.TH QCCWAVWAVELETLWT2D 3 "QCCPACK" "".SH NAMEQccWAVWaveletLWT2D, QccWAVWaveletInverseLWT2D \-forward and inverse separable 2D lazy wavelet transform.SH SYNOPSIS.B #include "libQccPack.h".sp.BI "int QccWAVWaveletLWT2D(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 );.br.BI "int QccWAVInverseWaveletLWT2D(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 );.SH DESCRIPTION.B QccWAVWaveletLWT2D()implements a separable lazy wavelet transform (LWT).Essentially, the.I input_matrixis partitioned into four subsets: the even-row-even-column samples,the even-row-odd-column samples, the odd-row-even-column samples, andthe odd-row-odd-column samples.These four subsets lie in the four quadrants of.IR output_matrix ..LP.I origin_rowand.I origin_colgive the row and column index numbers of the upper-left-corner sample of.IR input_matrix and are used to determine the phases of subsampling in eachlevel of the signal decomposition.In most cases,.I input_matrixstarts at (0, 0), so.I origin_rowand.I origin_colare both 0..LP.I subsample_pattern_rowand.I subsample_pattern_colmay both be either.B QCCWAVWAVELET_PHASE_EVENor.BR QCCWAVWAVELET_PHASE_ODD ,indicating whether even- or odd-phase subsampling is desiredalong each row and column, respectively.In the usual case, even subsampling is normally used..LPIn the case that.I num_rowsis even, all four "subbands" of the LWThave the same number of rows.  On the other hand, if.I num_rowsis odd, two of the four subbands will be one row longerthan the others. Which subbands will be longer will depend onwhether .IR origin_rowis odd or even.Likewise,.I num_colsand.I origin_coldetermine if the subbands have the same number of columns, andwhich ones are wider if not..LP.BR QccWAVWaveletLWT2D()is implemented as a separable decomposition using 1D LWTs via callsto.BR QccWAVWaveletLWT ()..LP.BR QccWAVWaveletInverseLWT2D()performs the opposite operation as.BR QccWAVWaveletLWT2D() .That is, the subbands are extracted from.I input_matrixand "interleaved" to produce.IR output_matrix ..LPFor both of these routines,.I output_matrixmust be allocated to sufficient size before calling the routine..SH "RETURN VALUES"Both.BR QccWAVWaveletLWT2D()and.BR QccWAVWaveletInverseLWT2D()return 0 on success and 1 on error..SH "SEE ALSO".BR QccWAVWaveletLWT (3),.BR QccWAVWaveletInverseLWT (3),.BR QccPackWAV (3),.BR QccPack (3).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.