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/*
* $RCSfile: SynWTFilterFloatLift9x7.java,v $
* $Revision: 1.1 $
* $Date: 2005/02/11 05:02:34 $
* $State: Exp $
*
* Class: SynWTFilterFloatLift9x7
*
* Description: A synthetizing wavelet filter implementing the
* lifting 9x7 transform.
*
*
*
* COPYRIGHT:
*
* This software module was originally developed by Raphaël Grosbois and
* Diego Santa Cruz (Swiss Federal Institute of Technology-EPFL); Joel
* Askelöf (Ericsson Radio Systems AB); and Bertrand Berthelot, David
* Bouchard, Félix Henry, Gerard Mozelle and Patrice Onno (Canon Research
* Centre France S.A) in the course of development of the JPEG2000
* standard as specified by ISO/IEC 15444 (JPEG 2000 Standard). This
* software module is an implementation of a part of the JPEG 2000
* Standard. Swiss Federal Institute of Technology-EPFL, Ericsson Radio
* Systems AB and Canon Research Centre France S.A (collectively JJ2000
* Partners) agree not to assert against ISO/IEC and users of the JPEG
* 2000 Standard (Users) any of their rights under the copyright, not
* including other intellectual property rights, for this software module
* with respect to the usage by ISO/IEC and Users of this software module
* or modifications thereof for use in hardware or software products
* claiming conformance to the JPEG 2000 Standard. Those intending to use
* this software module in hardware or software products are advised that
* their use may infringe existing patents. The original developers of
* this software module, JJ2000 Partners and ISO/IEC assume no liability
* for use of this software module or modifications thereof. No license
* or right to this software module is granted for non JPEG 2000 Standard
* conforming products. JJ2000 Partners have full right to use this
* software module for his/her own purpose, assign or donate this
* software module to any third party and to inhibit third parties from
* using this software module for non JPEG 2000 Standard conforming
* products. This copyright notice must be included in all copies or
* derivative works of this software module.
*
* Copyright (c) 1999/2000 JJ2000 Partners.
* */
package jj2000.j2k.wavelet.synthesis;
import jj2000.j2k.wavelet.*;
import jj2000.j2k.image.*;
import jj2000.j2k.*;
/**
* This class inherits from the synthesis wavelet filter definition for int
* data. It implements the inverse wavelet transform specifically for the 9x7
* filter. The implementation is based on the lifting scheme.
*
* <P>See the SynWTFilter class for details such as normalization, how to
* split odd-length signals, etc. In particular, this method assumes that the
* low-pass coefficient is computed first.
*
* @see SynWTFilter
* @see SynWTFilterFloat
* */
public class SynWTFilterFloatLift9x7 extends SynWTFilterFloat {
/** The value of the first lifting step coefficient */
public final static float ALPHA = -1.586134342f;
/** The value of the second lifting step coefficient */
public final static float BETA = -0.05298011854f;
/** The value of the third lifting step coefficient */
public final static float GAMMA = 0.8829110762f;
/** The value of the fourth lifting step coefficient */
public final static float DELTA = 0.4435068522f;
/** The value of the low-pass subband normalization factor */
public final static float KL = 0.8128930655f;
/** The value of the high-pass subband normalization factor */
public final static float KH = 1.230174106f;
/**
* An implementation of the synthetize_lpf() method that works on int
* data, for the inverse 9x7 wavelet transform using the lifting
* scheme. See the general description of the synthetize_lpf() method in
* the SynWTFilter class for more details.
*
* <P>The low-pass and high-pass subbands are normalized by respectively a
* factor of 1/KL and a factor of 1/KH
*
* <P>The coefficients of the first lifting step are [-DELTA 1 -DELTA].
*
* <P>The coefficients of the second lifting step are [-GAMMA 1 -GAMMA].
*
* <P>The coefficients of the third lifting step are [-BETA 1 -BETA].
*
* <P>The coefficients of the fourth lifting step are [-ALPHA 1 -ALPHA].
*
* @param lowSig This is the array that contains the low-pass input
* signal.
*
* @param lowOff This is the index in lowSig of the first sample to
* filter.
*
* @param lowLen This is the number of samples in the low-pass input
* signal to filter.
*
* @param lowStep This is the step, or interleave factor, of the low-pass
* input signal samples in the lowSig array.
*
* @param highSig This is the array that contains the high-pass input
* signal.
*
* @param highOff This is the index in highSig of the first sample to
* filter.
