Merge remote-tracking branch 'upstream/3.4' into merge-3.4

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+Out-of-focus Deblur Filter {#tutorial_out_of_focus_deblur_filter}
+==========================
+
+Goal
+----
+
+In this tutorial you will learn:
+
+-   what is a degradation image model
+-   what is PSF of out-of-focus image
+-   how to restore a blurred image
+-   what is Wiener filter
+
+Theory
+------
+
+@note The explanation is based on the books @cite gonzalez and @cite gruzman. Also, you can refer to Matlab's tutorial [Image Deblurring in Matlab] and an article [SmartDeblur].
+@note An out-of-focus image on this page is a real world  image. An out-of-focus was done manually by camera optics.
+
+### What is a degradation image model?
+
+A mathematical model of the image degradation in frequency domain representation is:
+
+\f[S = H\cdot U + N\f]
+
+where
+\f$S\f$ is a spectrum of blurred (degraded) image,
+\f$U\f$ is a spectrum of original true (undegraded) image,
+\f$H\f$ is frequency response of point spread function (PSF),
+\f$N\f$ is a spectrum of additive noise.
+
+Circular PSF is a good approximation of out-of-focus distortion. Such PSF is specified by only one parameter - radius \f$R\f$. Circular PSF is used in this work.
+
+![Circular point spread function](psf.png)
+
+### How to restore an blurred image?
+
+The objective of restoration (deblurring) is to obtain an estimate of the original image. Restoration formula in frequency domain is:
+
+\f[U' = H_w\cdot S\f]
+
+where
+\f$U'\f$ is spectrum of estimation of original image \f$U\f$,
+\f$H_w\f$ is restoration filter, for example, Wiener filter.
+
+### What is Wiener filter?
+
+Wiener filter is a way to restore a blurred image. Let's suppose that PSF is a real and symmetric signal, a power spectrum of the original true image and noise are not known,
+then simplified Wiener formula is:
+
+\f[H_w = \frac{H}{|H|^2+\frac{1}{SNR}} \f]
+
+where
+\f$SNR\f$ is signal-to-noise ratio.
+
+So, in order to recover an out-of-focus image by Wiener filter, it needs to know \f$SNR\f$ and \f$R\f$ of circular PSF.
+
+
+Source code
+-----------
+
+You can find source code in the `samples/cpp/tutorial_code/ImgProc/out_of_focus_deblur_filter/out_of_focus_deblur_filter.cpp` of the OpenCV source code library.
+
+@include cpp/tutorial_code/ImgProc/out_of_focus_deblur_filter/out_of_focus_deblur_filter.cpp
+
+Explanation
+-----------
+
+An out-of-focus image recovering algorithm consists of PSF generation, Wiener filter generation and filtering an blurred image in frequency domain:
+@snippet samples/cpp/tutorial_code/ImgProc/out_of_focus_deblur_filter/out_of_focus_deblur_filter.cpp main
+
+A function calcPSF() forms an circular PSF according to input parameter radius \f$R\f$:
+@snippet samples/cpp/tutorial_code/ImgProc/out_of_focus_deblur_filter/out_of_focus_deblur_filter.cpp calcPSF
+
+A function calcWnrFilter() synthesizes simplified Wiener filter \f$H_w\f$ according to formula described above:
+@snippet samples/cpp/tutorial_code/ImgProc/out_of_focus_deblur_filter/out_of_focus_deblur_filter.cpp calcWnrFilter
+
+A function fftshift() rearranges PSF. This code was just copied from tutorial @ref tutorial_discrete_fourier_transform "Discrete Fourier Transform":
+@snippet samples/cpp/tutorial_code/ImgProc/out_of_focus_deblur_filter/out_of_focus_deblur_filter.cpp fftshift
+
+A function filter2DFreq() filters an blurred image in frequency domain:
+@snippet samples/cpp/tutorial_code/ImgProc/out_of_focus_deblur_filter/out_of_focus_deblur_filter.cpp filter2DFreq
+
+Result
+------
+
+Below you can see real out-of-focus image:
+![Out-of-focus image](images/original.jpg)
+
+
+Below result was done by \f$R\f$ = 53 and \f$SNR\f$ = 5200 parameters:
+![The restored (deblurred) image](images/recovered.jpg)
+
+The Wiener filter was used, values of \f$R\f$ and \f$SNR\f$ were selected manually to give the best possible visual result.
+We can see that the result is not perfect, but it gives us a hint to the image content. With some difficulty, the text is readable.
+
+@note The parameter \f$R\f$ is the most important. So you should adjust \f$R\f$ first, then \f$SNR\f$.
+@note Sometimes you can observe the ringing effect in an restored image. This effect can be reduced by several methods. For example, you can taper input image edges.
+
+You can also find a quick video demonstration of this on
+[YouTube](https://youtu.be/0bEcE4B0XP4).
+@youtube{0bEcE4B0XP4}
+
+References
+------
+- [Image Deblurring in Matlab] - Image Deblurring in Matlab
+- [SmartDeblur] - SmartDeblur site
+
+<!-- invisible references list -->
+[Digital Image Processing]: http://web.ipac.caltech.edu/staff/fmasci/home/astro_refs/Digital_Image_Processing_2ndEd.pdf
+[Image Deblurring in Matlab]: https://www.mathworks.com/help/images/image-deblurring.html
+[SmartDeblur]: http://yuzhikov.com/articles/BlurredImagesRestoration1.htm
@@ -292,3 +292,13 @@ In this section you will learn about the image processing (manipulation) functio
    *Author:* Theodore Tsesmelis

    Where we learn to segment objects using Laplacian filtering, the Distance Transformation and the Watershed algorithm.
+
+-   @subpage tutorial_out_of_focus_deblur_filter
+
+    *Languages:* C++
+
+    *Compatibility:* \> OpenCV 2.0
+
+    *Author:* Karpushin Vladislav
+
+    You will learn how to recover an out-of-focus image by Wiener filter.