From c5687caf1a519a70e20de3f59798c00572499a85 Mon Sep 17 00:00:00 2001 From: Karpushin Vladislav Date: Fri, 14 Sep 2018 13:14:17 +0700 Subject: [PATCH] doc: add new tutorial anisotropic image segmentation --- doc/opencv.bib | 34 +++++++ .../anisotropic_image_segmentation.markdown | 91 ++++++++++++++++++ .../images/gst_coherency.jpg | Bin 0 -> 20377 bytes .../images/gst_input.jpg | Bin 0 -> 40733 bytes .../images/gst_orientation.jpg | Bin 0 -> 19463 bytes .../images/gst_result.jpg | Bin 0 -> 33021 bytes .../imgproc/table_of_content_imgproc.markdown | 10 ++ .../anisotropic_image_segmentation.cpp | 104 +++++++++++++++++++++ 8 files changed, 239 insertions(+) create mode 100755 doc/tutorials/imgproc/anisotropic_image_segmentation/anisotropic_image_segmentation.markdown create mode 100755 doc/tutorials/imgproc/anisotropic_image_segmentation/images/gst_coherency.jpg create mode 100755 doc/tutorials/imgproc/anisotropic_image_segmentation/images/gst_input.jpg create mode 100755 doc/tutorials/imgproc/anisotropic_image_segmentation/images/gst_orientation.jpg create mode 100755 doc/tutorials/imgproc/anisotropic_image_segmentation/images/gst_result.jpg create mode 100755 samples/cpp/tutorial_code/ImgProc/anisotropic_image_segmentation/anisotropic_image_segmentation.cpp diff --git a/doc/opencv.bib b/doc/opencv.bib index 7c8303f..de18a4e 100644 --- a/doc/opencv.bib +++ b/doc/opencv.bib @@ -1030,3 +1030,37 @@ year={2000}, publisher={Изд-во НГТУ Новосибирск} } + +@book{jahne2000computer, + title={Computer vision and applications: a guide for students and practitioners}, + author={Jahne, Bernd}, + year={2000}, + publisher={Elsevier} +} + +@book{bigun2006vision, + title={Vision with direction}, + author={Bigun, Josef}, + year={2006}, + publisher={Springer} +} + +@inproceedings{van1995estimators, + title={Estimators for orientation and anisotropy in digitized images}, + author={Van Vliet, Lucas J and Verbeek, Piet W}, + booktitle={ASCI}, + volume={95}, + pages={16--18}, + year={1995} +} + +@article{yang1996structure, + title={Structure adaptive anisotropic image filtering}, + author={Yang, Guang-Zhong and Burger, Peter and Firmin, David N and Underwood, SR}, + journal={Image and Vision Computing}, + volume={14}, + number={2}, + pages={135--145}, + year={1996}, + publisher={Elsevier} +} diff --git a/doc/tutorials/imgproc/anisotropic_image_segmentation/anisotropic_image_segmentation.markdown b/doc/tutorials/imgproc/anisotropic_image_segmentation/anisotropic_image_segmentation.markdown new file mode 100755 index 0000000..16df8ee --- /dev/null +++ b/doc/tutorials/imgproc/anisotropic_image_segmentation/anisotropic_image_segmentation.markdown @@ -0,0 +1,91 @@ +Anisotropic image segmentation by a gradient structure tensor {#tutorial_anisotropic_image_segmentation_by_a_gst} +========================== + +Goal +---- + +In this tutorial you will learn: + +- what the gradient structure tensor is +- how to estimate orientation and coherency of an anisotropic image by a gradient structure tensor +- how to segment an anisotropic image with a single local orientation by a gradient structure tensor + +Theory +------ + +@note The explanation is based on the books @cite jahne2000computer, @cite bigun2006vision and @cite van1995estimators. Good physical explanation