机器学习实践系列之14

来源：互联网发布：mac 最好的五笔输入法编辑：程序博客网时间：2024/05/18 03:49

关于 傅里叶变换，讲的太多了，这里我就不再啰嗦一遍了，原理的东西大家可以搜一下，推荐一篇文章：

如果看了此文你还不懂傅里叶变换，那就过来掐死我吧

这篇文章写得很不错了，从频域到傅里叶级数 讲的都比较细，而且都有配图，真看不懂的话就你掐死他吧！

（PS：冤冤相报何时了，我在一旁看热闹，横批：不嫌事大）

看下效果（居然暴漏了自己的迅雷，哈哈）：

参考代码：

/* linolzhang 2013.11   基于OpenCV的傅里叶变换及逆变换*/#include <iostream>  #include "opencv2/highgui/highgui.hpp"  #pragma comment(lib,"opencv_core2410.lib")  #pragma comment(lib,"opencv_highgui2410.lib")  //傅里叶正变换void fft2(IplImage *src, IplImage *dst){// 实部、虚部IplImage *image_Re = cvCreateImage(cvGetSize(src), IPL_DEPTH_64F, 1);IplImage *image_Im = cvCreateImage(cvGetSize(src), IPL_DEPTH_64F, 1);IplImage *Fourier = cvCreateImage(cvGetSize(src), IPL_DEPTH_64F, 2);cvConvertScale(src, image_Re); // 实部变换 u8 -> 64fcvZero(image_Im);              // 虚部变换 -> 0// MergecvMerge(image_Re, image_Im, 0, 0, Fourier);// DFT计算傅里叶变换cvDFT(Fourier, dst, CV_DXT_FORWARD);cvReleaseImage(&image_Re);cvReleaseImage(&image_Im);cvReleaseImage(&Fourier);}void fft2shift(IplImage *src, IplImage *dst){IplImage *image_Re = cvCreateImage(cvGetSize(src), IPL_DEPTH_64F, 1);IplImage *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 + MagcvLog(image_Re, image_Re); // log(1 + Mag)// Rearrange the quadrants of Fourier image so that the origin is at the image centerint cy = src->height / 2;int cx = src->width / 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(int j=0; j<cy; j++){for(int i=0; i<cx; i++){// 中心化，将整体份成四块进行对角交换double 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;double 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)]*255double minVal = 0, maxVal = 0;// Localize minimum and maximum valuescvMinMaxLoc( image_Re, &minVal, &maxVal );// Normalize image (0 - 255) to be observed as an u8 imagedouble scale = 255/(maxVal - minVal);double shift = -minVal * scale;cvConvertScale(image_Re, dst, scale, shift);cvReleaseImage(&image_Re);cvReleaseImage(&image_Im);}int main(int argc, char** argv){IplImage *src = NULL;if(argc != 2)  src = cvLoadImage("1.jpg", 0); // 加载源图像，转为单通道else  src = cvLoadImage(argv[1], 0);  IplImage *Fourier = cvCreateImage(cvGetSize(src),IPL_DEPTH_64F,2);  // 傅里叶系数IplImage *dst = cvCreateImage(cvGetSize(src),IPL_DEPTH_64F,2);IplImage *ImageRe = cvCreateImage(cvGetSize(src),IPL_DEPTH_64F,1);IplImage *ImageIm = cvCreateImage(cvGetSize(src),IPL_DEPTH_64F,1);IplImage *Image = cvCreateImage(cvGetSize(src),src->depth,src->nChannels);IplImage *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);// 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);double m,M;cvMinMaxLoc(ImageRe,&m,&M,NULL,NULL);double scale = 255/(M - m);double shift = -m * scale;// 将shift加在ImageRe各元素按比例缩放的结果上，存储为ImageDstcvConvertScale(ImageRe,ImageDst,scale,shift);cvShowImage("源图像",src); cvShowImage("傅里叶谱",Image);cvShowImage("傅里叶逆变换",ImageDst);cvWaitKey(0);// 释放资源cvReleaseImage(&src);cvReleaseImage(&Image);cvReleaseImage(&ImageIm);cvReleaseImage(&ImageRe);cvReleaseImage(&Fourier);cvReleaseImage(&dst);cvReleaseImage(&ImageDst);return 0;}

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