Opencv實現離散小波變換小結

最近用Opencv做圖像處理需要用到離散小波變換，但是Opencv沒有提供小波變換函數。本人能力有限，自己也沒寫。其實用MATLAB就是分分鐘的事，但是對於圖像處理，MATLAB傾向於搞研究， Opencv實用性更廣。在網上找點資源，發現資源很多，但是代碼單一，基本上就是這兩種：

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

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

鏈接1的程序好像有點小bug(評論這麼說)；本人也運行了程序，效果不是很理想。

鏈接2的程序應該是opencv1.0，作者用的IplImage數據類型，現在OpenCV升級到opencv3了。Mat數據類型比較流行。

對於離散小波變換的原理，鏈接3講的很好，也有代碼。對於初學者值得一看。

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

鏈接4的代碼寫得很好，通俗易懂，但只能進行一級小波分解。

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

 

小波簡介： http://www.blogbus.com/shijuanfeng-logs/221293135.html

 

源碼：

///  小波變換

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;

    /// 高通低通濾波器

    Mat lowFilter; 

    Mat highFilter;

    wavelet( _wname, lowFilter, highFilter );

    /// 小波變換

    int t=1;

    int row = N;

    int col = D;

    while( t<=_level )

    {

        ///先進行行小波變換

        for( int i=0; i<row; i++ ) 

        {

            /// 取出src中要處理的數據的一行

            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 );

            /// 將src這一行置爲oneRow中的數據

            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

        /// 小波列變換

        for ( int j=0; j<col; j++ )

        {

            /// 取出src數據的一行輸入

            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;

}

///  小波逆變換

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;

    /// 高通低通濾波器

    Mat lowFilter; 

    Mat highFilter;

    wavelet( _wname, lowFilter, highFilter );

    /// 小波變換

    int t=1;

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

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

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

    {

        /// 小波列逆變換

        for ( int j=0; j<col; j++ )

        {

            /// 取出src數據的一行輸入

            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

        ///行小波逆變換

        for( int i=0; i<row; i++ ) 

        {

            /// 取出src中要處理的數據的一行

            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 );

            /// 將src這一行置爲oneRow中的數據

            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;

}

////////////////////////////////////////////////////////////////////////////////////////////

/// 調用函數

/// 生成不同類型的小波，現在只有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);

    /// 頻域濾波，或時域卷積；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 );

    /// 下采樣

    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() );

    /// 數據拼接

    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() );

    /// 插值爲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 ); ///< 後一半

    //}

    /// 線性插值

    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，後一半高通

    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 );

    /// 結果相加

    dst1 = dst1 + dst2;

    return dst1;

}

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