diff --git a/doc/tutorials/imgproc/out_of_focus_deblur_filter/out_of_focus_deblur_filter.markdown b/doc/tutorials/imgproc/out_of_focus_deblur_filter/out_of_focus_deblur_filter.markdown index 993442168d..0e1da4efae 100755 --- a/doc/tutorials/imgproc/out_of_focus_deblur_filter/out_of_focus_deblur_filter.markdown +++ b/doc/tutorials/imgproc/out_of_focus_deblur_filter/out_of_focus_deblur_filter.markdown @@ -8,54 +8,54 @@ Goal In this tutorial you will learn: -- what is a degradation image model -- what is PSF of out-of-focus image +- what a degradation image model is +- what the PSF of an out-of-focus image is - how to restore a blurred image -- what is Wiener filter +- what is a 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. +@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 the article [SmartDeblur]. +@note The out-of-focus image on this page is a real world image. The out-of-focus was achieved manually by camera optics. ### What is a degradation image model? -A mathematical model of the image degradation in frequency domain representation is: +Here is a mathematical model of the image degradation in frequency domain representation: \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$H\f$ is a 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. +The circular PSF is a good approximation of out-of-focus distortion. Such a 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? +### How to restore a blurred image? -The objective of restoration (deblurring) is to obtain an estimate of the original image. Restoration formula in frequency domain is: +The objective of restoration (deblurring) is to obtain an estimate of the original image. The 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. +\f$U'\f$ is the spectrum of estimation of original image \f$U\f$, and +\f$H_w\f$ is the restoration filter, for example, the Wiener filter. -### What is Wiener filter? +### What is the 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: +The Wiener filter is a way to restore a blurred image. Let's suppose that the PSF is a real and symmetric signal, a power spectrum of the original true image and noise are not known, +then a 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. +So, in order to recover an out-of-focus image by Wiener filter, it needs to know the \f$SNR\f$ and \f$R\f$ of the circular PSF. Source code @@ -68,36 +68,36 @@ You can find source code in the `samples/cpp/tutorial_code/ImgProc/out_of_focus_ Explanation ----------- -An out-of-focus image recovering algorithm consists of PSF generation, Wiener filter generation and filtering an blurred image in frequency domain: +An out-of-focus image recovering algorithm consists of PSF generation, Wiener filter generation and filtering a 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$R\f$: +A function calcPSF() forms a 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: +A function calcWnrFilter() synthesizes the simplified Wiener filter \f$H_w\f$ according to the 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": +A function fftshift() rearranges the PSF. This code was just copied from the 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: +A function filter2DFreq() filters the blurred image in the 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: +Below you can see the 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: +And the following result has been computed with \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. +The Wiener filter was used, and 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's 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. +@note Sometimes you can observe the ringing effect in a restored image. This effect can be reduced with 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).