OpenCV实现傅里叶变换

#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;
}