基于Opencv的DFT离散傅里叶变换

傅立叶图像

常用函数

过程解释

代码

#include "opencv2/imgproc/imgproc.hpp"
#include "opencv2/highgui/highgui.hpp"
#include 
using namespace cv;
int main( )
{
 
	Mat srcImage = imread("lena.jpg", 0);
	if(!srcImage.data ) { printf("读取图片错误，请确定目录下是否有imread函数指定图片存在~！ \n"); return false; } 
	imshow("原始图像" , srcImage);   
	int m = getOptimalDFTSize( srcImage.rows );
	int n = getOptimalDFTSize( srcImage.cols ); 
	Mat padded;  
	copyMakeBorder(srcImage, padded, 0, m - srcImage.rows, 0, n - srcImage.cols, BORDER_CONSTANT, Scalar::all(0));
	Mat planes[] = {Mat_(padded), Mat::zeros(padded.size(), CV_32F)};
	Mat complexI;
	merge(planes, 2, complexI);         
	dft(complexI, complexI);           
	split(complexI, planes); 
	magnitude(planes[0], planes[1], planes[0]);
	Mat magnitudeImage = planes[0];
	magnitudeImage += Scalar::all(1);
	log(magnitudeImage, magnitudeImage);//求自然对数     
	magnitudeImage = magnitudeImage(Rect(0, 0, magnitudeImage.cols & -2, magnitudeImage.rows & -2));  
	int cx = magnitudeImage.cols/2;
	int cy = magnitudeImage.rows/2;
	Mat q0(magnitudeImage, Rect(0, 0, cx, cy));   // ROI区域的左上
	Mat q1(magnitudeImage, Rect(cx, 0, cx, cy));  // ROI区域的右上
	Mat q2(magnitudeImage, Rect(0, cy, cx, cy));  // ROI区域的左下
	Mat q3(magnitudeImage, Rect(cx, cy, cx, cy)); // ROI区域的右下
	Mat tmp;                           
	q0.copyTo(tmp);
	q3.copyTo(q0);
	tmp.copyTo(q3);
	q1.copyTo(tmp);                 
	q2.copyTo(q1);
	tmp.copyTo(q2);
	normalize(magnitudeImage, magnitudeImage, 0, 1, NORM_MINMAX); 
	imshow("频谱幅值", magnitudeImage);    
	waitKey();
	return 0;
}

效果

Matlab的实现代码

I = rgb2gray(imread('d:\lena.jpg'));  
fcoef=fft2(double(I));            %FFT变换  
tmp1 =log(1+abs(fcoef));  
spectrum = fftshift(fcoef);        %调整中心  
tmp2 = log(1+abs(spectrum));  
ifcoef = ifft2(fcoef);            %逆变换  
  
figure                            %显示处理结果  
subplot(2,2,1), imshow(I), title('source image');  
subplot(2,2,2), imshow(tmp1,[]), title('FFT image');  
subplot(2,2,3), imshow(tmp2,[]), title('shift FFT image');  
subplot(2,2,4), imshow(ifcoef,[]), title('IFFT image');  

Matlab的实现效果

参考网址

https://blog.csdn.net/qq_20823641/article/details/52335018