opencv 中 傅里叶变换 FFT

【原文：http://blog.csdn.net/abcjennifer/article/details/7359952】

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 void fft2(IplImage *src, IplImage *dst)
 {   //实部、虚部
     IplImage *image_Re = 0, *image_Im = 0, *Fourier = 0;
     //   int i, j;
     image_Re = cvCreateImage(cvGetSize(src), IPL_DEPTH_64F, 1);  //实部
     //Imaginary part
     image_Im = cvCreateImage(cvGetSize(src), IPL_DEPTH_64F, 1);  //虚部
     //2 channels (image_Re, image_Im)
     Fourier = cvCreateImage(cvGetSize(src), IPL_DEPTH_64F, 2);
     // Real part conversion from u8 to 64f (double)
     cvConvertScale(src, image_Re);
     // Imaginary part (zeros)
     cvZero(image_Im);
     // Join real and imaginary parts and stock them in Fourier image
     cvMerge(image_Re, image_Im, 0, 0, Fourier);

     // Application of the forward Fourier transform
     cvDFT(Fourier, dst, CV_DXT_FORWARD);
     cvReleaseImage(&image_Re);
     cvReleaseImage(&image_Im);
     cvReleaseImage(&Fourier);
 }

 void fft2shift(IplImage *src, IplImage *dst)
 {
     IplImage *image_Re = 0, *image_Im = 0;
     int nRow, nCol, i, j, cy, cx;
     double scale, shift, tmp13, tmp24;
     image_Re = cvCreateImage(cvGetSize(src), IPL_DEPTH_64F, 1);
     //Imaginary part
     image_Im = cvCreateImage(cvGetSize(src), IPL_DEPTH_64F, 1);
     cvSplit( src, image_Re, image_Im, 0, 0 );
     //具体原理见冈萨雷斯数字图像处理p123
     // Compute the magnitude of the spectrum Mag = sqrt(Re^2 + Im^2)
     //计算傅里叶谱
     cvPow( image_Re, image_Re, 2.0);
     cvPow( image_Im, image_Im, 2.0);
     cvAdd( image_Re, image_Im, image_Re);
     cvPow( image_Re, image_Re, 0.5 );
     //对数变换以增强灰度级细节(这种变换使以窄带低灰度输入图像值映射
     //一宽带输出值，具体可见冈萨雷斯数字图像处理p62)
     // Compute log(1 + Mag);
     cvAddS( image_Re, cvScalar(1.0), image_Re ); // 1 + Mag
     cvLog( image_Re, image_Re ); // log(1 + Mag)

     //Rearrange the quadrants of Fourier image so that the origin is at the image center
     nRow = src->height;
     nCol = src->width;
     cy = nRow/2; // image center
     cx = nCol/2;
     //CV_IMAGE_ELEM为OpenCV定义的宏，用来读取图像的像素值，这一部分就是进行中心变换
     for( j = 0; j < cy; j++ ){
         for( i = 0; i < cx; i++ ){
             //中心化，将整体份成四块进行对角交换
             tmp13 = CV_IMAGE_ELEM( image_Re, double, j, i);
             CV_IMAGE_ELEM( image_Re, double, j, i) = CV_IMAGE_ELEM(
                 image_Re, double, j+cy, i+cx);
             CV_IMAGE_ELEM( image_Re, double, j+cy, i+cx) = tmp13;

             tmp24 = CV_IMAGE_ELEM( image_Re, double, j, i+cx);
             CV_IMAGE_ELEM( image_Re, double, j, i+cx) =
                 CV_IMAGE_ELEM( image_Re, double, j+cy, i);
             CV_IMAGE_ELEM( image_Re, double, j+cy, i) = tmp24;
         }
     }
     //归一化处理将矩阵的元素值归一为[0,255]
     //[(f(x,y)-minVal)/(maxVal-minVal)]*255
     double minVal = 0, maxVal = 0;
     // Localize minimum and maximum values
     cvMinMaxLoc( image_Re, &minVal, &maxVal );
     // Normalize image (0 - 255) to be observed as an u8 image
     scale = 255/(maxVal - minVal);
     shift = -minVal * scale;
     cvConvertScale(image_Re, dst, scale, shift);
     cvReleaseImage(&image_Re);
     cvReleaseImage(&image_Im);
 }

 void CCVMFCView::OnFuliyeTransform()
 {
     IplImage *src;
     IplImage *Fourier;   //傅里叶系数
     IplImage *dst ;
     IplImage *ImageRe;
     IplImage *ImageIm;
     IplImage *Image;
     IplImage *ImageDst;
     double m,M;
     double scale;
     double shift;
     //src = workImg;
     if(workImg->nChannels==3)
         OnColorToGray();
     src=cvCreateImage(cvGetSize(workImg),IPL_DEPTH_64F,workImg->nChannels);  //源图像
     imageClone(workImg,&src);
     cvFlip(src);

     Fourier = cvCreateImage(cvGetSize(src),IPL_DEPTH_64F,2);
     dst = cvCreateImage(cvGetSize(src),IPL_DEPTH_64F,2);
     ImageRe = cvCreateImage(cvGetSize(src),IPL_DEPTH_64F,1);
     ImageIm = cvCreateImage(cvGetSize(src),IPL_DEPTH_64F,1);
     Image = cvCreateImage(cvGetSize(src),src->depth,src->nChannels);
     ImageDst = cvCreateImage(cvGetSize(src),src->depth,src->nChannels);
     fft2(src,Fourier);                  //傅里叶变换
     fft2shift(Fourier, Image);          //中心化
     cvDFT(Fourier,dst,CV_DXT_INV_SCALE);//实现傅里叶逆变换，并对结果进行缩放
     cvSplit(dst,ImageRe,ImageIm,0,0);

     cvNamedWindow("源图像",0);
     cvShowImage("源图像",src);
     //对数组每个元素平方并存储在第二个参数中
     cvPow(ImageRe,ImageRe,2);
     cvPow(ImageIm,ImageIm,2);
     cvAdd(ImageRe,ImageIm,ImageRe,NULL);
     cvPow(ImageRe,ImageRe,0.5);
     cvMinMaxLoc(ImageRe,&m,&M,NULL,NULL);
     scale = 255/(M - m);
     shift = -m * scale;
     //将shift加在ImageRe各元素按比例缩放的结果上，存储为ImageDst
     cvConvertScale(ImageRe,ImageDst,scale,shift);

     cvNamedWindow("傅里叶谱",0);
     cvShowImage("傅里叶谱",Image);
     cvNamedWindow("傅里叶逆变换",0);
     cvShowImage("傅里叶逆变换",ImageDst);
     //释放图像
     cvWaitKey(10000);
     cvReleaseImage(&src);
     cvReleaseImage(&Image);
     cvReleaseImage(&ImageIm);
     cvReleaseImage(&ImageRe);
     cvReleaseImage(&Fourier);
     cvReleaseImage(&dst);
     cvReleaseImage(&ImageDst);
     Invalidate();
 }