小波变换 C++ opencv 实现
小波简介： http://www.blogbus.com/shijuanfeng-logs/221293135.html
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_<float>(_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<row; 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<col; j++ )
{
oneRow.at<float>(0,j) = src.at<float>(i,j);
}
oneRow = waveletDecompose( oneRow, lowFilter, highFilter );
/// 将src这一行置为oneRow中的数据
for ( int j=0; j<col; j++ )
{
dst.at<float>(i,j) = oneRow.at<float>(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<col; j++ )
{
/// 取出src数据的一行输入
Mat oneCol = Mat::zeros( row, 1, src.type() );
for ( int i=0; i<row; i++ )
{
oneCol.at<float>(i,0) = dst.at<float>(i,j);
}
oneCol = ( waveletDecompose( oneCol.t(), lowFilter, highFilter ) ).t();
for ( int i=0; i<row; i++ )
{
dst.at<float>(i,j) = oneCol.at<float>(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_<float>(_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<col; j++ )
{
/// 取出src数据的一行输入
Mat oneCol = Mat::zeros( row, 1, src.type() );
for ( int i=0; i<row; i++ )
{
oneCol.at<float>(i,0) = src.at<float>(i,j);
}
oneCol = ( waveletReconstruct( oneCol.t(), lowFilter, highFilter ) ).t();
for ( int i=0; i<row; i++ )
{
dst.at<float>(i,j) = oneCol.at<float>(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<row; 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<col; j++ )
{
oneRow.at<float>(0,j) = dst.at<float>(i,j);
}
oneRow = waveletReconstruct( oneRow, lowFilter, highFilter );
/// 将src这一行置为oneRow中的数据
for ( int j=0; j<col; j++ )
{
dst.at<float>(i,j) = oneRow.at<float>(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<float>(0, 0) = 1/sqrtf(N);
_lowFilter.at<float>(0, 1) = 1/sqrtf(N);
_highFilter.at<float>(0, 0) = -1/sqrtf(N);
_highFilter.at<float>(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<N; i++ )
{
_lowFilter.at<float>(0, i) = l[i];
_highFilter.at<float>(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_<float>(_src);
int D = src.cols;
Mat &lowFilter = Mat_<float>(_lowFilter);
Mat &highFilter = Mat_<float>(_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<D/2; i++ )
{
src.at<float>(0, i) = downDst1.at<float>( 0, i );
src.at<float>(0, i+D/2) = downDst2.at<float>( 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_<float>(_src);
int D = src.cols;
Mat &lowFilter = Mat_<float>(_lowFilter);
Mat &highFilter = Mat_<float>(_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<D/2; i++,cnt+=2 )
//{
// Up1.at<float>( 0, cnt ) = src.at<float>( 0, i ); ///< 前一半
// Up2.at<float>( 0, cnt ) = src.at<float>( 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;
}