OpenCV计算机视觉图像频域傅里叶 DFT 变换低通滤波逆变换IDFT
实验室做图像的，经常用到这部分，为了检测屏幕，看过好多博客，试用过许多代码，这个算是我找到的比较好用的，也容易改。
傅里叶变换（DFT）变换
Mat padded; //expand input image to optimal sizeint a = getOptimalDFTSize(I.rows);int b = getOptimalDFTSize(I.cols); // on the border add zero valuescopyMakeBorder(I, padded, 0, a - I.rows, 0, b - I.cols, BORDER_CONSTANT, Scalar::all(0));for (int i = 0; i < padded.rows; i++)//中心化操作{float *ptr = padded.ptr<float>(i);for (int j = 0; j < padded.cols; j++)ptr[j] *= pow(-1, i + j);}Mat planes[] = { Mat_<float>(padded), Mat::zeros(padded.size(), CV_32F) };Mat complexI;merge(planes, 2, complexI); dft(complexI, complexI); // this way the result may fit in the source matrixcomplexI.convertTo(complexI, CV_32F);//转为浮点型数据*
处理DFT 变换的频谱图
Mat spectrogram1;spectrogram1 = complexI.clone();split(spectrogram1, planes);//分离通道 planes[0] = Re(DFT(I),planes[1]=Im(DFT(I)));magnitude(planes[0], planes[1], planes[0]);Mat magnitudeImage1 = planes[0];//进行对数尺度变换magnitudeImage1 += Scalar::all(1);log(magnitudeImage1, magnitudeImage1);normalize(magnitudeImage1, magnitudeImage1, 0, 1, NORM_MINMAX);magnitudeImage1 = magnitudeImage1 * 255;
想显示频谱图的话需要归一化到 0-255
高斯低通滤波
Mat gaussianBlur(padded.size(), CV_32FC2);//GuussianBlur low filterfloat D0 = 2 * 100 * 100;//该参数关乎滤波器的截止频率for (int i = 0; i < padded.rows; i++){float*p = gaussianBlur.ptr<float>(i);for (int j = 0; j < padded.cols; j++){float d = pow(i - padded.rows / 2, 2) + pow(j - padded.cols / 2, 2);p[2 * j] = expf(-d / D0);p[2 * j + 1] = expf(-d / D0);}}multiply(complexI, gaussianBlur, gaussianBlur);//滤波器和图像矩阵相乘
处理低通滤波后的频谱图
如果你想看一下滤波前后的频谱图有什么区别的话可以这样做
Mat spectrogram;spectrogram = gaussianBlur.clone();split(spectrogram, planes);//分离通道 planes[0] = Re(DFT(I),planes[1]=Im(DFT(I)));magnitude(planes[0], planes[1], planes[0]);Mat magnitudeImage = planes[0];//进行对数尺度变换magnitudeImage += Scalar::all(1);log(magnitudeImage, magnitudeImage);normalize(magnitudeImage, magnitudeImage, 0, 255, NORM_MINMAX);//magnitudeImage = magnitudeImage * 255;imwrite("\\\\Mac\\Home\\Downloads\\测试\\2低通滤波后的频谱图.bmp", magnitudeImage);//imwrite((*sendImg1).sNowTimeFileDir + to_string(cameraFlag) + to_string(pictureFlag) + "gaussian_spectrogram.png", magnitudeImage);
逆变换 IDFT
Mat iDft[] = { Mat::zeros(padded.size(),CV_32F),Mat::zeros(padded.size(),CV_32F) };idft(gaussianBlur, gaussianBlur, DFT_SCALE | DFT_REAL_OUTPUT); // IDFT进行DFT逆变换split(gaussianBlur, iDft);magnitude(iDft[0], iDft[1], iDft[0]);// normalize(iDft[0], iDft[0], 0, 1, CV_MINMAX);//iDft[0] = 255 * iDft[0];//去掉归一化Mat dst(iDft[0], Rect(0, 0, I.cols, I.rows));//之前扩过尺寸，现在截回来// Mat I(I, Rect(8, 5, I.cols - 10, I.rows - 10));blur(dst, dst, Size(7, 7));
完整版代码
