Opencv实现离散小波变换小结

最近用Opencv做图像处理需要用到离散小波变换，但是Opencv没有提供小波变换函数。本人能力有限，自己也没写。其实用MATLAB就是分分钟的事，但是对于图像处理，MATLAB倾向于搞研究， Opencv实用性更广。在网上找点资源，发现资源很多，但是代码单一，基本上就是这两种：

链接1：http://shijuanfeng.blogbus.com/logs/221385402.html

链接2： http://www.cnblogs.com/zhangzhi/archive/2009/09/19/1569888.html

链接1的程序好像有点小bug(评论这么说)；本人也运行了程序，效果不是很理想。

链接2的程序应该是opencv1.0，作者用的IplImage数据类型，现在OpenCV升级到opencv3了。Mat数据类型比较流行。

对于离散小波变换的原理，链接3讲的很好，也有代码。对于初学者值得一看。

链接3： http://blog.csdn.net/u010006643/article/details/50493566

链接4的代码写得很好，通俗易懂，但只能进行一级小波分解。

链接4：http://answers.opencv.org/question/42273/wavelet-transform/

 

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 
  
        {
 
  
            /// 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<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 
  
            {
 
  
                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 
  
        {
 
  
            /// 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<float>(i,0) = dst.at<float>(i,j);
 
  
            }
 
  
            oneCol = ( waveletDecompose( oneCol.t(), lowFilter, highFilter ) ).t();
 
  
        
 
  
            for ( int i=0; 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 
  
        {
 
  
            /// 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<float>(i,0) = src.at<float>(i,j);
 
  
            }
 
  
            oneCol = ( waveletReconstruct( oneCol.t(), lowFilter, highFilter ) ).t();
 
  
 
 
  
            for ( int i=0; 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 
  
        {
 
  
            /// 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<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 
  
            {
 
  
                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 
  
        {
 
  
            _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 
  
    {
 
  
        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
 
  
    //{
 
  
    //    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;
 
  
 
 
  
}
 
  
 
  

 
  

 
  
原文地址：http://blog.csdn.net/u012507022/article/details/50979009