OpenCV实现傅里叶变换

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<span style="font-size:18px;">#include <stdio.h>

#include <cv.h>

#include <cxcore.h>

#include <highgui.h>

/**************************************************************************

//傅里叶变换

//src IPL_DEPTH_8U

//dst IPL_DEPTH_64F

/**************************************************************************/

void fft2(IplImage *src, IplImage *dst)

{

IplImage *image_Re = 0, *image_Im = 0, *Fourier = 0; //实部、虚部

image_Re = cvCreateImage(cvGetSize(src), IPL_DEPTH_64F, 1); //实部

image_Im = cvCreateImage(cvGetSize(src), IPL_DEPTH_64F, 1); //虚部

Fourier = cvCreateImage(cvGetSize(src), IPL_DEPTH_64F, 2);//2 channels (image_Re, image_Im)

cvConvertScale(src, image_Re, 1, 0);// Real part conversion from u8 to 64f (double)

cvZero(image_Im);// Imaginary part (zeros)

cvMerge(image_Re, image_Im, 0, 0, Fourier);// Join real and imaginary parts and stock them in Fourier image

cvDFT(Fourier, dst, CV_DXT_FORWARD);// Application of the forward Fourier transform

cvReleaseImage(&image_Re);

cvReleaseImage(&image_Im);

cvReleaseImage(&Fourier);

}

/**************************************************************************

//中心化

//src IPL_DEPTH_64F

//dst IPL_DEPTH_8U

**************************************************************************/

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);

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;

cx = nCol/2; cy = nRow/2; // image center

//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);

}

/***********************************************************************/

int main()

{

IplImage *src; //源图像

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 = cvLoadImage("C:\\Users\\freeboy1015\\Desktop\\学习资料\\例图\\lena.jpg",0); //加载源图像，第二个参数表示将输入的图片转为单信道

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);

cvWaitKey(0);

cvReleaseImage(&src);

cvReleaseImage(&Image);

cvReleaseImage(&ImageIm);

cvReleaseImage(&ImageRe);

cvReleaseImage(&Fourier);

cvReleaseImage(&dst);

cvReleaseImage(&ImageDst);

cvDestroyAllWindows();

return 0;

}</span>