.TH QCCWAVWAVELETSHAPEADAPTIVEDWT1D 3 "QCCPACK" "".SH NAMEQccWAVWaveletShapeAdaptiveDWT1D, QccWAVWaveletInverseShapeAdaptiveDWT1D \- shape-adaptive discrete wavelet transform and inverse transform for a 1D signal.SH SYNOPSIS.B #include "libQccPack.h".sp.BI "int QccWAVWaveletShapeAdaptiveDWT1D(const QccVector " input_signal ", QccVector " input_mask ", QccVector " output_signal ", QccVector " output_mask ", int " signal_length ", int " num_scales ", const QccWAVWavelet *" wavelet );.br.BI "int QccWAVWaveletInverseShapeAdaptiveDWT1D(const QccVector " input_signal ", QccVector " input_mask ", QccVector " output_signal ", QccVector " output_mask ", int " signal_length ", int " num_scales ", const QccWAVWavelet *" wavelet );.SH DESCRIPTION.B QccWAVWaveletShapeAdaptiveDWT1D()performs a shape-adaptive discretewavelet transform (SA-DWT) of a one-dimensional signal..I num_scalesgives the number of scales, or levels, of the decomposition..BR QccWAVWaveletShapeAdaptiveDWT1D()implements a dyadic decomposition of.IR input_signal ;that is, the lowpass subband is recursively decomposed into lowpass andhighpass bands for each level of decomposition..I output_signalcontains the output of the SA-DWT;the subbands reside in .I output_signalstarting with the lowpass subband of the lowest (coarsest) level ofdecomposition (i.e., the baseband) with subsequent highpass subbandsof increasing resolution following..LP.I input_maskindicates where.I input_signalexists. That is, .I input_maskindicates the intervals of support of.IR input_signal .Where.I input_maskis less than or equal to.BR QCCALPHA_TRANSPARENT ,there is no signal, and where.I input_maskis greater than.BR QCCALPHA_TRANSPARENT ,the signal exists and is transformed(see.BR QccAlpha (3)).Essentially this shape-adaptive transform is performed by identifyingcontiguous non-transparent segments of the input signal, and transformingthese segments individually with a usual 1D DWT (via a call to.BR QccWAVWaveletDWT1D (3))with appropriateextension at the ends of each segment.Each segment is transformed so that the global subsampling scheme forthe signal is respected; that is, the starting index for each segment isdetermined to be either odd or even based upon its location relativeto the start of.IR input_signal ,and this determines whether odd or even subsampling is used in theDWT of the segment..LPThe transparency mask is transformed (with a Lazy wavelet transform)alongside the signal so that.IR output_maskindicates where valid coefficients, i.e., coefficients resulting fromnon-transparent segments in.IR input_signal ,reside in.IR output_signal ..LPCurrently, .BR QccWAVWaveletShapeAdaptiveDWT1D()supports only biorthogonal wavelets. These may beused with symmetric extension (lifting or filter-bankimplementations) or boundary-wavelet extension(lifting implementations only)..LPSegments within.I input_signalmay be of any length, odd or even.In the case of odd segment length, either the lowpass or highpasssubband at the next coarser scalewill be one sample longer thanthe other; which one is longer depends on whether the segmentstarts with an even- or odd-indexed sample relative to thestart of.IR input_signal .A segment of length one, i.e., an isolated signal sample,is somewhat of a degenerate case..BR QccWAVWaveletShapeAdaptiveDWT1D()handles a length-1 segment as follows.If the isolated  sample is even-indexed relative to the start of.IR input_signal ,then the sample value is multiplied by sqrt(2) and placed in thelowpass band. If the isolated sample is odd-index, it is divided bysqrt(2) and placed in the highpass band..LP.B QccWAVWaveletInverseShapeAdaptiveDWT1D()performs the inverse SA-DWT of.IR input_signalwhich is assumed to have been producedby.BR QccWAVWaveletShapeAdaptiveDWT1D() ..IR input_maskshould be the corresponding Lazy-wavelet transformed maskalso produced by.BR QccWAVWaveletShapeAdaptiveDWT1D() ..I num_scalesgives the number of levels of decomposition that exist in.IR input_signal ..LPFor both.BR QccWAVWaveletShapeAdaptiveDWT1D()and.BR QccWAVWaveletInverseShapeAdaptiveDWT1D() ,sufficient space for.I output_signaland.I output_maskmust be allocated prior to callingthe routines..SH "RETURN VALUES"These routinesreturn 0 on success and 1 on error..SH "NOTES"SA-DWTs have been recently included in Version 2 of the MPEG-4standard, wherein they are used for texture coding of arbitrarily shaped still objects.Li and Li (see below) elaborate at length on the shape-adaptive DWTused in MPEG-4, and also consider some variants not includedin the MPEG-4 standard..LPThe SA-DWT implemented in QccPack differs slightlyfrom 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 alwaysmultiplied by sqrt(2) and placed in the lowpass band regardless of theparity of the index of the sample. Another differenceis that the QccPack SA-DWTcan handle boundary-wavelet extension in addition to symmetric extensionfor lifting implementations of wavelets; MPEG-4 uses only symmetric extension.Finally, Li and Li describe several SA-DWT variants thatare currently not implemented in QccPack, namely, SA-DWTsusing orthonormal wavelets or biorthogonal wavelets with even-length symmetricfilters..SH "SEE ALSO".BR QccWAVWaveletDWT1D (3),.BR QccWAVWaveletInverseDWT1D (3),.BR QccWAVWavelet (3),.BR QccPackWAV (3),.BR QccPack (3).LPS. Li and W. Li, "Shape-Adaptive Discrete Wavelet Transforms forArbitrarily Shaped Visual Object Coding,".IR "IEEE Transactions on Circuits and Systems for Video Coding" ,vol. 10, pp. 725-743, August 2000..LPISO/IEC 14496-2, "Information Technology -- Coding of audio-visual objects --Part 2: Visual," .IR "MPEG-4 Standard" ,Amendment 1, July 2000..SH AUTHORCopyright (C) 1997-2005  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.