doc: add new tutorial motion deblur filter (#12215)

* doc: add new tutorial motion deblur filter

* Update motion_deblur_filter.markdown

a few minor changes

doc/tutorials/imgproc/motion_deblur_filter/motion_deblur_filter.markdown

+Motion Deblur Filter {#tutorial_motion_deblur_filter}
+==========================
+
+Goal
+----
+
+In this tutorial you will learn:
+
+-   what the PSF of a motion blur image is
+-   how to restore a motion blur image
+
+Theory
+------
+
+For the degradation image model theory and the Wiener filter theory you can refer to the tutorial @ref tutorial_out_of_focus_deblur_filter "Out-of-focus Deblur Filter".
+On this page only a linear motion blur distortion is considered. The motion blur image on this page is a real world image. The blur was caused by a moving subject.
+
+### What is the PSF of a motion blur image?
+
+The point spread function (PSF) of a linear motion blur distortion is a line segment. Such a PSF is specified by two parameters: \f$LEN\f$ is the length of the blur and \f$THETA\f$ is the angle of motion.
+
+![Point spread function of a linear motion blur distortion](images/motion_psf.png)
+
+### How to restore a blurred image?
+
+On this page the Wiener filter is used as the restoration filter, for details you can refer to the tutorial @ref tutorial_out_of_focus_deblur_filter "Out-of-focus Deblur Filter".
+In order to synthesize the Wiener filter for a motion blur case, it needs to specify the signal-to-noise ratio (\f$SNR\f$), \f$LEN\f$ and \f$THETA\f$ of the PSF.
+
+Source code
+-----------
+
+You can find source code in the `samples/cpp/tutorial_code/ImgProc/motion_deblur_filter/motion_deblur_filter.cpp` of the OpenCV source code library.
+
+@include cpp/tutorial_code/ImgProc/motion_deblur_filter/motion_deblur_filter.cpp
+
+Explanation
+-----------
+
+A motion blur image recovering algorithm consists of PSF generation, Wiener filter generation and filtering a blurred image in a frequency domain:
+@snippet samples/cpp/tutorial_code/ImgProc/motion_deblur_filter/motion_deblur_filter.cpp main
+
+A function calcPSF() forms a PSF according to input parameters \f$LEN\f$ and \f$THETA\f$ (in degrees):
+@snippet samples/cpp/tutorial_code/ImgProc/motion_deblur_filter/motion_deblur_filter.cpp calcPSF
+
+A function edgetaper() tapers the input image’s edges in order to reduce the ringing effect in a restored image:
+@snippet samples/cpp/tutorial_code/ImgProc/motion_deblur_filter/motion_deblur_filter.cpp edgetaper
+
+The functions calcWnrFilter(), fftshift() and filter2DFreq() realize an image filtration by a specified PSF in the frequency domain.  The functions are copied from the tutorial
+@ref tutorial_out_of_focus_deblur_filter "Out-of-focus Deblur Filter".
+
+Result
+------
+
+Below you can see the real world image with motion blur distortion. The license plate is not readable on both cars. The red markers show the car’s license plate location.
+![Motion blur image. The license plates are not readable](images/motion_original.jpg)
+
+
+Below you can see the restoration result for the black car license plate. The result has been computed with \f$LEN\f$ = 125, \f$THETA\f$ = 0, \f$SNR\f$ = 700.
+![The restored image of the black car license plate](images/black_car.jpg)
+
+Below you can see the restoration result for the white car license plate. The result has been computed with \f$LEN\f$ = 78, \f$THETA\f$ = 15, \f$SNR\f$ = 300.
+![The restored image of the white car license plate](images/white_car.jpg)
+
+The values of \f$SNR\f$, \f$LEN\f$ and \f$THETA\f$ were selected manually to give the best possible visual result. The \f$THETA\f$ parameter coincides with the car’s moving direction, and the
+\f$LEN\f$ parameter depends on the car’s moving speed.
+The result is not perfect, but at least it gives us a hint of the image’s content. With some effort, the car license plate is now readable.
+
+@note The parameters \f$LEN\f$ and \f$THETA\f$ are the most important. You should adjust \f$LEN\f$ and \f$THETA\f$ first, then \f$SNR\f$.
+
+You can also find a quick video demonstration of a license plate recovering method
+[YouTube](https://youtu.be/xSrE0hdhb4o).
+@youtube{xSrE0hdhb4o}

doc/tutorials/imgproc/table_of_content_imgproc.markdown

@@ -320,3 +320,13 @@ In this section you will learn about the image processing (manipulation) functio
     *Author:* Karpushin Vladislav
 
