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Merge remote-tracking branch 'upstream/3.4' into merge-3.4
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Alexander Alekhin
Alexander Alekhin
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Motion Deblur Filter {#tutorial_motion_deblur_filter}
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==========================
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Goal
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----
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In this tutorial you will learn:
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- what the PSF of a motion blur image is
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- how to restore a motion blur image
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Theory
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------
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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".
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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.
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### What is the PSF of a motion blur image?
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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.
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### How to restore a blurred image?
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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".
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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.
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Source code
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-----------
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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.
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@include cpp/tutorial_code/ImgProc/motion_deblur_filter/motion_deblur_filter.cpp
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Explanation
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-----------
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A motion blur image recovering algorithm consists of PSF generation, Wiener filter generation and filtering a blurred image in a frequency domain:
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@snippet samples/cpp/tutorial_code/ImgProc/motion_deblur_filter/motion_deblur_filter.cpp main
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A function calcPSF() forms a PSF according to input parameters \f$LEN\f$ and \f$THETA\f$ (in degrees):
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@snippet samples/cpp/tutorial_code/ImgProc/motion_deblur_filter/motion_deblur_filter.cpp calcPSF
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A function edgetaper() tapers the input image’s edges in order to reduce the ringing effect in a restored image:
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@snippet samples/cpp/tutorial_code/ImgProc/motion_deblur_filter/motion_deblur_filter.cpp edgetaper
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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
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@ref tutorial_out_of_focus_deblur_filter "Out-of-focus Deblur Filter".
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Result
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------
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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.
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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.
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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.
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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
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\f$LEN\f$ parameter depends on the car’s moving speed.
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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.
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@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$SNR\f$.
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You can also find a quick video demonstration of a license plate recovering method
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[YouTube](https://youtu.be/xSrE0hdhb4o).
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@youtube{xSrE0hdhb4o}
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+26
-26
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In this tutorial you will learn:
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- what is a degradation image model
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- what is PSF of out-of-focus image
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- what a degradation image model is
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- what the PSF of an out-of-focus image is
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- how to restore a blurred image
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- what is Wiener filter
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- what is a Wiener filter
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Theory
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------
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@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].
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@note An out-of-focus image on this page is a real world image. An out-of-focus was done manually by camera optics.
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@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].
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@note The out-of-focus image on this page is a real world image. The out-of-focus was achieved manually by camera optics.
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### What is a degradation image model?
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A mathematical model of the image degradation in frequency domain representation is:
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Here is a mathematical model of the image degradation in frequency domain representation:
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\f[S = H\cdot U + N\f]
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where
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\f$S\f$ is a spectrum of blurred (degraded) image,
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\f$U\f$ is a spectrum of original true (undegraded) image,
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\f$H\f$ is frequency response of point spread function (PSF),
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\f$H\f$ is a frequency response of point spread function (PSF),
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\f$N\f$ is a spectrum of additive noise.
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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.
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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.
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### How to restore an blurred image?
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### How to restore a blurred image?
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The objective of restoration (deblurring) is to obtain an estimate of the original image. Restoration formula in frequency domain is:
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The objective of restoration (deblurring) is to obtain an estimate of the original image. The restoration formula in frequency domain is:
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\f[U' = H_w\cdot S\f]
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where
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\f$U'\f$ is spectrum of estimation of original image \f$U\f$,
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\f$H_w\f$ is restoration filter, for example, Wiener filter.
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\f$U'\f$ is the spectrum of estimation of original image \f$U\f$, and
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\f$H_w\f$ is the restoration filter, for example, the Wiener filter.
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### What is Wiener filter?
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### What is the Wiener filter?
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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,
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then simplified Wiener formula is:
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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,
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then a simplified Wiener formula is:
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\f[H_w = \frac{H}{|H|^2+\frac{1}{SNR}} \f]
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where
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\f$SNR\f$ is signal-to-noise ratio.
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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.
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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.
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Source code
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@@ -68,36 +68,36 @@ You can find source code in the `samples/cpp/tutorial_code/ImgProc/out_of_focus_
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Explanation
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-----------
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An out-of-focus image recovering algorithm consists of PSF generation, Wiener filter generation and filtering an blurred image in frequency domain:
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An out-of-focus image recovering algorithm consists of PSF generation, Wiener filter generation and filtering a blurred image in frequency domain:
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@snippet samples/cpp/tutorial_code/ImgProc/out_of_focus_deblur_filter/out_of_focus_deblur_filter.cpp main
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A function calcPSF() forms an circular PSF according to input parameter radius \f$R\f$:
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A function calcPSF() forms a circular PSF according to input parameter radius \f$R\f$:
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@snippet samples/cpp/tutorial_code/ImgProc/out_of_focus_deblur_filter/out_of_focus_deblur_filter.cpp calcPSF
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A function calcWnrFilter() synthesizes simplified Wiener filter \f$H_w\f$ according to formula described above:
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A function calcWnrFilter() synthesizes the simplified Wiener filter \f$H_w\f$ according to the formula described above:
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@snippet samples/cpp/tutorial_code/ImgProc/out_of_focus_deblur_filter/out_of_focus_deblur_filter.cpp calcWnrFilter
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A function fftshift() rearranges PSF. This code was just copied from tutorial @ref tutorial_discrete_fourier_transform "Discrete Fourier Transform":
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A function fftshift() rearranges the PSF. This code was just copied from the tutorial @ref tutorial_discrete_fourier_transform "Discrete Fourier Transform":
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@snippet samples/cpp/tutorial_code/ImgProc/out_of_focus_deblur_filter/out_of_focus_deblur_filter.cpp fftshift
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A function filter2DFreq() filters an blurred image in frequency domain:
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A function filter2DFreq() filters the blurred image in the frequency domain:
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@snippet samples/cpp/tutorial_code/ImgProc/out_of_focus_deblur_filter/out_of_focus_deblur_filter.cpp filter2DFreq
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Result
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------
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Below you can see real out-of-focus image:
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Below you can see the real out-of-focus image:
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Below result was done by \f$R\f$ = 53 and \f$SNR\f$ = 5200 parameters:
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And the following result has been computed with \f$R\f$ = 53 and \f$SNR\f$ = 5200 parameters:
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The Wiener filter was used, values of \f$R\f$ and \f$SNR\f$ were selected manually to give the best possible visual result.
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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.
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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.
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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.
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@note The parameter \f$R\f$ is the most important. So you should adjust \f$R\f$ first, then \f$SNR\f$.
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@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.
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@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.
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You can also find a quick video demonstration of this on
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[YouTube](https://youtu.be/0bEcE4B0XP4).
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@@ -320,3 +320,13 @@ In this section you will learn about the image processing (manipulation) functio
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*Author:* Karpushin Vladislav
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You will learn how to recover an out-of-focus image by Wiener filter.
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- @subpage tutorial_motion_deblur_filter
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*Languages:* C++
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*Compatibility:* \> OpenCV 2.0
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*Author:* Karpushin Vladislav
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You will learn how to recover an image with motion blur distortion using a Wiener filter.
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