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Merge pull request #26729 from MaximSmolskiy:change-article-for-fitEllipseDirect-function

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Change article for fitEllipseDirect function
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19
doc/opencv.bib
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@ -424,20 +424,11 @@
publisher = {BMVA Press}, publisher = {BMVA Press},
url = {https://www.researchgate.net/profile/Robert_Fisher5/publication/2237785_A_Buyer's_Guide_to_Conic_Fitting/links/0fcfd50f59aeded518000000/A-Buyers-Guide-to-Conic-Fitting.pdf} url = {https://www.researchgate.net/profile/Robert_Fisher5/publication/2237785_A_Buyer's_Guide_to_Conic_Fitting/links/0fcfd50f59aeded518000000/A-Buyers-Guide-to-Conic-Fitting.pdf}
} }
@article{fitzgibbon1999, @inproceedings{oy1998NumericallySD,
abstract = {This work presents a new efficient method for fitting ellipses to scattered data. Previous algorithms either fitted general conics or were computationally expensive. By minimizing the algebraic distance subject to the constraint 4ac-b<sup>2</sup>=1, the new method incorporates the ellipticity constraint into the normalization factor. The proposed method combines several advantages: It is ellipse-specific, so that even bad data will always return an ellipse. It can be solved naturally by a generalized eigensystem. It is extremely robust, efficient, and easy to implement}, title = {Numerically Stable Direct Least Squares Fitting of Ellipses},
author = {Fitzgibbon, Andrew and Pilu, Maurizio and Fisher, Robert B.}, author = {Radim Hal oy and Jan Flusser},
doi = {10.1109/34.765658}, year = {1998},
isbn = {0162-8828}, url = {https://www.semanticscholar.org/paper/Numerically-Stable-Direct-Least-Squares-Fitting-of-oy-Flusser/9a8607575ba9c6016e9f3db5e52f5ed4d14d5dfd}
issn = {01628828},
journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
number = {5},
pages = {476--480},
pmid = {708},
title = {Direct least square fitting of ellipses},
volume = {21},
year = {1999},
url = {https://pdfs.semanticscholar.org/090d/25f94cb021bdd3400a2f547f989a6a5e07ec.pdf}
} }
@article{Gallego2014ACF, @article{Gallego2014ACF,
title = {A Compact Formula for the Derivative of a 3-D Rotation in Exponential Coordinates}, title = {A Compact Formula for the Derivative of a 3-D Rotation in Exponential Coordinates},

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modules/imgproc/include/opencv2/imgproc.hpp
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@ -4344,7 +4344,7 @@ CV_EXPORTS_W RotatedRect fitEllipseAMS( InputArray points );
The function calculates the ellipse that fits a set of 2D points. The function calculates the ellipse that fits a set of 2D points.
It returns the rotated rectangle in which the ellipse is inscribed. It returns the rotated rectangle in which the ellipse is inscribed.
The Direct least square (Direct) method by @cite Fitzgibbon1999 is used. The Direct least square (Direct) method by @cite oy1998NumericallySD is used.
For an ellipse, this basis set is \f$ \chi= \left(x^2, x y, y^2, x, y, 1\right) \f$, For an ellipse, this basis set is \f$ \chi= \left(x^2, x y, y^2, x, y, 1\right) \f$,
which is a set of six free coefficients \f$ A^T=\left\{A_{\text{xx}},A_{\text{xy}},A_{\text{yy}},A_x,A_y,A_0\right\} \f$. which is a set of six free coefficients \f$ A^T=\left\{A_{\text{xx}},A_{\text{xy}},A_{\text{yy}},A_x,A_y,A_0\right\} \f$.

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samples/cpp/fitellipse.cpp
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@ -5,7 +5,7 @@
* contours and approximate it by ellipses using three methods. * contours and approximate it by ellipses using three methods.
* 1: OpenCV's original method fitEllipse which implements Fitzgibbon 1995 method. * 1: OpenCV's original method fitEllipse which implements Fitzgibbon 1995 method.
* 2: The Approximate Mean Square (AMS) method fitEllipseAMS proposed by Taubin 1991 * 2: The Approximate Mean Square (AMS) method fitEllipseAMS proposed by Taubin 1991
* 3: The Direct least square (Direct) method fitEllipseDirect proposed by Fitzgibbon1999. * 3: The Direct least square (Direct) method fitEllipseDirect proposed by oy1998NumericallySD.
* *
* Trackbar specify threshold parameter. * Trackbar specify threshold parameter.
* *