     You will learn how to recover an out-of-focus image by Wiener filter.
+
+-   @subpage tutorial_motion_deblur_filter
+
+    *Languages:* C++
+
+    *Compatibility:* \> OpenCV 2.0
+
+    *Author:* Karpushin Vladislav
+
+    You will learn how to recover an image with motion blur distortion using a Wiener filter.

samples/cpp/tutorial_code/ImgProc/motion_deblur_filter/motion_deblur_filter.cpp

+/**
+* @brief You will learn how to recover an image with motion blur distortion using a Wiener filter
+* @author Karpushin Vladislav, karpushin@ngs.ru, https://github.com/VladKarpushin
+*/
+#include <iostream>
+#include "opencv2/imgproc.hpp"
+#include "opencv2/imgcodecs.hpp"
+
+using namespace cv;
+using namespace std;
+
+void help();
+void calcPSF(Mat& outputImg, Size filterSize, int len, double theta);
+void fftshift(const Mat& inputImg, Mat& outputImg);
+void filter2DFreq(const Mat& inputImg, Mat& outputImg, const Mat& H);
+void calcWnrFilter(const Mat& input_h_PSF, Mat& output_G, double nsr);
+void edgetaper(const Mat& inputImg, Mat& outputImg, double gamma = 5.0, double beta = 0.2);
+
+const String keys =
+"{help h usage ? |             | print this message				}"
+"{image          |input.png    | input image name				}"
+"{LEN            |125          | length of a motion				}"
+"{THETA          |0            | angle of a motion in degrees	}"
+"{SNR            |700          | signal to noise ratio			}"
+;
+
+int main(int argc, char *argv[])
+{
+    help();
+    CommandLineParser parser(argc, argv, keys);
+    if (parser.has("help"))
+    {
+        parser.printMessage();
+        return 0;
+    }
+
+    int LEN = parser.get<int>("LEN");
+    double THETA = parser.get<double>("THETA");
+    int snr = parser.get<int>("SNR");
+    string strInFileName = parser.get<String>("image");
+
+    if (!parser.check())
+    {
+        parser.printErrors();
+        return 0;
+    }
+
+    Mat imgIn;
+    imgIn = imread(strInFileName, IMREAD_GRAYSCALE);
+    if (imgIn.empty()) //check whether the image is loaded or not
+    {
+        cout << "ERROR : Image cannot be loaded..!!" << endl;
+        return -1;
+    }
+
+    Mat imgOut;
+
+//! [main]
+    // it needs to process even image only
+    Rect roi = Rect(0, 0, imgIn.cols & -2, imgIn.rows & -2);
+
+    //Hw calculation (start)
+    Mat Hw, h;
+    calcPSF(h, roi.size(), LEN, THETA);
+    calcWnrFilter(h, Hw, 1.0 / double(snr));
+    //Hw calculation (stop)
+
+    imgIn.convertTo(imgIn, CV_32F);
+    edgetaper(imgIn, imgIn);
+
+    // filtering (start)
+    filter2DFreq(imgIn(roi), imgOut, Hw);
+    // filtering (stop)
+//! [main]
+
+    imgOut.convertTo(imgOut, CV_8U);
+    normalize(imgOut, imgOut, 0, 255, NORM_MINMAX);
+    imwrite("result.jpg", imgOut);
+    return 0;
+}
+
+void help()
+{
+    cout << "2018-08-14" << endl;
+    cout << "Motion_deblur_v2" << endl;
+    cout << "You will learn how to recover an image with motion blur distortion using a Wiener filter" << endl;
