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}
+}
--- /dev/null
+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:
+
+
+Below you can see the orientation and coherency of the anisotropic image:
+
+
+
+Below you can see the segmentation result:
+
+
+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
+
+<!-- invisible references list -->
+[Structure tensor]: https://en.wikipedia.org/wiki/Structure_tensor
--- /dev/null
+/**
+* @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 <iostream>
+#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]
projects / platform / upstream / opencv.git / commitdiff
