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/*
* $RCSfile: AnWTFilterFloatLift9x7.java,v $
* $Revision: 1.1 $
* $Date: 2005/02/11 05:02:29 $
* $State: Exp $
*
* Class: AnWTFilterFloatLift9x7
*
* Description: An analyzing 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.analysis;
import jj2000.j2k.wavelet.*;
import jj2000.j2k.image.*;
import jj2000.j2k.*;
import jj2000.j2k.codestream.writer.*;
/**
* This class inherits from the analysis wavelet filter definition
* for int data. It implements the forward wavelet transform
* specifically for the 9x7 filter. The implementation is based on
* the lifting scheme.
*
* <P>See the AnWTFilter 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 AnWTFilter
* @see AnWTFilterFloat
* */
public class AnWTFilterFloatLift9x7 extends AnWTFilterFloat {
/** The low-pass synthesis filter of the 9x7 wavelet transform */
private final static float LPSynthesisFilter[] =
{ -0.091272f, -0.057544f, 0.591272f, 1.115087f,
0.591272f, -0.057544f, -0.091272f};
/** The high-pass synthesis filter of the 9x7 wavelet transform */
private final static float HPSynthesisFilter[] =
{ 0.026749f, 0.016864f, -0.078223f, -0.266864f,
0.602949f,
-0.266864f, -0.078223f, 0.016864f, 0.026749f };
/** 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 = 0.443568522f;
/** The value of the low-pass subband normalization factor */
public final static float KL = 0.8128930655f;//1.149604398f;
/** The value of the high-pass subband normalization factor */
public final static float KH = 1.230174106f;//0.8698644523f;
/**
* An implementation of the analyze_lpf() method that works on int
* data, for the forward 9x7 wavelet transform using the
* lifting scheme. See the general description of the analyze_lpf()
* method in the AnWTFilter class for more details.
*
* <P>The coefficients of the first lifting step are [ALPHA 1 ALPHA].
*
* <P>The coefficients of the second lifting step are [BETA 1 BETA].
*
* <P>The coefficients of the third lifting step are [GAMMA 1 GAMMA].
*
* <P>The coefficients of the fourth lifting step are [DELTA 1 DELTA].
*
* <P>The low-pass and high-pass subbands are normalized by respectively
* a factor of KL and a factor of KH
*
* @param inSig This is the array that contains the input
* signal.
*
* @param inOff This is the index in inSig of the first sample to
* filter.
*
* @param inLen This is the number of samples in the input signal
* to filter.
*
* @param inStep This is the step, or interleave factor, of the
* input signal samples in the inSig array.
*
* @param lowSig This is the array where the low-pass output
* signal is placed.
*
* @param lowOff This is the index in lowSig of the element where
* to put the first low-pass output sample.
*
* @param lowStep This is the step, or interleave factor, of the
* low-pass output samples in the lowSig array.
*
* @param highSig This is the array where the high-pass output
* signal is placed.
*
* @param highOff This is the index in highSig of the element where
* to put the first high-pass output sample.
*
* @param highStep This is the step, or interleave factor, of the
* high-pass output samples in the highSig array.
* */
public
void analyze_lpf(float inSig[], int inOff, int inLen, int inStep,
float lowSig[], int lowOff, int lowStep,
float highSig[], int highOff, int highStep) {
int i,maxi;
int iStep = 2 * inStep; //Subsampling in inSig
int ik; //Indexing inSig
int lk; //Indexing lowSig
int hk; //Indexing highSig
// Generate intermediate high frequency subband
//Initialize counters
ik = inOff + inStep;
lk = lowOff;
hk = highOff;
//Apply first lifting step to each "inner" sample
for( i = 1, maxi = inLen-1; i < maxi; i += 2 ) {
highSig[hk] = inSig[ik] +
ALPHA*(inSig[ik-inStep] + inSig[ik+inStep]);
ik += iStep;
hk += highStep;
}
//Handle head boundary effect if input signal has even length
if(inLen % 2 == 0) {
highSig[hk] = inSig[ik] + 2*ALPHA*inSig[ik-inStep];
}
// Generate intermediate low frequency subband
//Initialize counters
ik = inOff;
lk = lowOff;
hk = highOff;
if(inLen>1) {
lowSig[lk] = inSig[ik] + 2*BETA*highSig[hk];
}
else {
lowSig[lk] = inSig[ik];
}
ik += iStep;
lk += lowStep;
hk += highStep;
//Apply lifting step to each "inner" sample
