From a8e9a3a88df83ae118b54e975056c687ac3d30d2 Mon Sep 17 00:00:00 2001 From: Karpushin Vladislav Date: Tue, 24 Jul 2018 16:54:17 +0700 Subject: [PATCH] doc: add new tutorial "Out of focus deblur filter" In this tutorial you will learn: - what is a degradation image model - what is a PSF of an out-of-focus image - how to restore a blurred image - what is the Wiener filter --- doc/opencv.bib | 14 ++ .../out_of_focus_deblur_filter/images/original.jpg | Bin 0 -> 14447 bytes .../out_of_focus_deblur_filter/images/psf.png | Bin 0 -> 630 bytes .../images/recovered.jpg | Bin 0 -> 42725 bytes .../out_of_focus_deblur_filter.markdown | 112 ++++++++++++++++ .../imgproc/table_of_content_imgproc.markdown | 10 ++ .../out_of_focus_deblur_filter.cpp | 149 +++++++++++++++++++++ 7 files changed, 285 insertions(+) create mode 100755 doc/tutorials/imgproc/out_of_focus_deblur_filter/images/original.jpg create mode 100755 doc/tutorials/imgproc/out_of_focus_deblur_filter/images/psf.png create mode 100755 doc/tutorials/imgproc/out_of_focus_deblur_filter/images/recovered.jpg create mode 100755 doc/tutorials/imgproc/out_of_focus_deblur_filter/out_of_focus_deblur_filter.markdown create mode 100755 samples/cpp/tutorial_code/ImgProc/out_of_focus_deblur_filter/out_of_focus_deblur_filter.cpp diff --git a/doc/opencv.bib b/doc/opencv.bib index edb7033..7c8303f 100644 --- a/doc/opencv.bib +++ b/doc/opencv.bib @@ -1016,3 +1016,17 @@ year = {2017}, organization = {IEEE} } + +@ARTICLE{gonzalez, + title={Digital Image Fundamentals, Digital Imaging Processing}, + author={Gonzalez, Rafael C and others}, + year={1987}, + publisher={Addison Wesley Publishing Company} +} + +@ARTICLE{gruzman, + title={Цифровая обработка изображений в информационных системах}, + author={Грузман, И.С. and Киричук, В.С. and Косых, В.П. and Перетягин, Г.И. and Спектор, А.А.}, + year={2000}, + publisher={Изд-во НГТУ Новосибирск} +} diff --git a/doc/tutorials/imgproc/out_of_focus_deblur_filter/images/original.jpg 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za>jL%E`F@8DN1@z(~TrRjmSaD{Ko>f9I;9;^*1=am1_p@yyd$L0!!hrG=%Ut7=M%M zug(Qxr*`ZnXFU!s_r9kOn)O?-tjs!+a2Xoz@)@N608z-!@(xYbL=3=ydSpg$cB>J2 z4(Olf8eq-*PkaEG6KOn*i2hqq$15C*=``6_tq&G4(@`RHIHXAIpx`nt+82== y0m;A|0!YZRka@uJ7B)D*S(~ZGB%;;e+)DMxgJ>rJVox>uU?!U(B;+|eXaCtUnwZD{ literal 0 HcmV?d00001 diff --git a/doc/tutorials/imgproc/out_of_focus_deblur_filter/out_of_focus_deblur_filter.markdown b/doc/tutorials/imgproc/out_of_focus_deblur_filter/out_of_focus_deblur_filter.markdown new file mode 100755 index 0000000..abab071 --- /dev/null +++ b/doc/tutorials/imgproc/out_of_focus_deblur_filter/out_of_focus_deblur_filter.markdown @@ -0,0 +1,112 @@ +Out-of-focus Deblur Filter {#tutorial_out_of_focus_deblur_filter} +========================== + +Goal +---- + +In this tutorial you will learn: + +- what is a degradation image model +- what is PSF of out-of-focus image +- how to restore a blurred image +- what is Wiener filter + +Theory +------ + +@note The explanation is based on the books @cite gonzalez and @cite gruzman. Also, you can refer to Matlab's tutorial [Image Deblurring in Matlab] and an article [SmartDeblur]. +@note An out-of-focus image on this page is a real world image. An out-of-focus was done manually by camera optics. + +### What is a degradation image model? + +A mathematical model of the image degradation in frequency domain representation is: + +\f[S = H\cdot U + N\f] + +where +\f$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 + + +[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 diff --git a/doc/tutorials/imgproc/table_of_content_imgproc.markdown b/doc/tutorials/imgproc/table_of_content_imgproc.markdown index 59c985e..3d82c0c 100644 --- a/doc/tutorials/imgproc/table_of_content_imgproc.markdown +++ b/doc/tutorials/imgproc/table_of_content_imgproc.markdown @@ -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. diff --git a/samples/cpp/tutorial_code/ImgProc/out_of_focus_deblur_filter/out_of_focus_deblur_filter.cpp b/samples/cpp/tutorial_code/ImgProc/out_of_focus_deblur_filter/out_of_focus_deblur_filter.cpp new file mode 100755 index 0000000..059df8b --- /dev/null +++ b/samples/cpp/tutorial_code/ImgProc/out_of_focus_deblur_filter/out_of_focus_deblur_filter.cpp @@ -0,0 +1,149 @@ +/** +* @brief You will learn how to recover an out-of-focus image by Wiener filter +* @author Karpushin Vladislav, karpushin@ngs.ru, https://github.com/VladKarpushin +*/ +#include +#include "opencv2/imgproc.hpp" +#include "opencv2/imgcodecs.hpp" + +using namespace cv; +using namespace std; + +void help(); +void calcPSF(Mat& outputImg, Size filterSize, int R); +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); + +const String keys = +"{help h usage ? | | print this message }" +"{image |original.JPG | input image name }" +"{R |53 | radius }" +"{SNR |5200 | 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 R = parser.get("R"); + int snr = parser.get("SNR"); + string strInFileName = parser.get("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(), R); + calcWnrFilter(h, Hw, 1.0 / double(snr)); + //Hw calculation (stop) + + // 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 << "2018-07-12" << endl; + cout << "DeBlur_v8" << endl; + cout << "You will learn how to recover an out-of-focus image by Wiener filter" << endl; +} + +//! [calcPSF] +void calcPSF(Mat& outputImg, Size filterSize, int R) +{ + Mat h(filterSize, CV_32F, Scalar(0)); + Point point(filterSize.width / 2, filterSize.height / 2); + circle(h, point, R, 255, -1, 8); + 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_(inputImg.clone()), Mat::zeros(inputImg.size(), CV_32F) }; + Mat complexI; + merge(planes, 2, complexI); + dft(complexI, complexI, DFT_SCALE); + + Mat planesH[2] = { Mat_(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_(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] -- 2.7.4