C++ Image 2D Fast Fourier Transform

Question

I have to implement 2D FFT transform on the image (I cannot use library to do it for me - part of the course). I use CImg to load and save images. I have made the following code:

CImg<Complex> FastFourier(CImg<unsigned char> &originalImage)
{
    //check size in the main.cpp
    CImg<Complex> resultantImage = TransformToComplex(originalImage);
    vector< vector< vector< Complex > > > vectorImage = imageToVector(resultantImage);
    //cout << "Transform to complex" << endl;
    int size = originalImage.width();

    for(int i = 0; i < size; i++)
        FastFourier1D(vectorImage[i], false);

    vectorImage = rotateVector(vectorImage);

    for(int i = 0; i < size; i++)
       FastFourier1D(vectorImage[i], false);

    vectorImage = rotateVector(vectorImage);

    resultantImage = vectorToImage(vectorImage);

    return resultantImage;
}

And:

void FastFourier1D(vector< vector< Complex > > &input, bool inverse)
{
    int size = input.size();
    double angle;

    if(size <= 1)
        return;

    int channels = input[0].size();
    vector< vector< Complex > > even;
    vector< vector< Complex > > odd;

    for(int i = 0; i < size; i+=2)
    {
        vector< Complex > tempEven;
        vector< Complex > tempOdd;
        for(int channelIterator = 0; channelIterator < channels; channelIterator++)
        {
            tempEven.push_back(input[i][channelIterator]);
            tempOdd.push_back(input[i + 1][channelIterator]);
        }

        even.push_back(tempEven);
        odd.push_back(tempOdd);
    }

    FastFourier1D(even, inverse);
    FastFourier1D(odd, inverse);

    for(int channelIterator = 0; channelIterator < channels; channelIterator++)
    {
        for(int i = 0; i < size / 2; i++)
        {
           if(inverse == false)
               angle = -2.0 * (double)PI * (double)i / (double)size;
           else
               angle = 2.0 * (double)PI * (double)i / (double)size;

           double real = cos(angle);
           double imaginary = sin(angle);

           Complex W;
           W.setRP(real);
           W.setIP(imaginary);

           W = W * odd[i][channelIterator];

           input[i][channelIterator] = even[i][channelIterator] + W;
           input[(size / 2) + i][channelIterator] = even[i][channelIterator] - W;
       }
    }
}

However the results are not good. Input image:

FFT (without any transform):

Inverse FFT:

Inverse FFT

As you can see, it has colors of lena, but does not look like lena. Could you help me? Is there any mistake?

In your first code snippet, both times `FastFourier1D` is called, you pass `false` into `inverse`. Is this intentional? — Obicere, Dec 31 '17 at 01:34
Yes, it is intentional because it is „forward” fourier. Inverse is pretty much the same with „true” passed. I have to call it twice because in 2D fourier I have to change rows with columns after first pass. — mgrzellak, Dec 31 '17 at 01:40
Just a suggestion for debugging. Why not trying simpler images instead of Lena? See this for ideas: www.fmwconcepts.com/misc_tests/FFT_tests/index.html — VladP, Jan 03 '18 at 16:05
If this isn't an homework, you can use [`std::complex`](http://en.cppreference.com/w/cpp/numeric/complex) instead of your own class. — Bob__, Jan 06 '18 at 14:14
Thanks, as I wrote in the answer I found out my multiplication operator had wrong implementation. Now, everything works correctly. — mgrzellak, Jan 07 '18 at 15:36

score 1 · Accepted Answer · edited Nov 02 '19 at 03:07

I found out that the answer was an incorrect implementation of multiplication operator in my Complex class.

Complex Complex::operator*(const Complex& a)
{
    Complex number;
    double RP = realPart * a.getRP() - imaginaryPart * a.getIP(); // this line was wrong
    double IP = realPart * a.getIP() + imaginaryPart * a.getRP();
    number.setRP(RP);
    number.setIP(IP);
    return number;
}

In real part, I forgot about minus. Now the whole implementation is working and fourier successfully converts an image into frequency domain and makes inverse into spatial domain as well.

C++ Image 2D Fast Fourier Transform

1 Answers1