/// 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(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(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(i,0) = dst.at(i,j);
}
oneCol = ( waveletDecompose( oneCol.t(), lowFilter, highFilter ) ).t();
for ( int i=0; i(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(i,0) = src.at(i,j);
}
oneCol = ( waveletReconstruct( oneCol.t(), lowFilter, highFilter ) ).t();
for ( int i=0; i(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(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(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(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(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( 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;
}
#include
#include
#include
using namespace std;
//二维离散变换小波源代码
void DWT(IplImage *pImage, int nLayer)
{
// 执行条件
if (pImage)
{
if (pImage->nChannels == 1 &&
pImage->depth == IPL_DEPTH_32F &&
((pImage->width >> nLayer) << nLayer) == pImage->width &&
((pImage->height >> nLayer) << nLayer) == pImage->height)
{
int i, x, y, n;
float fValue = 0;
float fRadius = sqrt(2.0f);
int nWidth = pImage->width;
int nHeight = pImage->height;
int nHalfW = nWidth / 2;
int nHalfH = nHeight / 2;
float **pData = new float*[pImage->height];
float *pRow = new float[pImage->width];
float *pColumn = new float[pImage->height];
for (i = 0; i < pImage->height; i++) pData[i] = (float*) (pImage->imageData + pImage->widthStep * i);
// 多层小波变换
for (n = 0; n < nLayer; n++, nWidth /= 2, nHeight /= 2, nHalfW /= 2, nHalfH /= 2)
{
// 水平变换
for (y = 0; y < nHeight; y++)
{
// 奇偶分离
memcpy(pRow, pData[y], sizeof(float) * nWidth);
for (i = 0; i < nHalfW; i++)
{
x = i * 2;
pData[y][i] = pRow[x];
pData[y][nHalfW + i] = pRow[x + 1];
}
// 提升小波变换
for (i = 0; i < nHalfW - 1; i++)
{
fValue = (pData[y][i] + pData[y][i + 1]) / 2;
pData[y][nHalfW + i] -= fValue;
}
fValue = (pData[y][nHalfW - 1] + pData[y][nHalfW - 2]) / 2;
pData[y][nWidth - 1] -= fValue;
fValue = (pData[y][nHalfW] + pData[y][nHalfW + 1]) / 4;
pData[y][0] += fValue;
for (i = 1; i < nHalfW; i++)
{
fValue = (pData[y][nHalfW + i] + pData[y][nHalfW + i - 1]) / 4;
pData[y][i] += fValue;
}
// 频带系数
for (i = 0; i < nHalfW; i++)
{
pData[y][i] *= fRadius;
pData[y][nHalfW + i] /= fRadius;
}
}
// 垂直变换
for (x = 0; x < nWidth; x++)
{
// 奇偶分离
for (i = 0; i < nHalfH; i++)
{
y = i * 2;
pColumn[i] = pData[y][x];
pColumn[nHalfH + i] = pData[y + 1][x];
}
for (i = 0; i < nHeight; i++)
{
pData[i][x] = pColumn[i];
}
// 提升小波变换
for (i = 0; i < nHalfH - 1; i++)
{
fValue = (pData[i][x] + pData[i + 1][x]) / 2;
pData[nHalfH + i][x] -= fValue;
}
fValue = (pData[nHalfH - 1][x] + pData[nHalfH - 2][x]) / 2;
pData[nHeight - 1][x] -= fValue;
fValue = (pData[nHalfH][x] + pData[nHalfH + 1][x]) / 4;
pData[0][x] += fValue;
for (i = 1; i < nHalfH; i++)
{
fValue = (pData[nHalfH + i][x] + pData[nHalfH + i - 1][x]) / 4;
pData[i][x] += fValue;
}
// 频带系数
for (i = 0; i < nHalfH; i++)
{
pData[i][x] *= fRadius;
pData[nHalfH + i][x] /= fRadius;
}
}
}
delete[] pData;
delete[] pRow;
delete[] pColumn;
}
}
}
// 二维离散小波恢复（单通道浮点图像）
void IDWT(IplImage *pImage, int nLayer)
{
// 执行条件
if (pImage)
{
if (pImage->nChannels == 1 &&
pImage->depth == IPL_DEPTH_32F &&
((pImage->width >> nLayer) << nLayer) == pImage->width &&
((pImage->height >> nLayer) << nLayer) == pImage->height)
