DFT to spatial domain in OpenCV is not working

Question

I have created dft of an image and after some adjustment with filters i want to convert it back to the real image but every time when i do that it gives me wrong result ..seems like its not converting it back. ForierTransform and createGaussianHighPassFilter are my own functions rest of the code i am using like below for the inversion back to real image.

Mat fft = ForierTransform(HeightPadded,WidthPadded);
Mat ghpf = createGaussianHighPassFilter(Size(WidthPadded, HeightPadded), db);
Mat res;
cv::multiply(fft,ghpf,res);
imshow("fftXhighpass1", res);
idft(res,res,DFT_INVERSE,res.rows);
cv::Mat croped = res(cv::Rect(0, 0, img.cols,img.rows));

//res.convertTo(res,CV_32S);
imshow("fftXhighpass", res);

even if i dont apply the filter i am unable to reverse back dft result ... here is my dft code is , i could not find any sample to reverse dft back to normal image..

Mat ForierTransform(int M,int N)
{
    Mat img = imread("thumb1-small-test.jpg", CV_LOAD_IMAGE_GRAYSCALE);
    Mat padded;
    copyMakeBorder(img, padded, 0, M - img.rows, 0, N - img.cols, BORDER_CONSTANT, Scalar::all(0));

    Mat planes[] = {Mat_<float>(padded), Mat::zeros(padded.size(), CV_32F)};
    Mat complexImg;
    merge(planes, 2, complexImg);

    dft(complexImg, complexImg);


    split(complexImg, planes);
    magnitude(planes[0], planes[1], planes[0]);
    Mat mag = planes[0];
    mag += Scalar::all(1);
    log(mag, mag);

        // crop the spectrum, if it has an odd number of rows or columns
    mag = mag(Rect(0, 0, mag.cols & -2, mag.rows & -2));


    normalize(mag, mag, 0, 1, CV_MINMAX);
    return mag;
}

kindly help

[EDIT: After I found the solution with the help of mevatron] (below is the correct code)

 Mat ForierTransform(int M,int N)
{
    Mat img = imread("thumb1-small-test.jpg", CV_LOAD_IMAGE_GRAYSCALE);
    Mat padded;
    copyMakeBorder(img, padded, 0, M - img.rows, 0, N - img.cols, BORDER_CONSTANT, Scalar::all(0));

    Mat planes[] = {Mat_<float>(padded), Mat::zeros(padded.size(), CV_32F)};
    Mat complexImg;
    merge(planes, 2, complexImg);

    dft(complexImg, complexImg);

    return complexImg;
}

Mat img = imread("thumb1-small-test.jpg",CV_LOAD_IMAGE_GRAYSCALE);
int WidthPadded=0,HeightPadded=0;
WidthPadded=img.cols*2;
HeightPadded=img.rows*2;
int M = getOptimalDFTSize( img.rows );
//Create a Gaussian Highpass filter 5% the height of the Fourier transform
double db  = 0.05 * HeightPadded;


Mat fft = ForierTransform(HeightPadded,WidthPadded);
Mat ghpf = createGaussianHighPassFilter(Size(WidthPadded, HeightPadded), db);
Mat res;

cv::mulSpectrums(fft,ghpf,res,DFT_COMPLEX_OUTPUT);


idft(res,res,DFT_COMPLEX_OUTPUT,img.rows);

Mat padded;
copyMakeBorder(img, padded, 0, img.rows, 0, img.cols, BORDER_CONSTANT, Scalar::all(0));
Mat planes[] = {Mat_<float>(padded), Mat::zeros(padded.size(), CV_32F)};
split(res, planes);
magnitude(planes[0], planes[1], planes[0]);
Mat mag = planes[0];
mag += Scalar::all(1);
log(mag, mag);

// crop the spectrum, if it has an odd number of rows or columns
mag = mag(Rect(0, 0, mag.cols & -2, mag.rows & -2));

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

normalize(mag, mag, 1, 0, CV_MINMAX);

cv::Mat croped = mag(cv::Rect(cx, cy, img.cols,img.rows));
cv::threshold(croped , croped , 0.56, 1, cv::THRESH_BINARY);

imshow("fftPLUShpf", mag);
imshow("cropedBinary", croped);

It now can able to display ridges valley of finger , and can be more optimize with respect to threshold as well

Answer 1

I see a few problems going on here.

First, you need to use the mulSpectrums function to convolve two FFTs, and not multiply.

Second, the createGaussianHighPassFilter is only outputting a single channel non-complex filter. You'll probably need to just set the complex channel to Mat::zeros like you did for your input image.

Third, don't convert the output of the FFT to log-magnitude spectrum. It will not combine correctly with the filter, and you won't get the same thing when performing the inverse. So, just return complexImg right after the DFT is executed. Log-magnitude spectrum is useful for a human to look at the data, but not for what you are trying to do.

Finally, make sure you pay attention to the difference to between the full-complex output of dft and the Complex Conjugate Symmetric (CCS) packed output. Intel has a good page on how this data is formatted here. In your case, for simplicity I would keep everything in full-complex mode to make your life easier.

Hope that helps!