提供函数DWT()和IDWT()，前者完成任意层次的小波变换，后者完成任意层次的小波逆变换。输入图像要求必须是单通道浮点图像，对图像大小也有要求（1层变换：w,h必须是2的倍数；2层变换：w,h必须是4的倍数；3层变换：w,h必须是8的倍数......），变换后的结果直接保存在输入图像中。
1、函数参数简单，图像指针pImage和变换层数nLayer。2、一个函数直接完成多层次二维小波变换，尽量减少下标运算，避免不必要的函数调用，以提高执行效率。3、变换过程中，使用了一个指针数组pData用于保存每行数据的起始位置，pRow和pColumn用于保存一行和一列临时数据，用于奇偶分离或合并，内存消耗较少。- 代码:
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// 二维离散小波变换（单通道浮点图像）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; } }}
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// 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); // 本行代码有点多余，但有利用养成良好的编程习惯 cvReleaseImage(&pWavelet);}// 显示图像pSrc// ...cvReleaseImage(&pSrc);