Drawing spectrum of an image in C++ (fftw, OpenCV)

Question

I'm trying to create a program that will draw a 2d greyscale spectrum of a given image. I'm using OpenCV and FFTW libraries. By using tips and codes from the internet and modifying them I've managed to load an image, calculate fft of this image and recreate the image from the fft (it's the same). What I'm unable to do is to draw the fourier spectrum itself. Could you please help me? Here's the code (less important lines removed):

/* Copy input image */

/* Create output image */

/* Allocate input data for FFTW */
in   = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) * N);
dft  = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) * N);

/* Create plans */
plan_f = fftw_plan_dft_2d(w, h, in, dft, FFTW_FORWARD, FFTW_ESTIMATE);

/* Populate input data in row-major order */
for (i = 0, k = 0; i < h; i++) 
{
    for (j = 0; j < w; j++, k++)
    {
        in[k][0] = ((uchar*)(img1->imageData + i * img1->widthStep))[j];
        in[k][1] = 0.;
    }
}

/* forward DFT */
fftw_execute(plan_f);

/* spectrum */
for (i = 0, k = 0; i < h; i++)
{
    for (j = 0; j < w; j++, k++)
        ((uchar*)(img2->imageData + i * img2->widthStep))[j] = sqrt(pow(dft[k][0],2) + pow(dft[k][1],2));
}       

cvShowImage("iplimage_dft(): original", img1);
cvShowImage("iplimage_dft(): result", img2);
cvWaitKey(0);

/* Free memory */

}

The problem is in the "Spectrum" section. Instead of a spectrum I get some noise. What am I doing wrong? I would be grateful for your help.

Sounds like a scaling problem - you should check the range of your FFT output magnitude values. — Paul R, Jul 31 '11 at 17:30
And could you suggest how should I do that? From what I read on different forums, if it was about the magnitude I would get a black image (with a white dot in the center). Thank you for your answer. — Narren, Jul 31 '11 at 17:50
Since you're not doing any range checking on the magnitude, then if it's large it will wrap modulo 2 when you assign it to an 8 bit pixel (and it will look like noise). That's why I said you should check the range - e.g. add another loop to find the max and min magnitude and then scale your values accordingly so that you know they will fit in an 8 bit range. — Paul R, Jul 31 '11 at 18:25
Apply log scaling to the power spectrum then rescale data to fit in [0,255]. — jeff7, Aug 01 '11 at 11:31
I checked the highest value (and the lowest), then I divided output data by that value and multiplied it by 255. I now have a black image with one white dot. I read that such problem is when we work with integers instead of float. But in my case, as you can see I'm saving output data directly to the image img2. There are no variables in between. What am I doing wrong now? — Narren, Aug 02 '11 at 14:33

score 2 · Answer 1 · answered Aug 16 '12 at 08:22

You need to draw magnitude of spectrum. here is the code.

void ForwardFFT(Mat &Src, Mat *FImg)
{
    int M = getOptimalDFTSize( Src.rows );
    int N = getOptimalDFTSize( Src.cols );
    Mat padded;    
    copyMakeBorder(Src, padded, 0, M - Src.rows, 0, N - Src.cols, BORDER_CONSTANT, Scalar::all(0));
    // Создаем комплексное представление изображения
    // planes[0] содержит само изображение, planes[1] его мнимую часть (заполнено нулями)
    Mat planes[] = {Mat_<float>(padded), Mat::zeros(padded.size(), CV_32F)};
    Mat complexImg;
    merge(planes, 2, complexImg); 
    dft(complexImg, complexImg);    
    // После преобразования результат так-же состоит из действительной и мнимой части
    split(complexImg, planes);

    // обрежем спектр, если у него нечетное количество строк или столбцов
    planes[0] = planes[0](Rect(0, 0, planes[0].cols & -2, planes[0].rows & -2));
    planes[1] = planes[1](Rect(0, 0, planes[1].cols & -2, planes[1].rows & -2));

    Recomb(planes[0],planes[0]);
    Recomb(planes[1],planes[1]);
    // Нормализуем спектр
    planes[0]/=float(M*N);
    planes[1]/=float(M*N);
    FImg[0]=planes[0].clone();
    FImg[1]=planes[1].clone();
}
void ForwardFFT_Mag_Phase(Mat &src, Mat &Mag,Mat &Phase)
{
    Mat planes[2];
    ForwardFFT(src,planes);
    Mag.zeros(planes[0].rows,planes[0].cols,CV_32F);
    Phase.zeros(planes[0].rows,planes[0].cols,CV_32F);
    cv::cartToPolar(planes[0],planes[1],Mag,Phase);
}
Mat LogMag;
    LogMag.zeros(Mag.rows,Mag.cols,CV_32F);
    LogMag=(Mag+1);
    cv::log(LogMag,LogMag);
    //---------------------------------------------------
    imshow("Логарифм амплитуды", LogMag);
    imshow("Фаза", Phase);
    imshow("Результат фильтрации", img);

score 0 · Answer 2 · answered Sep 01 '11 at 07:38

Can you try to do the IFFT step and see if you recover the original image ? then , you can check step by step where is your problem. Another solution to find the problem is to do this process with a small matrix predefined by you ,and calculate it FFT in MATLAB, and check step by step, it worked for me!

Drawing spectrum of an image in C++ (fftw, OpenCV)

2 Answers2