.IR signal ,
then the sample value is placed unchanged in the
lowpass band. If the isolated sample is odd-index, it is
placed unchanged in the highpass band.
.LP
.B QccWAVWaveletInverseShapeAdaptiveDWT1DInt()
performs the inverse SA-DWT of
.IR signal
which is assumed to have been produced
by
.BR QccWAVWaveletShapeAdaptiveDWT1DInt() .
.IR mask
should be the corresponding Lazy-wavelet transformed mask
also produced by
.BR QccWAVWaveletShapeAdaptiveDWT1DInt() .
.I num_scales
gives the number of levels of decomposition that exist in
.IR signal .
.SH "SHAPE-ADAPTIVE DWTS"
SA-DWTs have been recently included in Version 2 of the MPEG-4
standard, wherein they are used for 
texture coding of arbitrarily shaped still objects.
Li and Li (see below) elaborate at length on the shape-adaptive DWT
used in MPEG-4, and also consider some variants not included
in the MPEG-4 standard.
.LP
The SA-DWT implemented in QccPack differs slightly
from the transform specified by MPEG-4.
The most significant difference is in the handling of isolated samples 
(i.e., segments with length one). In MPEG-4, isolated samples are always
placed in the lowpass band regardless of the
parity of the index of the sample. Another difference
is that the QccPack SA-DWT
can handle boundary-wavelet extension in addition to symmetric extension
for lifting implementations of wavelets; MPEG-4 uses only symmetric extension.
Finally, Li and Li describe several SA-DWT variants that
are currently not implemented in QccPack, namely, SA-DWTs
using orthonormal wavelets or biorthogonal wavelets with even-length symmetric
filters.
.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 QccWAVWaveletDWT1DInt (3),
.BR QccWAVWaveletInverseDWT1DInt (3),
.BR QccWAVWavelet (3),
.BR QccPackWAV (3),
.BR QccPack (3)
.LP
S. Li and W. Li, "Shape-Adaptive Discrete Wavelet Transforms for
Arbitrarily Shaped Visual Object Coding,"
.IR "IEEE Transactions on Circuits and Systems for Video Coding" ,
vol. 10, pp. 725-743, August 2000.

ISO/IEC 14496-2, "Information Technology -- Coding of audio-visual objects --
Part 2: Visual," 
.IR "MPEG-4 Standard" ,
Amendment 1, July 2000.

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
.\"  The programs herein are free software; you can redistribute them an.or
.\"  modify them under the terms of the GNU General Public License
.\"  as published by the Free Software Foundation; either version 2
.\"  of the License, or (at your option) any later version.
.\"  
.\"  These programs are distributed in the hope that they will be useful,
.\"  but WITHOUT ANY WARRANTY; without even the implied warranty of
.\"  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
.\"  GNU General Public License for more details.
.\"  
.\"  You should have received a copy of the GNU General Public License
.\"  along with these programs; if not, write to the Free Software
.\"  Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.