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Merge pull request #18225 from dmici:fix_missing_0.5_factor_in_anisotropic_segmentation_tutorial

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Alexander Alekhin 2020-09-01 20:49:59 +00:00
commit f9fbd29c14
3 changed files with 11 additions and 9 deletions
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2
doc/tutorials/imgproc/anisotropic_image_segmentation/anisotropic_image_segmentation.markdown
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@ -37,7 +37,7 @@ J_{12} & J_{22}
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]
\f[\lambda_{1,2} = \frac{1}{2} \left [ J_{11} + J_{22} \pm \sqrt{(J_{11} - J_{22})^{2} + 4J_{12}^{2}} \right ] \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?

10
samples/cpp/tutorial_code/ImgProc/anisotropic_image_segmentation/anisotropic_image_segmentation.cpp
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@ -74,8 +74,8 @@ void calcGST(const Mat& inputImg, Mat& imgCoherencyOut, Mat& imgOrientationOut,
// 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)
// lambda1 = 0.5*(J11 + J22 + sqrt((J11-J22)^2 + 4*J12^2))
// lambda2 = 0.5*(J11 + J22 - sqrt((J11-J22)^2 + 4*J12^2))
Mat tmp1, tmp2, tmp3, tmp4;
tmp1 = J11 + J22;
tmp2 = J11 - J22;
@ -84,8 +84,10 @@ void calcGST(const Mat& inputImg, Mat& imgCoherencyOut, Mat& imgOrientationOut,
sqrt(tmp2 + 4.0 * tmp3, tmp4);
Mat lambda1, lambda2;
lambda1 = tmp1 + tmp4; // biggest eigenvalue
lambda2 = tmp1 - tmp4; // smallest eigenvalue
lambda1 = tmp1 + tmp4;
lambda1 = 0.5*lambda1; // biggest eigenvalue
lambda2 = tmp1 - tmp4;
lambda2 = 0.5*lambda2; // smallest eigenvalue
// eigenvalue calculation (stop)
// Coherency calculation (start)

8
samples/python/tutorial_code/imgProc/anisotropic_image_segmentation/anisotropic_image_segmentation.py
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@ -31,16 +31,16 @@ def calcGST(inputIMG, w):
# GST components calculations (stop)
# eigenvalue calculation (start)
# lambda1 = J11 + J22 + sqrt((J11-J22)^2 + 4*J12^2)
# lambda2 = J11 + J22 - sqrt((J11-J22)^2 + 4*J12^2)
# lambda1 = 0.5*(J11 + J22 + sqrt((J11-J22)^2 + 4*J12^2))
# lambda2 = 0.5*(J11 + J22 - sqrt((J11-J22)^2 + 4*J12^2))
tmp1 = J11 + J22
tmp2 = J11 - J22
tmp2 = cv.multiply(tmp2, tmp2)
tmp3 = cv.multiply(J12, J12)
tmp4 = np.sqrt(tmp2 + 4.0 * tmp3)
lambda1 = tmp1 + tmp4 # biggest eigenvalue
lambda2 = tmp1 - tmp4 # smallest eigenvalue
lambda1 = 0.5*(tmp1 + tmp4) # biggest eigenvalue
lambda2 = 0.5*(tmp1 - tmp4) # smallest eigenvalue
# eigenvalue calculation (stop)
# Coherency calculation (start)