implementation of DFT in C++

Question

I want to implement the DFT (Discrete Fourier Transform) in C++ language to process images.

As I was studying the theory, I got to know, that I can divide the 2D DFT into two 1D DFT parts. Firstly, for each row I perform 1D DFT then I do it for each column. Of course, I should make operations on complex numbers.

Here occur some problems, because I am not sure where to use real, and where imaginary part of the complex number. I found somewhere, that the values of the input image pixels I should treat as a real part with the imaginary part set as 0.

I made an implementation of that, but I suppose that the result image is incorrect.

I would be grateful if someone could help me with that one.

For reading and saving images I use CImg library.

void DFT (CImg<unsigned char> image)
{
    int w=512;
    int h=512;
    int rgb=3;
    complex <double> ***obrazek=new complex <double>**[w];
    for (int b=0;b<w;b++) //making 3-dimensional table to store DFT values
    {
        obrazek[b]=new complex <double>*[h];
        for (int a=0;a<h;a++)
        {
            obrazek[b][a]=new complex <double>[rgb];
        }
    }

    CImg<unsigned char> kopia(image.width(),image.height(),1,3,0);

    complex<double> sum=0;
    complex<double> sum2=0;
    double pi = 3.14;

    for (int i=0; i<512; i++){
    for (int j=0; j<512; j++){
    for (int c=0; c<3; c++){
        complex<double> cplx(image(i,j,c), 0);
        obrazek[i][j][c]=cplx;
    }}}

    for (int c=0; c<3; c++) //for rows
    {
            for (int y=0; y<512; y++)
            {
                sum=0;
                for (int x=0; x<512; x++)
                {
                    sum+=(obrazek[x][y][c].real())*cos((2*pi*x*y)/512)-(obrazek[x][y][c].imag())*sin((2*pi*x*y)/512);
                    obrazek[x][y][c]=sum;
                }
            }
    }

    for (int c=0; c<3; c++) //for columns
    {
            for (int y=0; y<512; y++)//r
            {
                sum2=0;
                for (int x=0; x<512; x++)
                {
                    sum2+=(obrazek[y][x][c].real())*cos((2*pi*x*y)/512)-(obrazek[y][x][c].imag())*sin((2*pi*x*y)/512);
                    obrazek[y][x][c]=sum2;
                }
            }
    }

    for (int i=0; i<512; i++){
    for (int j=0; j<512; j++){
    for (int c=0; c<3; c++){
        kopia(i,j,c)=obrazek[i][j][c].real();
    }}}

    CImgDisplay image_disp(kopia,"dft");

    while (!image_disp.is_closed() )
    {

        image_disp.wait();

    }
    saving(kopia);
}