opencv 中 快速傅里叶变换 FFT

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();
}