+}
+
+//! [calcPSF]
+void calcPSF(Mat& outputImg, Size filterSize, int len, double theta)
+{
+    Mat h(filterSize, CV_32F, Scalar(0));
+    Point point(filterSize.width / 2, filterSize.height / 2);
+    ellipse(h, point, Size(0, cvRound(float(len) / 2.0)), 90.0 - theta, 0, 360, Scalar(255), FILLED);
+    Scalar summa = sum(h);
+    outputImg = h / summa[0];
+}
+//! [calcPSF]
+
+//! [fftshift]
+void fftshift(const Mat& inputImg, Mat& outputImg)
+{
+    outputImg = inputImg.clone();
+    int cx = outputImg.cols / 2;
+    int cy = outputImg.rows / 2;
+    Mat q0(outputImg, Rect(0, 0, cx, cy));
+    Mat q1(outputImg, Rect(cx, 0, cx, cy));
+    Mat q2(outputImg, Rect(0, cy, cx, cy));
+    Mat q3(outputImg, Rect(cx, cy, cx, cy));
+    Mat tmp;
+    q0.copyTo(tmp);
+    q3.copyTo(q0);
+    tmp.copyTo(q3);
+    q1.copyTo(tmp);
+    q2.copyTo(q1);
+    tmp.copyTo(q2);
+}
+//! [fftshift]
+
+//! [filter2DFreq]
+void filter2DFreq(const Mat& inputImg, Mat& outputImg, const Mat& H)
+{
+    Mat planes[2] = { Mat_<float>(inputImg.clone()), Mat::zeros(inputImg.size(), CV_32F) };
+    Mat complexI;
+    merge(planes, 2, complexI);
+    dft(complexI, complexI, DFT_SCALE);
+
+    Mat planesH[2] = { Mat_<float>(H.clone()), Mat::zeros(H.size(), CV_32F) };
+    Mat complexH;
+    merge(planesH, 2, complexH);
+    Mat complexIH;
+    mulSpectrums(complexI, complexH, complexIH, 0);
+
+    idft(complexIH, complexIH);
+    split(complexIH, planes);
+    outputImg = planes[0];
+}
+//! [filter2DFreq]
+
+//! [calcWnrFilter]
+void calcWnrFilter(const Mat& input_h_PSF, Mat& output_G, double nsr)
+{
+    Mat h_PSF_shifted;
+    fftshift(input_h_PSF, h_PSF_shifted);
+    Mat planes[2] = { Mat_<float>(h_PSF_shifted.clone()), Mat::zeros(h_PSF_shifted.size(), CV_32F) };
+    Mat complexI;
+    merge(planes, 2, complexI);
+    dft(complexI, complexI);
+    split(complexI, planes);
+    Mat denom;
+    pow(abs(planes[0]), 2, denom);
+    denom += nsr;
+    divide(planes[0], denom, output_G);
+}
+//! [calcWnrFilter]
+
+//! [edgetaper]
+void edgetaper(const Mat& inputImg, Mat& outputImg, double gamma, double beta)
+{
+    int Nx = inputImg.cols;
+    int Ny = inputImg.rows;
+    Mat w1(1, Nx, CV_32F, Scalar(0));
+    Mat w2(Ny, 1, CV_32F, Scalar(0));
+
+    float* p1 = w1.ptr<float>(0);
+    float* p2 = w2.ptr<float>(0);
+    float dx = float(2.0 * CV_PI / Nx);
+    float x = float(-CV_PI);
+    for (int i = 0; i < Nx; i++)
+    {
+        p1[i] = float(0.5 * (tanh((x + gamma / 2) / beta) - tanh((x - gamma / 2) / beta)));
+        x += dx;
+    }
+    float dy = float(2.0 * CV_PI / Ny);
+    float y = float(-CV_PI);
+    for (int i = 0; i < Ny; i++)
+    {
+        p2[i] = float(0.5 * (tanh((y + gamma / 2) / beta) - tanh((y - gamma / 2) / beta)));
+        y += dy;
+    }
+    Mat w = w2 * w1;
+    multiply(inputImg, w, outputImg);
+}
+//! [edgetaper]