of a gradient structure tensor is given in @cite yang1996structure. Also, you can refer to a wikipedia page [Structure tensor]. +@note A anisotropic image on this page is a real world image. + +### What is the gradient structure tensor? + +In mathematics, the gradient structure tensor (also referred to as the second-moment matrix, the second order moment tensor, the inertia tensor, etc.) is a matrix derived from the gradient of a function. It summarizes the predominant directions of the gradient in a specified neighborhood of a point, and the degree to which those directions are coherent (coherency). The gradient structure tensor is widely used in image processing and computer vision for 2D/3D image segmentation, motion detection, adaptive filtration, local image features detection, etc. + +Important features of anisotropic images include orientation and coherency of a local anisotropy. In this paper we will show how to estimate orientation and coherency, and how to segment an anisotropic image with a single local orientation by a gradient structure tensor. + +The gradient structure tensor of an image is a 2x2 symmetric matrix. Eigenvectors of the gradient structure tensor indicate local orientation, whereas eigenvalues give coherency (a measure of anisotropism). + +The gradient structure tensor \f$J\f$ of an image \f$Z\f$ can be written as: + +\f[J = \begin{bmatrix} +J_{11} & J_{12} \\ +J_{12} & J_{22} +\end{bmatrix}\f] + +where \f$J_{11} = M[Z_{x}^{2}]\f$, \f$J_{22} = M[Z_{y}^{2}]\f$, \f$J_{12} = M[Z_{x}Z_{y}]\f$ - components of the tensor, \f$M[]\f$ is a symbol of mathematical expectation (we can consider this operation as averaging in a window w), \f$Z_{x}\f$ and \f$Z_{y}\f$ are partial derivatives of an image \f$Z\f$ with respect to \f$x\f$ and \f$y\f$. + +The eigenvalues of the tensor can be found in the below formula: +\f[\lambda_{1,2} = J_{11} + J_{22} \pm \sqrt{(J_{11} - J_{22})^{2} + 4J_{12}^{2}}\f] +where \f$\lambda_1\f$ - largest eigenvalue, \f$\lambda_2\f$ - smallest eigenvalue. + +### How to estimate orientation and coherency of an anisotropic image by gradient structure tensor? + +The orientation of an anisotropic image: +\f[\alpha = 0.5arctg\frac{2J_{12}}{J_{22} - J_{11}}\f] + +Coherency: +\f[C = \frac{\lambda_1 - \lambda_2}{\lambda_1 + \lambda_2}\f] + +The coherency ranges from 0 to 1. For ideal local orientation (\f$\lambda_2\f$ = 0, \f$\lambda_1\f$ > 0) it is one, for an isotropic gray value structure (\f$\lambda_1\f$ = \f$\lambda_2\f$ > 0) it is zero. + +Source code +----------- + +You can find source code in the `samples/cpp/tutorial_code/ImgProc/anisotropic_image_segmentation/anisotropic_image_segmentation.cpp` of the OpenCV source code library. + +@include cpp/tutorial_code/ImgProc/anisotropic_image_segmentation/anisotropic_image_segmentation.cpp + +Explanation +----------- +An anisotropic image segmentation algorithm consists of a gradient structure tensor calculation, an orientation calculation, a coherency calculation and an orientation and coherency thresholding: +@snippet samples/cpp/tutorial_code/ImgProc/anisotropic_image_segmentation/anisotropic_image_segmentation.cpp main + +A function calcGST() calculates orientation and coherency by using a gradient structure tensor. An input parameter w defines