.TH QCCWAVWAVELETDWT2D 3 "QCCPACK" "".SH NAMEQccWAVWaveletDWT2D, QccWAVWaveletInverseDWT2D \- separable 2D discrete wavelet transform and inverse transform for a 2D signal.SH SYNOPSIS.B #include "libQccPack.h".sp.BI "int QccWAVWaveletDWT2D(const QccMatrix " input_matrix ", QccMatrix " output_matrix ", int " num_rows ", int " num_cols ", int " origin_row ", int " origin_col ", int " subsample_pattern_row ", int " subsample_pattern_col ", int " num_scales ", const QccWAVWavelet *" wavelet );.br.BI "int QccWAVWaveletInverseDWT2D(const QccMatrix " input_matrix ", QccMatrix " output_matrix ", int " num_rows ", int " num_cols ", int " origin_row ", int " origin_col ", int " subsample_pattern_row ", int " subsample_pattern_col ", int " num_scales ", const QccWAVWavelet *" wavelet );.SH DESCRIPTION.B QccWAVWaveletDWT2D()performs a separable 2Ddiscrete wavelet transform (DWT) of a two-dimensional signal,.IR input_matrix ,which is represented as a matrix of.I num_rowsrows and.I num_colscolumns..I origin_rowand.I origin_colindicates the row and column indices, respectively, of the upper-leftcorner of the image.Usually, one assumes that the upper-left corner of the image isindexed as (0, 0) - in this case, both.I origin_rowand.I origin_colwould be zero..I num_scalesgives the number of scales, or levels, of the decomposition..BR QccWAVWaveletDWT2D()implements a dyadic, or octave, decomposition of.IR input_matrix ;that is, the low-low subband (baseband)is recursively decomposed into a lowpass andthree highpass bands for each level of decomposition, each of which beingone quarter the size of the baseband that was decomposed..I output_matrixcontains the output of the DWT;the subbands reside in .I output_matrixwith the baseband in the upper-left corner, with highpass subbandssuccessively "nested" from the upper-left corner to lower-right corner..BR QccWAVWaveletDWT2D()calls.BR QccWAVWaveletAnalysis2D (3)for each level of decomposition, using the basebandsubband for the current level of decomposition as input.As a result, the transform recursively decomposes the upper-left corner ofthe input matrix..LP.B QccWAVWaveletInverseDWT2D()performs the corresponding separable 2D inverse DWT of.IR input_matrixwhich is assumed to have been producedby.BR QccWAVWaveletDWT2D() ..I num_scalesgives the number of levels of decomposition that exist in.IR input_matrix ..B QccWAVWaveletInverseDWT2D()calls.BR QccWAVWaveletSynthesis2D (3)for each level of synthesis..LPFor both.BR QccWAVWaveletDWT2D()and.BR QccWAVWaveletInverseDWT2D() ,sufficient space for.I output_matrixmust be allocated prior to callingthe routines..LP.I subsample_pattern_rowand.I subsample_pattern_colindicate the even- or odd-phase subsampling to be used at each levelof row and column decomposition.In most applications, even subsampling at alllevels is desired, in which case both .I subsample_pattern_rowand.I subsample_pattern_colshould be set to zero.In more general settings, when some mixture of even- and odd-phase subsamplingis desired, .I subsample_pattern_rowand.I subsample_pattern_colcan be integers between 0 and.IR "(2 ^ num_levels) - 1" .In these integers, the .IR j thbit (where.I j= 1 is the least-significant bit) indicates whether the.IR j thlevel of decomposition employseven or odd subsampling (0 = even, 1 = odd).For example, if.I subsample_pattern_rowis 5, then the first and third row decompositions use odd-phasesubsampling, while all others use even subsampling..LPUse.BR QccWAVSubbandPyramidDWT (3)and.BR QccWAVSubbandPyramidInverseDWT (3)to perform a 2D separable DWT or inverse DWT on a.B QccWAVSubbandPyramiddata structure (which is the recommended way to do it, since the.B QccWAVSubbandPyramidstructure stores the number of levels of decomposition along withthe transform coefficients)..SH "RETURN VALUES"These routinesreturn 0 on success and 1 on error..SH "SEE ALSO".BR QccWAVWaveletAnalysis2D (3),.BR QccWAVWaveletSynthesis2D (3),.BR QccWAVSubbandPyramidDWT (3),.BR QccWAVSubbandPyramidInverseDWT (3),.BR QccWAVWavelet (3),.BR QccPackWAV (3),.BR QccPack (3).LPM. Antonini, M. Barlaud, P. Mathieu, and I. Daubechies,"Image Coding Using Wavelet Transform,".IR "IEEE Transactions on Image Processing" ,vol. 1, pp. 205-220, April 1992..LPI. Daubechies and W. Sweldens,"Factoring Wavelet Transforms Into Lifting Steps,".IR "J. Fourier Anal. Appl." ,vol. 4, no. 3, pp. 245-267, 1998..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.