for( i = 2, maxi = inLen-1; i < maxi; i += 2 ) {
lowSig[lk] = inSig[ik] +
BETA*(highSig[hk-highStep] + highSig[hk]);
ik += iStep;
lk += lowStep;
hk += highStep;
}
//Handle head boundary effect if input signal has odd length
if((inLen % 2 == 1)&&(inLen>2)) {
lowSig[lk] = inSig[ik] + 2*BETA*highSig[hk-highStep];
}
// Generate high frequency subband
//Initialize counters
lk = lowOff;
hk = highOff;
//Apply first lifting step to each "inner" sample
for(i = 1, maxi = inLen-1; i < maxi; i += 2) {
highSig[hk] += GAMMA*(lowSig[lk] + lowSig[lk+lowStep]);
lk += lowStep;
hk += highStep;
}
//Handle head boundary effect if input signal has even length
if(inLen % 2 == 0) {
highSig[hk] += 2*GAMMA*lowSig[lk];
}
// Generate low frequency subband
//Initialize counters
lk = lowOff;
hk = highOff;
//Handle tail boundary effect
//If access the overlap then perform the lifting step
if(inLen>1){
lowSig[lk] += 2*DELTA*highSig[hk];
}
lk += lowStep;
hk += highStep;
//Apply lifting step to each "inner" sample
for(i = 2, maxi = inLen-1; i < maxi; i += 2) {
lowSig[lk] +=
DELTA*(highSig[hk - highStep] + highSig[hk]);
lk += lowStep;
hk += highStep;
}
//Handle head boundary effect if input signal has odd length
if((inLen % 2 == 1)&&(inLen>2)) {
lowSig[lk] += 2*DELTA*highSig[hk-highStep];
}
// Normalize low and high frequency subbands
//Re-initialize counters
lk = lowOff;
hk = highOff;
//Normalize each sample
for( i=0 ; i<(inLen>>1); i++ ) {
lowSig[lk] *= KL;
highSig[hk] *= KH;
lk += lowStep;
hk += highStep;
}
//If the input signal has odd length then normalize the last low-pass
//coefficient (if input signal is length one filter is identity)
if( inLen%2==1 && inLen != 1) {
lowSig[lk] *= KL;
}
}
/**
* An implementation of the analyze_hpf() method that works on int
* data, for the forward 9x7 wavelet transform using the
* lifting scheme. See the general description of the analyze_hpf() method
* in the AnWTFilter class for more details.
*
* <P>The coefficients of the first lifting step are [ALPHA 1 ALPHA].
*
* <P>The coefficients of the second lifting step are [BETA 1 BETA].
*
* <P>The coefficients of the third lifting step are [GAMMA 1 GAMMA].
*
* <P>The coefficients of the fourth lifting step are [DELTA 1 DELTA].
*
* <P>The low-pass and high-pass subbands are normalized by respectively
* a factor of KL and a factor of KH
*
* @param inSig This is the array that contains the input
* signal.
*
* @param inOff This is the index in inSig of the first sample to
* filter.
*
* @param inLen This is the number of samples in the input signal
* to filter.
*
* @param inStep This is the step, or interleave factor, of the
* input signal samples in the inSig array.
*
* @param lowSig This is the array where the low-pass output
* signal is placed.
*
* @param lowOff This is the index in lowSig of the element where
* to put the first low-pass output sample.
*
* @param lowStep This is the step, or interleave factor, of the
* low-pass output samples in the lowSig array.
*
* @param highSig This is the array where the high-pass output
* signal is placed.
*
* @param highOff This is the index in highSig of the element where
* to put the first high-pass output sample.
*
* @param highStep This is the step, or interleave factor, of the
* high-pass output samples in the highSig array.
*
* @see AnWTFilter#analyze_hpf
* */
public void analyze_hpf(float inSig[], int inOff, int inLen, int inStep,
float lowSig[], int lowOff, int lowStep,
float highSig[], int highOff, int highStep) {
int i,maxi;
int iStep = 2 * inStep; //Subsampling in inSig
int ik; //Indexing inSig
int lk; //Indexing lowSig
int hk; //Indexing highSig
// Generate intermediate high frequency subband
//Initialize counters
ik = inOff;
lk = lowOff;
hk = highOff;
if ( inLen>1 ) {
// apply symmetric extension.
highSig[hk] = inSig[ik] + 2*ALPHA*inSig[ik+inStep];
}
else {
// Normalize for Nyquist gain
highSig[hk] = inSig[ik]*2;
}
ik += iStep;
hk += highStep;
//Apply first lifting step to each "inner" sample
for( i = 2 ; i < inLen-1 ; i += 2 ) {
highSig[hk] = inSig[ik] +
ALPHA*(inSig[ik-inStep] + inSig[ik+inStep]);
ik += iStep;
hk += highStep;
}
//If input signal has odd length then we perform the lifting step
// i.e. apply a symmetric extension.