{
int i, x, y, n;
float fValue = 0;
float fRadius = sqrt(2.0f);
int nWidth = pImage->width >> (nLayer - 1);
int nHeight = pImage->height >> (nLayer - 1);
int nHalfW = nWidth / 2;
int nHalfH = nHeight / 2;
float **pData = new float*[pImage->height];
float *pRow = new float[pImage->width];
float *pColumn = new float[pImage->height];
for (i = 0; i < pImage->height; i++)
{
pData[i] = (float*) (pImage->imageData + pImage->widthStep * i);
}
// 多层小波恢复
for (n = 0; n < nLayer; n++, nWidth *= 2, nHeight *= 2, nHalfW *= 2, nHalfH *= 2)
{
// 垂直恢复
for (x = 0; x < nWidth; x++)
{
// 频带系数
for (i = 0; i < nHalfH; i++)
{
pData[i][x] /= fRadius;
pData[nHalfH + i][x] *= fRadius;
}
// 提升小波恢复
fValue = (pData[nHalfH][x] + pData[nHalfH + 1][x]) / 4;
pData[0][x] -= fValue;
for (i = 1; i < nHalfH; i++)
{
fValue = (pData[nHalfH + i][x] + pData[nHalfH + i - 1][x]) / 4;
pData[i][x] -= fValue;
}
for (i = 0; i < nHalfH - 1; i++)
{
fValue = (pData[i][x] + pData[i + 1][x]) / 2;
pData[nHalfH + i][x] += fValue;
}
fValue = (pData[nHalfH - 1][x] + pData[nHalfH - 2][x]) / 2;
pData[nHeight - 1][x] += fValue;
// 奇偶合并
for (i = 0; i < nHalfH; i++)
{
y = i * 2;
pColumn[y] = pData[i][x];
pColumn[y + 1] = pData[nHalfH + i][x];
}
for (i = 0; i < nHeight; i++) pData[i][x] = pColumn[i];
}
// 水平恢复
for (y = 0; y < nHeight; y++)
{
// 频带系数
for (i = 0; i < nHalfW; i++)
{
pData[y][i] /= fRadius;
pData[y][nHalfW + i] *= fRadius;
}
// 提升小波恢复
fValue = (pData[y][nHalfW] + pData[y][nHalfW + 1]) / 4;
pData[y][0] -= fValue;
for (i = 1; i < nHalfW; i++)
{
fValue = (pData[y][nHalfW + i] + pData[y][nHalfW + i - 1]) / 4;
pData[y][i] -= fValue;
}
for (i = 0; i < nHalfW - 1; i++)
{
fValue = (pData[y][i] + pData[y][i + 1]) / 2;
pData[y][nHalfW + i] += fValue;
}
fValue = (pData[y][nHalfW - 1] + pData[y][nHalfW - 2]) / 2;
pData[y][nWidth - 1] += fValue;
// 奇偶合并
for (i = 0; i < nHalfW; i++)
{
x = i * 2;
pRow[x] = pData[y][i];
pRow[x + 1] = pData[y][nHalfW + i];
}
memcpy(pData[y], pRow, sizeof(float) * nWidth);
}
}
delete[] pData;
delete[] pRow;
delete[] pColumn;
}
}
}
int main()
{
// 小波变换层数
int nLayer = 2;
// 输入彩色图像
IplImage *pSrc = cvLoadImage("lena.jpg", CV_LOAD_IMAGE_COLOR);
// 计算小波图象大小
CvSize size = cvGetSize(pSrc);
if ((pSrc->width >> nLayer) << nLayer != pSrc->width) size.width = ((pSrc->width >> nLayer) + 1) << nLayer;
if ((pSrc->height >> nLayer) << nLayer != pSrc->height) size.height = ((pSrc->height >> nLayer) + 1) << nLayer;
// 创建小波图象
IplImage *pWavelet = cvCreateImage(size, IPL_DEPTH_32F, pSrc->nChannels);
if (pWavelet) {
// 小波图象赋值
cvSetImageROI(pWavelet, cvRect(0, 0, pSrc->width, pSrc->height));
cvConvertScale(pSrc, pWavelet, 1, -128);
cvResetImageROI(pWavelet);
// 彩色图像小波变换
IplImage *pImage = cvCreateImage(cvGetSize(pWavelet), IPL_DEPTH_32F, 1);
if (pImage) {
for (int i = 1; i <= pWavelet->nChannels; i++) {
cvSetImageCOI(pWavelet, i);
cvCopy(pWavelet, pImage, NULL);
// 二维离散小波变换
DWT(pImage, nLayer);
// 二维离散小波恢复
// IDWT(pImage, nLayer);
cvCopy(pImage, pWavelet, NULL);
}
cvSetImageCOI(pWavelet, 0);
cvReleaseImage(&pImage);
}
// 小波变换图象
cvSetImageROI(pWavelet, cvRect(0, 0, pSrc->width, pSrc->height));
cvConvertScale(pWavelet, pSrc, 1, 128);
cvResetImageROI(pWavelet);
cvReleaseImage(&pWavelet);
}
// 显示图像pSrc
cv::namedWindow("result");
cvShowImage("result",pSrc);
cv::waitKey(0);
cvReleaseImage(&pSrc);
}