a window size: +@snippet samples/cpp/tutorial_code/ImgProc/anisotropic_image_segmentation/anisotropic_image_segmentation.cpp calcGST + +The below code applies a thresholds LowThr and HighThr to image orientation and a threshold C_Thr to image coherency calculated by the previous function. LowThr and HighThr define orientation range: +@snippet samples/cpp/tutorial_code/ImgProc/anisotropic_image_segmentation/anisotropic_image_segmentation.cpp thresholding + +And finally we combine thresholding results: +@snippet samples/cpp/tutorial_code/ImgProc/anisotropic_image_segmentation/anisotropic_image_segmentation.cpp combining + +Result +------ + +Below you can see the real anisotropic image with single direction: +![Anisotropic image with the single direction](images/gst_input.jpg) + +Below you can see the orientation and coherency of the anisotropic image: +![Orientation](images/gst_orientation.jpg) +![Coherency](images/gst_coherency.jpg) + +Below you can see the segmentation result: +![Segmentation result](images/gst_result.jpg) + +The result has been computed with w = 52, C_Thr = 0.43, LowThr = 35, HighThr = 57. We can see that the algorithm selected only the areas with one single direction. + +References +------ +- [Structure tensor] - structure tensor description on the wikipedia + + +[Structure tensor]: https://en.wikipedia.org/wiki/Structure_tensor diff --git a/doc/tutorials/imgproc/anisotropic_image_segmentation/images/gst_coherency.jpg b/doc/tutorials/imgproc/anisotropic_image_segmentation/images/gst_coherency.jpg new file mode 100755 index 0000000000000000000000000000000000000000..87d0881cfc7bcdb451c9e987d2dd3b1c84d54da3 GIT binary patch literal 20377 zcmX7P1z1z>`~DOO0Vzegq&_l2L^>v*bf`$jKqN=!$O%eFhlHdk9h)GdyF(g=Gzf8XE#J=e~4&b4#SyPfxa-sisW=Xq}a+^hoVwA3`!0Jm-d0Jn%6;AR1!3b=ji zf9-$!+y85KNdC7cy>o};4jCyK+5dgW?^2MF-z6s_qoAU=OZmS>Jffzer2gN@O$UIA z;?{HGc8eZx(*xilKAiObo=NQC|F>JWN$!x6krVHwB3^)`Blbx`LhOl@*bVXO5aRcM zJM^RsJmSh^_g~wPKk|I=G%UG*f>))wlkv?2hEL+1SNL7ZhfK^Yto#Ck|2-CZCMhK? zBP*x+;-#9phNhOmTSFsb6H_zW_jdLUj!w?rKE8hb(15^?pCTfoqCdx^q<%?D&&d3m 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MW)iGw_TT*f0K4^W-2eap literal 0 HcmV?d00001 diff --git a/doc/tutorials/imgproc/table_of_content_imgproc.markdown b/doc/tutorials/imgproc/table_of_content_imgproc.markdown index bea1e1b..badc30d 100644 --- a/doc/tutorials/imgproc/table_of_content_imgproc.markdown +++ b/doc/tutorials/imgproc/table_of_content_imgproc.markdown @@ -330,3 +330,13 @@ In this section you will learn about the image processing (manipulation) functio *Author:* Karpushin Vladislav You will learn how to recover an image with motion blur distortion using a Wiener filter. + +- @subpage tutorial_anisotropic_image_segmentation_by_a_gst + + *Languages:* C++ + + *Compatibility:* \> OpenCV 2.0 + + *Author:* Karpushin Vladislav + + You will learn how to segment an anisotropic image with a single local orientation by a gradient structure tensor. diff --git a/samples/cpp/tutorial_code/ImgProc/anisotropic_image_segmentation/anisotropic_image_segmentation.cpp b/samples/cpp/tutorial_code/ImgProc/anisotropic_image_segmentation/anisotropic_image_segmentation.cpp new file mode 100755 index 0000000..345fd06 --- /dev/null +++ b/samples/cpp/tutorial_code/ImgProc/anisotropic_image_segmentation/anisotropic_image_segmentation.cpp @@ -0,0 +1,104 @@ +/** +* @brief You will learn how to segment an anisotropic image with a single local orientation by a gradient structure tensor (GST) +* @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 calcGST(const Mat& inputImg, Mat& imgCoherencyOut, Mat& imgOrientationOut, int w); + +int main() +{ + int W = 52; // window size is WxW + double C_Thr = 0.43; // threshold for coherency + int LowThr = 35; // threshold1 for orientation, it ranges from 0 to 180 + int HighThr = 57; // threshold2 for orientation, it ranges from 0 to 180 + + Mat imgIn = imread("input.jpg", IMREAD_GRAYSCALE); + if (imgIn.empty()) //check whether the image is loaded or not + { + cout << "ERROR : Image cannot be loaded..!!" << endl; + return -1; + } + + //! [main] + Mat imgCoherency, imgOrientation; + calcGST(imgIn, imgCoherency, imgOrientation, W); + + //! [thresholding] + Mat imgCoherencyBin; + imgCoherencyBin = imgCoherency > C_Thr; + Mat imgOrientationBin; + inRange(imgOrientation, Scalar(LowThr), Scalar(HighThr), imgOrientationBin); + //! [thresholding] + + //! [combining] + Mat imgBin; + imgBin = imgCoherencyBin & imgOrientationBin; + //! [combining] + //! [main] + + normalize(imgCoherency, imgCoherency, 0, 255, NORM_MINMAX); + normalize(imgOrientation, imgOrientation, 0, 255, NORM_MINMAX); + imwrite("result.jpg", 0.5*(imgIn + imgBin)); + imwrite("Coherency.jpg", imgCoherency); + imwrite("Orientation.jpg", imgOrientation); + return 0; +} +//! [calcGST] +void calcGST(const Mat& inputImg, Mat& imgCoherencyOut, Mat& imgOrientationOut, int w) +{ + Mat img; + inputImg.convertTo(img, CV_64F); + + // GST components calculation (start) + // J = (J11 J12; J12 J22) - GST + Mat imgDiffX, imgDiffY, imgDiffXY; + Sobel(img, imgDiffX, CV_64F, 1, 0, 3); + Sobel(img, imgDiffY, CV_64F, 0, 1, 3); + multiply(imgDiffX, imgDiffY, imgDiffXY); + + Mat imgDiffXX, imgDiffYY; + multiply(imgDiffX, imgDiffX, imgDiffXX); + multiply(imgDiffY, imgDiffY, imgDiffYY); + + Mat J11, J22, J12; // J11, J22 and J12 are GST components + boxFilter(imgDiffXX, J11, CV_64F, Size(w, w)); + boxFilter(imgDiffYY, J22, CV_64F, Size(w, w)); + boxFilter(imgDiffXY, J12, CV_64F, Size(w, w)); + // GST components calculation (stop) + + // eigenvalue calculation (start) + // lambda1 = J11 + J22 + sqrt((J11-J22)^2 + 4*J12^2) + // lambda2 = J11 + J22 - sqrt((J11-J22)^2 + 4*J12^2) + Mat tmp1, tmp2, tmp3, tmp4; + tmp1 = J11 + J22; + tmp2 = J11 - J22; + multiply(tmp2, tmp2, tmp2); + multiply(J12, J12, tmp3); + sqrt(tmp2 + 4.0 * tmp3, tmp4); + + Mat lambda1, lambda2; + lambda1 = tmp1 + tmp4; // biggest eigenvalue + lambda2 = tmp1 - tmp4; // smallest eigenvalue + // eigenvalue calculation (stop) + + // Coherency calculation (start) + // Coherency = (lambda1 - lambda2)/(lambda1 + lambda2)) - measure of anisotropism + // Coherency is anisotropy degree (consistency of local orientation) + divide(lambda1 - lambda2, lambda1 + lambda2, imgCoherencyOut); + // Coherency calculation (stop) + + // orientation angle calculation (start) + // tan(2*Alpha) = 2*J12/(J22 - J11) + // Alpha = 0.5 atan2(2*J12/(J22 - J11)) + phase(J22 - J11, 2.0*J12, imgOrientationOut, true); + imgOrientationOut = 0.5*imgOrientationOut; + // orientation angle calculation (stop) +} +//! [calcGST] -- 2.7.4