*
* @param highLen This is the number of samples in the high-pass input
* signal to filter.
*
* @param highStep This is the step, or interleave factor, of the
* high-pass input signal samples in the highSig array.
*
* @param outSig This is the array where the output signal is placed. It
* should be long enough to contain the output signal.
*
* @param outOff This is the index in outSig of the element where to put
* the first output sample.
*
* @param outStep This is the step, or interleave factor, of the output
* samples in the outSig array.
*
* @see SynWTFilter#synthetize_lpf
* */
public
void synthetize_lpf(float[] lowSig,int lowOff,int lowLen,int lowStep,
float[] highSig,int highOff,int highLen,
int highStep,
float[] outSig, int outOff, int outStep) {
int i;
int outLen = lowLen + highLen; //Length of the output signal
int iStep = 2*outStep; //Upsampling in outSig
int ik; //Indexing outSig
int lk; //Indexing lowSig
int hk; //Indexing highSig
// Generate intermediate low frequency subband
float sample = 0;
//Initialize counters
lk = lowOff;
hk = highOff;
ik = outOff;
//Handle tail boundary effect. Use symmetric extension
if(outLen>1) {
outSig[ik] = lowSig[lk]/KL - 2*DELTA*highSig[hk]/KH;
}
else {
outSig[ik] = lowSig[lk];
}
lk += lowStep;
hk += highStep;
ik += iStep;
//Apply lifting step to each "inner" sample
for(i=2; i<outLen-1; i+=2, ik+=iStep, lk+=lowStep, hk+=highStep) {
outSig[ik] = lowSig[lk]/KL -
DELTA*(highSig[hk-highStep] + highSig[hk])/KH;
}
//Handle head boundary effect if input signal has odd length
if(outLen%2 == 1) {
if(outLen>2){
outSig[ik] = lowSig[lk]/KL -
2*DELTA*highSig[hk-highStep]/KH;
}
}
// Generate intermediate high frequency subband
//Initialize counters
lk = lowOff;
hk = highOff;
ik = outOff + outStep;
//Apply lifting step to each "inner" sample
for(i = 1; i<outLen-1; i+=2, ik+=iStep, hk+=highStep, lk+=lowStep) {
outSig[ik] = highSig[hk]/KH -
GAMMA*(outSig[ik-outStep] + outSig[ik+outStep]);
}
//Handle head boundary effect if output signal has even length
if(outLen % 2 == 0) {
outSig[ik] = highSig[hk]/KH - 2*GAMMA*outSig[ik-outStep];
}
// Generate even samples (inverse low-pass filter)
//Initialize counters
ik = outOff;
//Handle tail boundary effect
//If access the overlap then perform the lifting step.
if(outLen>1) {
outSig[ik] -= 2*BETA*outSig[ik+outStep];
}
ik += iStep;
//Apply lifting step to each "inner" sample
for(i=2; i<outLen-1; i+=2, ik+=iStep) {
outSig[ik] -= BETA*(outSig[ik-outStep] + outSig[ik+outStep]);
}
//Handle head boundary effect if input signal has odd length
if(outLen%2 == 1 && outLen>2) {
outSig[ik] -= 2*BETA*outSig[ik-outStep];
}
// Generate odd samples (inverse high pass-filter)
//Initialize counters
ik = outOff + outStep;
//Apply first lifting step to each "inner" sample
for(i=1; i<outLen-1; i+=2, ik+=iStep) {
outSig[ik] -= ALPHA*(outSig[ik-outStep] + outSig[ik+outStep]);
}
//Handle head boundary effect if input signal has even length
if(outLen%2 == 0) {
outSig[ik] -= 2*ALPHA*outSig[ik-outStep];
}
}
/**
* An implementation of the synthetize_hpf() method that works on int
* data, for the inverse 9x7 wavelet transform using the lifting
* scheme. See the general description of the synthetize_hpf() method in
* the SynWTFilter class for more details.
*
* <P>The low-pass and high-pass subbands are normalized by respectively
* a factor of 1/KL and a factor of 1/KH
*
* <P>The coefficients of the first lifting step are [-DELTA 1 -DELTA].
*
* <P>The coefficients of the second lifting step are [-GAMMA 1 -GAMMA].
*
* <P>The coefficients of the third lifting step are [-BETA 1 -BETA].
*
* <P>The coefficients of the fourth lifting step are [-ALPHA 1 -ALPHA].
*
* @param lowSig This is the array that contains the low-pass
* input signal.