void dftprocess(Mat &imgIn, Mat &imgOut, int cameraFlag, int pictureFlag){long t0 = GetTickCount();Mat I;cvtColor(imgIn, I, CV_BGR2GRAY);//Mat I = imread(filename, CV_LOAD_IMAGE_GRAYSCALE);I.convertTo(I, CV_32F);blur(I, I, Size(5, 5));Mat padded; //expand input image to optimal sizeint a = getOptimalDFTSize(I.rows);int b = getOptimalDFTSize(I.cols); // on the border add zero valuescopyMakeBorder(I, padded, 0, a - I.rows, 0, b - I.cols, BORDER_CONSTANT, Scalar::all(0));for (int i = 0; i < padded.rows; i++)//中心化操作{float *ptr = padded.ptr<float>(i);for (int j = 0; j < padded.cols; j++)ptr[j] *= pow(-1, i + j);}Mat planes[] = { Mat_<float>(padded), Mat::zeros(padded.size(), CV_32F) };Mat complexI;merge(planes, 2, complexI); // Add to the expanded another plane with zerosdft(complexI, complexI); // this way the result may fit in the source matrixcomplexI.convertTo(complexI, CV_32F);//转为浮点型数据*//****************************写DFT变换后的频谱图*********************Mat spectrogram1;spectrogram1 = complexI.clone();split(spectrogram1, planes);//分离通道 planes[0] = Re(DFT(I),planes[1]=Im(DFT(I)));magnitude(planes[0], planes[1], planes[0]);Mat magnitudeImage1 = planes[0];//进行对数尺度变换magnitudeImage1 += Scalar::all(1);log(magnitudeImage1, magnitudeImage1);normalize(magnitudeImage1, magnitudeImage1, 0, 1, NORM_MINMAX);magnitudeImage1 = magnitudeImage1 * 255;//imwrite((*sendImg1).sNowTimeFileDir + to_string(cameraFlag) + to_string(pictureFlag) + "DFT_spectrogram.png", magnitudeImage1);imwrite("\\\\Mac\\Home\\Downloads\\测试\\1DFTimg.bmp", magnitudeImage1);/************************gaussian****************************/Mat gaussianBlur(padded.size(), CV_32FC2);//GuussianBlur low filterfloat D0 = 2 * 100000 * 100000;//低通截止频率设为100最合适for (int i = 0; i < padded.rows; i++){float*p = gaussianBlur.ptr<float>(i);for (int j = 0; j < padded.cols; j++){float d = pow(i - padded.rows / 2, 2) + pow(j - padded.cols / 2, 2);p[2 * j] = expf(-d / D0);p[2 * j + 1] = expf(-d / D0);}}multiply(complexI, gaussianBlur, gaussianBlur);//****************************写高斯滤波后的频谱图*********************Mat spectrogram;spectrogram = gaussianBlur.clone();split(spectrogram, planes);//分离通道 planes[0] = Re(DFT(I),planes[1]=Im(DFT(I)));magnitude(planes[0], planes[1], planes[0]);Mat magnitudeImage = planes[0];//进行对数尺度变换magnitudeImage += Scalar::all(1);log(magnitudeImage, magnitudeImage);normalize(magnitudeImage, magnitudeImage, 0, 255, NORM_MINMAX);//magnitudeImage = magnitudeImage * 255;imwrite("\\\\Mac\\Home\\Downloads\\测试\\2低通滤波后的频谱图.bmp", magnitudeImage);//imwrite((*sendImg1).sNowTimeFileDir + to_string(cameraFlag) + to_string(pictureFlag) + "gaussian_spectrogram.png", magnitudeImage);/**********************逆变换****************************/Mat iDft[] = { Mat::zeros(padded.size(),CV_32F),Mat::zeros(padded.size(),CV_32F) };idft(gaussianBlur, gaussianBlur, DFT_SCALE | DFT_REAL_OUTPUT); // IDFT进行DFT逆变换split(gaussianBlur, iDft);magnitude(iDft[0], iDft[1], iDft[0]);// normalize(iDft[0], iDft[0], 0, 1, CV_MINMAX);//iDft[0] = 255 * iDft[0];//去掉归一化Mat dst(iDft[0], Rect(0, 0, I.cols, I.rows));// Mat I(I, Rect(8, 5, I.cols - 10, I.rows - 10));blur(dst, dst, Size(7, 7));//imwrite("C:\\dsm0730高斯测试\\对逆变换截取图.png", dst);imwrite("\\\\Mac\\Home\\Downloads\\测试\\3IDFTimg.bmp", dst);
行吧，第一篇博客诞生了。冈萨雷斯的数字图像处理太深奥，我就是个菜菜。实验室项目中多次用到频域变换，干脆我就写个博客吧。欢迎留言