if( (inLen%2==1) && (inLen>1) ) {
highSig[hk] = inSig[ik] + 2*ALPHA*inSig[ik-inStep];
}
// Generate intermediate low frequency subband
//Initialize counters
//ik = inOff + inStep;
ik = inOff + inStep;
lk = lowOff;
hk = highOff;
//Apply lifting step to each "inner" sample
// we are at the component boundary
for(i = 1; i < inLen-1; i += 2) {
lowSig[lk] = inSig[ik] +
BETA*(highSig[hk] + highSig[hk+highStep]);
ik += iStep;
lk += lowStep;
hk += highStep;
}
if ( inLen>1 && inLen%2==0 ) {
// symetric extension
lowSig[lk] = inSig[ik]+2*BETA*highSig[hk];
}
// Generate high frequency subband
//Initialize counters
lk = lowOff;
hk = highOff;
if ( inLen>1 ) {
// symmetric extension.
highSig[hk] += GAMMA*2*lowSig[lk];
}
//lk += lowStep;
hk += highStep;
//Apply first lifting step to each "inner" sample
for(i = 2 ; i < inLen-1 ; i += 2) {
highSig[hk] += GAMMA*(lowSig[lk] + lowSig[lk+lowStep]);
lk += lowStep;
hk += highStep;
}
//Handle head boundary effect
if ( inLen>1 && inLen%2==1 ) {
// symmetric extension.
highSig[hk] += GAMMA*2*lowSig[lk];
}
// Generate low frequency subband
//Initialize counters
lk = lowOff;
hk = highOff;
// we are at the component boundary
for(i = 1 ; i < inLen-1; i += 2) {
lowSig[lk] += DELTA*(highSig[hk] + highSig[hk+highStep]);
lk += lowStep;
hk += highStep;
}
if ( inLen>1 && inLen%2==0 ) {
lowSig[lk] += DELTA*2*highSig[hk];
}
// Normalize low and high frequency subbands
//Re-initialize counters
lk = lowOff;
hk = highOff;
//Normalize each sample
for( i=0 ; i<(inLen>>1); i++ ) {
lowSig[lk] *= KL;
highSig[hk] *= KH;
lk += lowStep;
hk += highStep;
}
//If the input signal has odd length then normalize the last high-pass
//coefficient (if input signal is length one filter is identity)
if( inLen%2==1 && inLen != 1) {
highSig[hk] *= KH;
}
}
/**
* 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 time-reversed low-pass synthesis waveform of the
* filter, which is the low-pass filter. This is the time-reversed
* impulse response of the low-pass synthesis filter. It is used
* to calculate the L2-norm of the synthesis basis functions for a
* particular subband (also called energy weight).
*
* <P>The returned array may not be modified (i.e. a reference to
* the internal array may be returned by the implementation of
* this method).
*
* @return The time-reversed low-pass synthesis waveform of the
* filter.
* */
public float[] getLPSynthesisFilter() {
return LPSynthesisFilter;
}
/**
* Returns the time-reversed high-pass synthesis waveform of the
* filter, which is the high-pass filter. This is the
* time-reversed impulse response of the high-pass synthesis
* filter. It is used to calculate the L2-norm of the synthesis
* basis functions for a particular subband (also called energy
* weight).
*
* <P>The returned array may not be modified (i.e. a reference to
* the internal array may be returned by the implementation of
* this method).
*
* @return The time-reversed high-pass synthesis waveform of the
* filter.
* */
public float[] getHPSynthesisFilter() {
return HPSynthesisFilter;
}
/**
* 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 >= 4 && headOvrlp >= 3 ) return true;
else return false;
}
//Else if the input signal has odd length.
else {
if( tailOvrlp >= 4 && headOvrlp >= 4 ) return true;
else return false;
}
}
/**
* Tests if the 'obj' object is the same filter as this one. Two filters
* are the same if the same filter code should be output for both filters
* by the encodeFilterCode() method.
*
* <P>Currently the implementation of this method only tests if 'obj' is
* also of the class AnWTFilterFloatLift9x7
*
* @param The object against which to test inequality.
* */
public boolean equals(Object obj) {
// To spped up test, first test for reference equality
return obj == this ||
obj instanceof AnWTFilterFloatLift9x7;
}
/**
* Returns the type of filter used according to the FilterTypes
* interface(W9x7).
*
* @see FilterTypes
*
* @return The filter type.
* */
public int getFilterType(){
return FilterTypes.W9X7;
}
/** Debugging method */
public String toString(){
return "w9x7";
}
}