*
* @param lowOff This is the index in lowSig of the first sample to
* filter.
*
* @param lowLen This is the number of samples in the low-pass input
* signal to filter.
*
* @param lowStep This is the step, or interleave factor, of the low-pass
* input signal samples in the lowSig array.
*
* @param highSig This is the array that contains the high-pass input
* signal.
*
* @param highOff This is the index in highSig of the first sample to
* filter.
*
* @param highLen This is the number of samples in the high-pass input
* signal to filter.
*
* @param highStep This is the step, or interleave factor, of the
* high-pass input signal samples in the highSig array.
*
* @param outSig This is the array where the output signal is placed. It
* should be long enough to contain the output signal.
*
* @param outOff This is the index in outSig of the element where to put
* the first output sample.
*
* @param outStep This is the step, or interleave factor, of the output
* samples in the outSig array.
*
* @see SynWTFilter#synthetize_hpf
* */
public
void synthetize_hpf(float[] lowSig,int lowOff,int lowLen,int lowStep,
float[] highSig,int highOff,int highLen,
int highStep,float[] outSig,int outOff,
int outStep) {
int i;
int outLen = lowLen + highLen; //Length of the output signal
int iStep = 2*outStep; //Upsampling in outSig
int ik; //Indexing outSig
int lk; //Indexing lowSig
int hk; //Indexing highSig
// Initialize counters
lk = lowOff;
hk = highOff;
if(outLen!=1) {
int outLen2 = outLen>>1;
// "Inverse normalize" each sample
for(i=0; i<outLen2; i++) {
lowSig[lk] /= KL;
highSig[hk] /= KH;
lk += lowStep;
hk += highStep;
}
// "Inverse normalise" last high pass coefficient
if(outLen%2==1) {
highSig[hk] /= KH;
}
} else {
// Normalize for Nyquist gain
highSig[highOff] /= 2;
}
// Generate intermediate low frequency subband
//Initialize counters
lk = lowOff;
hk = highOff;
ik = outOff + outStep;
//Apply lifting step to each "inner" sample
for(i=1; i<outLen-1; i+=2 ) {
outSig[ik] = lowSig[lk] -
DELTA*(highSig[hk] + highSig[hk+highStep]);
ik += iStep;
lk += lowStep;
hk += highStep;
}
if(outLen%2==0 && outLen>1) {
//Use symmetric extension
outSig[ik] = lowSig[lk] - 2*DELTA*highSig[hk];
}
// Generate intermediate high frequency subband
//Initialize counters
hk = highOff;
ik = outOff;
if(outLen>1) {
outSig[ik] = highSig[hk] - 2*GAMMA*outSig[ik+outStep];
} else {
outSig[ik] = highSig[hk];
}
ik += iStep;
hk += highStep;
//Apply lifting step to each "inner" sample
for(i=2; i<outLen-1; i+=2 ) {
outSig[ik] = highSig[hk] -
GAMMA*(outSig[ik-outStep] + outSig[ik+outStep]);
ik += iStep;
hk += highStep;
}
//Handle head boundary effect if output signal has even length
if(outLen%2==1 && outLen>1) {
//Use symmetric extension
outSig[ik] = highSig[hk] - 2*GAMMA*outSig[ik-outStep];
}
// Generate even samples (inverse low-pass filter)
//Initialize counters
ik = outOff + outStep;
//Apply lifting step to each "inner" sample
for(i=1; i<outLen-1; i+=2 ) {
outSig[ik] -= BETA*(outSig[ik-outStep] + outSig[ik+outStep]);
ik += iStep;
}
if(outLen%2==0 && outLen>1) {
// symmetric extension.
outSig[ik] -= 2*BETA*outSig[ik-outStep];
}
// Generate odd samples (inverse high pass-filter)
//Initialize counters
ik = outOff;
if(outLen>1) {
// symmetric extension.
outSig[ik] -= 2*ALPHA*outSig[ik+outStep];
}
ik += iStep;
//Apply first lifting step to each "inner" sample
for(i=2; i<outLen-1 ; i+=2) {
outSig[ik] -= ALPHA*(outSig[ik-outStep] + outSig[ik+outStep]);
ik += iStep;
}
//Handle head boundary effect if input signal has even length
if((outLen%2==1) && (outLen>1)) {
//Use symmetric extension
outSig[ik] -= 2*ALPHA*outSig[ik-outStep];
}
}
/**
* Returns the negative support of the low-pass analysis filter. That is
* the number of taps of the filter in the negative direction.
