小波简介： 

 

源码：

///  小波变换

Mat WDT( const Mat &_src, const string _wname, const int _level )const

{

int reValue = THID_ERR_NONE;

Mat src = Mat_
     
      (_src);
     

Mat dst = Mat::zeros( src.rows, src.cols, src.type() );

int N = src.rows;

int D = src.cols;

/// 高通低通滤波器

Mat lowFilter;

Mat highFilter;

wavelet( _wname, lowFilter, highFilter );

/// 小波变换

int t=1;

int row = N;

int col = D;

while( t<=_level )

{

///先进行行小波变换

for( int i=0; i

{

/// 取出src中要处理的数据的一行

Mat oneRow = Mat::zeros( 1,col, src.type() );

for ( int j=0; j

{

oneRow.at
     
      (0,j) = src.at
      
       (i,j);
      
     

}

oneRow = waveletDecompose( oneRow, lowFilter, highFilter );

/// 将src这一行置为oneRow中的数据

for ( int j=0; j

{

dst.at
     
      (i,j) = oneRow.at
      
       (0,j);
      
     

}

}

#if 0

//normalize( dst, dst, 0, 255, NORM_MINMAX );

IplImage dstImg1 = IplImage(dst);

cvSaveImage( "dst.jpg", &dstImg1 );

#endif

/// 小波列变换

for ( int j=0; j

{

/// 取出src数据的一行输入

Mat oneCol = Mat::zeros( row, 1, src.type() );

for ( int i=0; i

{

oneCol.at
     
      (i,0) = dst.at
      
       (i,j);
      
     

}

oneCol = ( waveletDecompose( oneCol.t(), lowFilter, highFilter ) ).t();

for ( int i=0; i

{

dst.at
     
      (i,j) = oneCol.at
      
       (i,0);
      
     

}

}

#if 0

//normalize( dst, dst, 0, 255, NORM_MINMAX );

IplImage dstImg2 = IplImage(dst);

cvSaveImage( "dst.jpg", &dstImg2 );

#endif

/// 更新

row /= 2;

col /=2;

t++;

src = dst;

}

return dst;

}

///  小波逆变换

Mat IWDT( const Mat &_src, const string _wname, const int _level )const

{

int reValue = THID_ERR_NONE;

Mat src = Mat_
     
      (_src);
     

Mat dst = Mat::zeros( src.rows, src.cols, src.type() );

int N = src.rows;

int D = src.cols;

/// 高通低通滤波器

Mat lowFilter;

Mat highFilter;

wavelet( _wname, lowFilter, highFilter );

/// 小波变换

int t=1;

int row = N/std::pow( 2., _level-1);

int col = D/std::pow(2., _level-1);

while ( row<=N && col<=D )

{

/// 小波列逆变换

for ( int j=0; j

{

/// 取出src数据的一行输入

Mat oneCol = Mat::zeros( row, 1, src.type() );

for ( int i=0; i

{

oneCol.at
     
      (i,0) = src.at
      
       (i,j);
      
     

}

oneCol = ( waveletReconstruct( oneCol.t(), lowFilter, highFilter ) ).t();

for ( int i=0; i

{

dst.at
     
      (i,j) = oneCol.at
      
       (i,0);
      
     

}

}

#if 0

//normalize( dst, dst, 0, 255, NORM_MINMAX );

IplImage dstImg2 = IplImage(dst);

cvSaveImage( "dst.jpg", &dstImg2 );

#endif

///行小波逆变换

for( int i=0; i

{

/// 取出src中要处理的数据的一行

Mat oneRow = Mat::zeros( 1,col, src.type() );

for ( int j=0; j

{

oneRow.at
     
      (0,j) = dst.at
      
       (i,j);
      
     

}

oneRow = waveletReconstruct( oneRow, lowFilter, highFilter );

/// 将src这一行置为oneRow中的数据

for ( int j=0; j

{

dst.at
     
      (i,j) = oneRow.at
      
       (0,j);
      
     

}

}

#if 0

//normalize( dst, dst, 0, 255, NORM_MINMAX );

IplImage dstImg1 = IplImage(dst);

cvSaveImage( "dst.jpg", &dstImg1 );

#endif

row *= 2;

col *= 2;

src = dst;

}

return dst;

