corrade-vassal – Rev 1
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/*
* CVS identifier:
*
* $Id: SynWTFilterFloatLift9x7.java,v 1.15 2002/05/22 15:01:56 grosbois 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.
* */
using System;
using CSJ2K.j2k.wavelet;
using CSJ2K.j2k.image;
using CSJ2K.j2k;
namespace CSJ2K.j2k.wavelet.synthesis
{
/// <summary> 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.
///
/// </summary>
/// <seealso cref="SynWTFilter">
/// </seealso>
/// <seealso cref="SynWTFilterFloat">
///
/// </seealso>
public class SynWTFilterFloatLift9x7:SynWTFilterFloat
{
/// <summary> Returns the negative support of the low-pass analysis filter. That is
/// the number of taps of the filter in the negative direction.
///
/// </summary>
/// <returns> 2
///
/// </returns>
override public int AnLowNegSupport
{
get
{
return 4;
}
}
/// <summary> Returns the positive support of the low-pass analysis filter. That is
/// the number of taps of the filter in the negative direction.
///
/// </summary>
/// <returns> The number of taps of the low-pass analysis filter in the
/// positive direction
///
/// </returns>
override public int AnLowPosSupport
{
get
{
return 4;
}
}
/// <summary> Returns the negative support of the high-pass analysis filter. That is
/// the number of taps of the filter in the negative direction.
///
/// </summary>
/// <returns> The number of taps of the high-pass analysis filter in
/// the negative direction
///
/// </returns>
override public int AnHighNegSupport
{
get
{
return 3;
}
}
/// <summary> Returns the positive support of the high-pass analysis filter. That is
/// the number of taps of the filter in the negative direction.
///
/// </summary>
/// <returns> The number of taps of the high-pass analysis filter in the
/// positive direction
///
/// </returns>
override public int AnHighPosSupport
{
get
{
return 3;
}
}
/// <summary> 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
///
/// </summary>
/// <returns> The number of taps of the low-pass synthesis filter in the
/// negative direction
///
/// </returns>
override public int SynLowNegSupport
{
get
{
return 3;
}
}
/// <summary> 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
///
/// </summary>
/// <returns> The number of taps of the low-pass synthesis filter in the
/// positive direction
///
/// </returns>
override public int SynLowPosSupport
{
get
{
return 3;
}
}
/// <summary> 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
///
/// </summary>
/// <returns> The number of taps of the high-pass synthesis filter in the
/// negative direction
///
/// </returns>
override public int SynHighNegSupport
{
get
{
return 4;
}
}
/// <summary> 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
///
/// </summary>
/// <returns> The number of taps of the high-pass synthesis filter in the
/// positive direction
///
/// </returns>
override public int SynHighPosSupport
{
get
{
return 4;
}
}
/// <summary> 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.
///
/// </summary>
/// <returns> WT_FILTER_INT_LIFT.
///
/// </returns>
override public int ImplType
{
get
{
return CSJ2K.j2k.wavelet.WaveletFilter_Fields.WT_FILTER_FLOAT_LIFT;
}
}
/// <summary> Returns the reversibility of the filter. A filter is considered
/// reversible if it is suitable for lossless coding.
///
/// </summary>
/// <returns> true since the 9x7 is reversible, provided the appropriate
/// rounding is performed.
///
/// </returns>
override public bool Reversible
{
get
{
return false;
}
}
/// <summary>The value of the first lifting step coefficient </summary>
public const float ALPHA = - 1.586134342f;
/// <summary>The value of the second lifting step coefficient </summary>
public const float BETA = - 0.05298011854f;
/// <summary>The value of the third lifting step coefficient </summary>
public const float GAMMA = 0.8829110762f;
/// <summary>The value of the fourth lifting step coefficient </summary>
public const float DELTA = 0.4435068522f;
/// <summary>The value of the low-pass subband normalization factor </summary>
public const float KL = 0.8128930655f;
/// <summary>The value of the high-pass subband normalization factor </summary>
public const float KH = 1.230174106f;
/// <summary> 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].
///
/// </summary>
/// <param name="lowSig">This is the array that contains the low-pass input
/// signal.
///
/// </param>
/// <param name="lowOff">This is the index in lowSig of the first sample to
/// filter.
///
/// </param>
/// <param name="lowLen">This is the number of samples in the low-pass input
/// signal to filter.
///
/// </param>
/// <param name="lowStep">This is the step, or interleave factor, of the low-pass
/// input signal samples in the lowSig array.
///
/// </param>
/// <param name="highSig">This is the array that contains the high-pass input
/// signal.
///
/// </param>
/// <param name="highOff">This is the index in highSig of the first sample to
/// filter.
///
/// </param>
/// <param name="highLen">This is the number of samples in the high-pass input
/// signal to filter.
///
/// </param>
/// <param name="highStep">This is the step, or interleave factor, of the
/// high-pass input signal samples in the highSig array.
///
/// </param>
/// <param name="outSig">This is the array where the output signal is placed. It
/// should be long enough to contain the output signal.
///
/// </param>
/// <param name="outOff">This is the index in outSig of the element where to put
/// the first output sample.
///
/// </param>
/// <param name="outStep">This is the step, or interleave factor, of the output
/// samples in the outSig array.
///
/// </param>
/// <seealso cref="SynWTFilter.synthetize_lpf">
///
/// </seealso>
public override 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];
}
}
/// <summary> 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].
///
/// </summary>
/// <param name="lowSig">This is the array that contains the low-pass
/// input signal.
///
/// </param>
/// <param name="lowOff">This is the index in lowSig of the first sample to
/// filter.
///
/// </param>
/// <param name="lowLen">This is the number of samples in the low-pass input
/// signal to filter.
///
/// </param>
/// <param name="lowStep">This is the step, or interleave factor, of the low-pass
/// input signal samples in the lowSig array.
///
/// </param>
/// <param name="highSig">This is the array that contains the high-pass input
/// signal.
///
/// </param>
/// <param name="highOff">This is the index in highSig of the first sample to
/// filter.
///
/// </param>
/// <param name="highLen">This is the number of samples in the high-pass input
/// signal to filter.
///
/// </param>
/// <param name="highStep">This is the step, or interleave factor, of the
/// high-pass input signal samples in the highSig array.
///
/// </param>
/// <param name="outSig">This is the array where the output signal is placed. It
/// should be long enough to contain the output signal.
///
/// </param>
/// <param name="outOff">This is the index in outSig of the element where to put
/// the first output sample.
///
/// </param>
/// <param name="outStep">This is the step, or interleave factor, of the output
/// samples in the outSig array.
///
/// </param>
/// <seealso cref="SynWTFilter.synthetize_hpf">
///
/// </seealso>
public override 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];
}
}
/// <summary> 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.
///
/// </summary>
/// <param name="tailOvrlp">This is the number of samples in the input
/// signal before the first sample to filter that can be used for
/// overlap.
///
/// </param>
/// <param name="headOvrlp">This is the number of samples in the input
/// signal after the last sample to filter that can be used for
/// overlap.
///
/// </param>
/// <param name="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.
///
/// </param>
/// <returns> true if both overlaps are greater than 2, and correct
/// processing is applied in the analyze() method.
///
///
///
/// </returns>
public override bool 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;
}
}
/// <summary> Returns a string of information about the synthesis wavelet filter
///
/// </summary>
/// <returns> wavelet filter type.
///
///
/// </returns>
public override System.String ToString()
{
return "w9x7 (lifting)";
}
}
}
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