*
* @return 2
* */
public int getAnLowNegSupport() {
return 4;
}
/**
* Returns the positive support of the low-pass analysis filter. That is
* the number of taps of the filter in the negative direction.
*
* @return The number of taps of the low-pass analysis filter in the
* positive direction
* */
public int getAnLowPosSupport() {
return 4;
}
/**
* Returns the negative support of the high-pass analysis filter. That is
* the number of taps of the filter in the negative direction.
*
* @return The number of taps of the high-pass analysis filter in
* the negative direction
* */
public int getAnHighNegSupport() {
return 3;
}
/**
* Returns the positive support of the high-pass analysis filter. That is
* the number of taps of the filter in the negative direction.
*
* @return The number of taps of the high-pass analysis filter in the
* positive direction
* */
public int getAnHighPosSupport() {
return 3;
}
/**
* Returns the negative support of the low-pass synthesis filter. That is
* the number of taps of the filter in the negative direction.
*
* <P>A MORE PRECISE DEFINITION IS NEEDED
*
* @return The number of taps of the low-pass synthesis filter in the
* negative direction
* */
public int getSynLowNegSupport() {
return 3;
}
/**
* Returns the positive support of the low-pass synthesis filter. That is
* the number of taps of the filter in the negative direction.
*
* <P>A MORE PRECISE DEFINITION IS NEEDED
*
* @return The number of taps of the low-pass synthesis filter in the
* positive direction
* */
public int getSynLowPosSupport() {
return 3;
}
/**
* Returns the negative support of the high-pass synthesis filter. That is
* the number of taps of the filter in the negative direction.
*
* <P>A MORE PRECISE DEFINITION IS NEEDED
*
* @return The number of taps of the high-pass synthesis filter in the
* negative direction
* */
public int getSynHighNegSupport() {
return 4;
}
/**
* Returns the positive support of the high-pass synthesis filter. That is
* the number of taps of the filter in the negative direction.
*
* <P>A MORE PRECISE DEFINITION IS NEEDED
*
* @return The number of taps of the high-pass synthesis filter in the
* positive direction
* */
public int getSynHighPosSupport() {
return 4;
}
/**
* Returns the implementation type of this filter, as defined in this
* class, such as WT_FILTER_INT_LIFT, WT_FILTER_FLOAT_LIFT,
* WT_FILTER_FLOAT_CONVOL.
*
* @return WT_FILTER_INT_LIFT.
* */
public int getImplType() {
return WT_FILTER_FLOAT_LIFT;
}
/**
* Returns the reversibility of the filter. A filter is considered
* reversible if it is suitable for lossless coding.
*
* @return true since the 9x7 is reversible, provided the appropriate
* rounding is performed.
* */
public boolean isReversible() {
return false;
}
/**
* Returns true if the wavelet filter computes or uses the
* same "inner" subband coefficient as the full frame wavelet transform,
* and false otherwise. In particular, for block based transforms with
* reduced overlap, this method should return false. The term "inner"
* indicates that this applies only with respect to the coefficient that
* are not affected by image boundaries processings such as symmetric
* extension, since there is not reference method for this.
*
* <P>The result depends on the length of the allowed overlap when
* compared to the overlap required by the wavelet filter. It also
* depends on how overlap processing is implemented in the wavelet
* filter.
*
* @param tailOvrlp This is the number of samples in the input
* signal before the first sample to filter that can be used for
* overlap.
*
* @param headOvrlp This is the number of samples in the input
* signal after the last sample to filter that can be used for
* overlap.
*
* @param inLen This is the lenght of the input signal to filter.The
* required number of samples in the input signal after the last sample
* depends on the length of the input signal.
*
* @return true if both overlaps are greater than 2, and correct
* processing is applied in the analyze() method.
*
*
*
*/
public boolean isSameAsFullWT(int tailOvrlp, int headOvrlp, int inLen) {
//If the input signal has even length.
if(inLen % 2 == 0) {
if(tailOvrlp >= 2 && headOvrlp >= 1) return true;
else return false;
}
//Else if the input signal has odd length.
else {
if(tailOvrlp >= 2 && headOvrlp >= 2) return true;
else return false;
}
}
/**
* Returns a string of information about the synthesis wavelet filter
*
* @return wavelet filter type.
*
*
*/
public String toString(){
return "w9x7 (lifting)";
}
}