OpenCV中的逆傅立叶变换

问题描述

我是 OpenCV 和图像处理算法的新手.我需要在 C++ 中的 OpenCV 中进行逆离散傅立叶变换，但我不知道如何.我在互联网上搜索，我没有找到答案.我正在使用此页面中的此代码在我的程序中进行傅立叶变换:http://opencv.itseez.com/doc/tutorials/core/discrete_fourier_transform/discrete_fourier_transform.html.我试图与该代码相反，但我不知道我做错了什么.我的代码在这里(我认为整个代码是错误的):

I am new in OpenCV and image processing algorithms. I need to do inverse discrete fourier transformation in OpenCV in C++, but I don't know how. I searched over internet and I didn't find answer. I am doing fourier transformation in my program with this code from this page: http://opencv.itseez.com/doc/tutorials/core/discrete_fourier_transform/discrete_fourier_transform.html. I have tried to do inverse to that code, but I don't know where I am doing wrong. My code is here (I think that whole code is wrong):

void doFourierInverse(const Mat &src, Mat &dst) {
  normalize(src, dst, 0, -1, CV_MINMAX); 

  int cx = dst.cols/2;
  int cy = dst.rows/2;

  Mat q0(dst, Rect(0, 0, cx, cy));   
  Mat q1(dst, Rect(cx, 0, cx, cy));  
  Mat q2(dst, Rect(0, cy, cx, cy));  
  Mat q3(dst, Rect(cx, cy, cx, cy)); 

  Mat tmp;         
  q0.copyTo(tmp);
  q3.copyTo(q0);
  tmp.copyTo(q3);

  q1.copyTo(tmp);      
  q2.copyTo(q1);
  tmp.copyTo(q2);

  dst = dst(Rect(0, 0, dst.cols & -2, dst.rows & -2));

  exp(dst, dst);
  dst -= Scalar::all(1);  

  Mat planes[2];

  polarToCart(dst, Mat::zeros(dst.rows, dst.cols, dst.type()), planes[0], planes[1]);

  merge(planes, 2, dst);    

  idft(dst, dst, DFT_INVERSE | DFT_SCALE); 

  split(dst, planes);   

  dst = planes[0];
}

推荐答案

实际上，您不必交换不同的象限，只有当您是人类并且希望 FFT 结果看起来更自然时才需要它(即中间为 0 频率，左/下为负频率，上/右为正频率).

Actually, you don't have to swap the different quadrants, it's needed only if you're a human and want a more natural looking visualization of the FFT result (i.e. with the 0 frequency in the middle, negative frequencies left/bottom and positive frequencies up/right).

要反转 FFT，您需要将前向变换的结果按原样"(或在您想要的频率过滤之后)传递给相同的 dft() 函数，只需添加标志 DFT_INVERSE.如果你还记得你关于 FFT 的数学，前向和后向变换在公式中有着非常紧密的扭结......

To invert the FFT, you need to pass the result of the forward transform "as is" (or after the frequency filtering you wanted) to the same dft() function, only adding the flag DFT_INVERSE. If you remember your math about FFT, the forward and backward transforms have very tight kinks in the formulation...

--- 编辑---

究竟是什么不起作用?以下代码确实执行了前向后向 FFT，一切都按预期工作.

What exactly doesn't work ? The following code does perform forward-then-backward FFT, and everything works just fine as expected.

// Load an image
cv::Mat inputImage = cv::imread(argv[argc-1], 0);

// Go float
cv::Mat fImage;
inputImage.convertTo(fImage, CV_32F);

// FFT
std::cout << "Direct transform...
";
cv::Mat fourierTransform;
cv::dft(fImage, fourierTransform, cv::DFT_SCALE|cv::DFT_COMPLEX_OUTPUT);

// Some processing
doSomethingWithTheSpectrum();

// IFFT
std::cout << "Inverse transform...
";
cv::Mat inverseTransform;
cv::dft(fourierTransform, inverseTransform, cv::DFT_INVERSE|cv::DFT_REAL_OUTPUT);

// Back to 8-bits
cv::Mat finalImage;
inverseTransform.convertTo(finalImage, CV_8U);

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