i want to use a homomorphic filter to work on underwater image. I tried to code it with the codes found on the internet but i have always a black image... I tried to normalized my result but didn't work.

Here my functions :

```
void HomomorphicFilter::butterworth_homomorphic_filter(Mat &dft_Filter, int D, int n, float high_h_v_TB, float low_h_v_TB)
{
Mat single(dft_Filter.rows, dft_Filter.cols, CV_32F);
Point centre = Point(dft_Filter.rows/2, dft_Filter.cols/2);
double radius;
float upper = (high_h_v_TB * 0.01);
float lower = (low_h_v_TB * 0.01);

//create essentially create a butterworth highpass filter
//with additional scaling and offset
for(int i = 0; i < dft_Filter.rows; i++)
{
    for(int j = 0; j < dft_Filter.cols; j++)
    {
        radius = (double) sqrt(pow((i - centre.x), 2.0) + pow((double) (j - centre.y), 2.0));
        single.at<float>(i,j) =((upper - lower) * (1/(1 + pow((double) (D/radius), (double) (2*n))))) + lower;
    }
}
//normalize(single, single, 0, 1, CV_MINMAX);
//Apply filter
mulSpectrums( dft_Filter, single, dft_Filter, 0);
}

void HomomorphicFilter::Shifting_DFT(Mat &fImage)
{
//For visualization purposes we may also rearrange the quadrants of the result, so that the origin (0,0), corresponds to the image center.
Mat tmp, q0, q1, q2, q3;

/*First crop the image, if it has an odd number of rows or columns.
Operator & bit to bit by -2 (two's complement : -2 = 111111111....10) to eliminate the first bit 2^0 (In case of odd number on row or col, we take the even number in below)*/
fImage = fImage(Rect(0, 0, fImage.cols & -2, fImage.rows & -2));
int cx = fImage.cols/2;
int cy = fImage.rows/2;

/*Rearrange the quadrants of Fourier image so that the origin is at the image center*/
q0 = fImage(Rect(0, 0, cx, cy));
q1 = fImage(Rect(cx, 0, cx, cy));
q2 = fImage(Rect(0, cy, cx, cy));
q3 = fImage(Rect(cx, cy, cx, cy));

/*We reverse each quadrant of the frame with its other quadrant diagonally opposite*/
/*We reverse q0 and q3*/
q0.copyTo(tmp);
q3.copyTo(q0);
tmp.copyTo(q3);

/*We reverse q1 and q2*/
q1.copyTo(tmp);
q2.copyTo(q1);
tmp.copyTo(q2);
}

void HomomorphicFilter::Fourier_Transform(Mat frame_bw, Mat &image_phase, Mat &image_mag)
{
Mat frame_log;
frame_bw.convertTo(frame_log, CV_32F);
/*Take the natural log of the input (compute log(1 + Mag)*/
frame_log += 1;
log( frame_log, frame_log); // log(1 + Mag)

/*2. Expand the image to an optimal size
The performance of the DFT depends of the image size. It tends to be the fastest for image sizes that are multiple of 2, 3 or 5.
We can use the copyMakeBorder() function to expand the borders of an image.*/
Mat padded;
int M = getOptimalDFTSize(frame_log.rows);
int N = getOptimalDFTSize(frame_log.cols);
copyMakeBorder(frame_log, padded, 0, M - frame_log.rows, 0, N - frame_log.cols, BORDER_CONSTANT, Scalar::all(0));

/*Make place for both the complex and real values
The result of the DFT is a complex. Then the result is 2 images (Imaginary + Real), and the frequency domains range is much larger than the spatial one. Therefore we need to store in float !
That's why we will convert our input image "padded" to float and expand it to another channel to hold the complex values.
Planes is an arrow of 2 matrix (planes[0] = Real part, planes[1] = Imaginary part)*/
Mat image_planes[] = {Mat_<float>(padded), Mat::zeros(padded.size(), CV_32F)};
Mat image_complex;
/*Creates one multichannel array out of several single-channel ones.*/
merge(image_planes, 2, image_complex);

/*Make the DFT
The result of thee DFT is a complex image : "image_complex"*/
dft(image_complex, image_complex);

/***************************/
//Create spectrum magnitude//
/***************************/
/*Transform the real and complex values to magnitude
NB: We separe Real part to Imaginary part*/
split(image_complex, image_planes);
//Starting with this part we have the real part of the image in planes[0] and the imaginary in planes[1]
phase(image_planes[0], image_planes[1], image_phase);
magnitude(image_planes[0], image_planes[1], image_mag);
}

void HomomorphicFilter::Inv_Fourier_Transform(Mat image_phase, Mat image_mag, Mat &inverseTransform)
{
/*Calculates x and y coordinates of 2D vectors from their magnitude and angle.*/
Mat result_planes[2];
polarToCart(image_mag, image_phase, result_planes[0], result_planes[1]);

/*Creates one multichannel array out of several single-channel ones.*/
Mat result_complex;
merge(result_planes, 2, result_complex);

/*Make the IDFT*/
dft(result_complex, inverseTransform, DFT_INVERSE|DFT_REAL_OUTPUT);

/*Take the exponential*/
exp(inverseTransform, inverseTransform);
}

```

and here my main code :

```
    /**************************/
    /****Homomorphic filter****/
    /**************************/
    /**********************************************/
    //Getting the frequency and magnitude of image//
    /**********************************************/
    Mat image_phase, image_mag;
    HomomorphicFilter().Fourier_Transform(frame_bw, image_phase, image_mag);
    /******************/
    //Shifting the DFT//
    /******************/
    HomomorphicFilter().Shifting_DFT(image_mag);
    /********************************/
    //Butterworth homomorphic filter//
    /********************************/
    int high_h_v_TB = 101;
    int low_h_v_TB = 99;
    int D = 10;// radius of band pass filter parameter
    int order = 2;// order of band pass filter parameter
    HomomorphicFilter().butterworth_homomorphic_filter(image_mag, D, order, high_h_v_TB, low_h_v_TB);
    /******************/
    //Shifting the DFT//
    /******************/
    HomomorphicFilter().Shifting_DFT(image_mag);
    /*******************************/
    //Inv Discret Fourier Transform//
    /*******************************/
    Mat inverseTransform;
    HomomorphicFilter().Inv_Fourier_Transform(image_phase, image_mag, inverseTransform);
    imshow("Result", inverseTransform);

```

If someone can explain me my mistakes, I would appreciate a lot :). Thank you and sorry for my poor english.

EDIT : Now, i have something but it's not perfect ... I modified 2 things in my code.
I applied log(mag + 1) after dft and not on the input image.
I removed exp() after idft.

here the results (i can post only 2 links ...) : 

my input image : [![http://i.imgur.com/Kw0Wdo4.png](https://i.stack.imgur.com/8o4HH.png)](https://i.stack.imgur.com/8o4HH.png)
final result : [![http://i.imgur.com/7AX9j5u.png](https://i.stack.imgur.com/x1ug4.png)](https://i.stack.imgur.com/x1ug4.png)

after having seen several topics, i find similar results on my butterworth filter and on my magnitude after dft/shifting.
Unfortunately, my final result isn't very good. Why i have so much "noise" ?