}

/// 调用函数

/// 生成不同类型的小波，现在只有haar，sym2

void wavelet( const string _wname, Mat &_lowFilter, Mat &_highFilter )const

{

if ( _wname=="haar" || _wname=="db1" )

{

int N = 2;

_lowFilter = Mat::zeros( 1, N, CV_32F );

_highFilter = Mat::zeros( 1, N, CV_32F );

_lowFilter.at
     
      (0, 0) = 1/sqrtf(N);
     

_lowFilter.at
     
      (0, 1) = 1/sqrtf(N);
     

_highFilter.at
     
      (0, 0) = -1/sqrtf(N);
     

_highFilter.at
     
      (0, 1) = 1/sqrtf(N);
     

}

if ( _wname =="sym2" )

{

int N = 4;

float h[] = {-0.483, 0.836, -0.224, -0.129 };

float l[] = {-0.129, 0.224,    0.837, 0.483 };

_lowFilter = Mat::zeros( 1, N, CV_32F );

_highFilter = Mat::zeros( 1, N, CV_32F );

for ( int i=0; i

{

_lowFilter.at
     
      (0, i) = l[i];
     

_highFilter.at
     
      (0, i) = h[i];
     

}

}

}

/// 小波分解

Mat waveletDecompose( const Mat &_src, const Mat &_lowFilter, const Mat &_highFilter )const

{

assert( _src.rows==1 && _lowFilter.rows==1 && _highFilter.rows==1 );

assert( _src.cols>=_lowFilter.cols && _src.cols>=_highFilter.cols );

Mat &src = Mat_
     
      (_src);
     

int D = src.cols;

Mat &lowFilter = Mat_
     
      (_lowFilter);
     

Mat &highFilter = Mat_
     
      (_highFilter);
     

/// 频域滤波，或时域卷积；ifft( fft(x) * fft(filter)) = cov(x,filter)

Mat dst1 = Mat::zeros( 1, D, src.type() );

Mat dst2 = Mat::zeros( 1, D, src.type()  );

filter2D( src, dst1, -1, lowFilter );

filter2D( src, dst2, -1, highFilter );

/// 下采样

Mat downDst1 = Mat::zeros( 1, D/2, src.type() );

Mat downDst2 = Mat::zeros( 1, D/2, src.type() );

resize( dst1, downDst1, downDst1.size() );

resize( dst2, downDst2, downDst2.size() );

/// 数据拼接

for ( int i=0; i

{

src.at
     
      (0, i) = downDst1.at
      
       ( 0, i );
      
     

src.at
     
      (0, i+D/2) = downDst2.at
      
       ( 0, i );
      
     

}

return src;

}

/// 小波重建

Mat waveletReconstruct( const Mat &_src, const Mat &_lowFilter, const Mat &_highFilter )const

{

assert( _src.rows==1 && _lowFilter.rows==1 && _highFilter.rows==1 );

assert( _src.cols>=_lowFilter.cols && _src.cols>=_highFilter.cols );

Mat &src = Mat_
     
      (_src);
     

int D = src.cols;

Mat &lowFilter = Mat_
     
      (_lowFilter);
     

Mat &highFilter = Mat_
     
      (_highFilter);
     

/// 插值;

Mat Up1 = Mat::zeros( 1, D, src.type() );

Mat Up2 = Mat::zeros( 1, D, src.type() );

/// 插值为0

//for ( int i=0, cnt=1; i

//{

//    Up1.at
     
      ( 0, cnt ) = src.at
      
       ( 0, i );     ///< 前一半
      
     

//    Up2.at
     
      ( 0, cnt ) = src.at
      
       ( 0, i+D/2 ); ///< 后一半
      
     

//}

/// 线性插值

Mat roi1( src, Rect(0, 0, D/2, 1) );

Mat roi2( src, Rect(D/2, 0, D/2, 1) );

resize( roi1, Up1, Up1.size(), 0, 0, INTER_CUBIC );

resize( roi2, Up2, Up2.size(), 0, 0, INTER_CUBIC );

/// 前一半低通，后一半高通

Mat dst1 = Mat::zeros( 1, D, src.type() );

Mat dst2= Mat::zeros( 1, D, src.type() );

filter2D( Up1, dst1, -1, lowFilter );

filter2D( Up2, dst2, -1, highFilter );

/// 结果相加

dst1 = dst1 + dst2;

return dst1;

}