From 0be2c7018b49dbafb8f1fa719826e9a7af1e8156 Mon Sep 17 00:00:00 2001
From: Ganesh Kathiresan <ganesh3597@gmail.com>
Date: Tue, 21 Apr 2020 16:08:58 +0530
Subject: [PATCH] Formula Fixes for 3.4 branch

Foumula fix 1

Foumula fix 2

Foumula fix 3

Foumula fix 4

Foumula fix 5

Foumula fix 8
---
 doc/tutorials/ml/non_linear_svms/non_linear_svms.markdown | 2 +-
 modules/calib3d/include/opencv2/calib3d.hpp               | 2 +-
 modules/imgproc/include/opencv2/imgproc.hpp               | 6 +++---
 modules/video/include/opencv2/video/tracking.hpp          | 2 +-
 4 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/doc/tutorials/ml/non_linear_svms/non_linear_svms.markdown b/doc/tutorials/ml/non_linear_svms/non_linear_svms.markdown
index 74a15597ac..7ad1266983 100644
--- a/doc/tutorials/ml/non_linear_svms/non_linear_svms.markdown
+++ b/doc/tutorials/ml/non_linear_svms/non_linear_svms.markdown
@@ -43,7 +43,7 @@ There are multiple ways in which this model can be modified so it takes into acc
 misclassification errors. For example, one could think of minimizing the same quantity plus a
 constant times the number of misclassification errors in the training data, i.e.:
 
-\f[\min ||\beta||^{2} + C \text{(\# misclassication errors)}\f]
+\f[\min ||\beta||^{2} + C \text{(misclassification errors)}\f]
 
 However, this one is not a very good solution since, among some other reasons, we do not distinguish
 between samples that are misclassified with a small distance to their appropriate decision region or
diff --git a/modules/calib3d/include/opencv2/calib3d.hpp b/modules/calib3d/include/opencv2/calib3d.hpp
index efb4618745..e5fd50e123 100644
--- a/modules/calib3d/include/opencv2/calib3d.hpp
+++ b/modules/calib3d/include/opencv2/calib3d.hpp
@@ -1760,7 +1760,7 @@ Optionally, it computes the essential matrix E:
 where \f$T_i\f$ are components of the translation vector \f$T\f$ : \f$T=[T_0, T_1, T_2]^T\f$ .
 And the function can also compute the fundamental matrix F:
 
-\f[F = cameraMatrix2^{-T} E cameraMatrix1^{-1}\f]
+\f[F = cameraMatrix2^{-T}\cdot E \cdot cameraMatrix1^{-1}\f]
 
 Besides the stereo-related information, the function can also perform a full calibration of each of
 the two cameras. However, due to the high dimensionality of the parameter space and noise in the
diff --git a/modules/imgproc/include/opencv2/imgproc.hpp b/modules/imgproc/include/opencv2/imgproc.hpp
index 5c82dd658f..97dc794fee 100644
--- a/modules/imgproc/include/opencv2/imgproc.hpp
+++ b/modules/imgproc/include/opencv2/imgproc.hpp
@@ -226,7 +226,7 @@ enum MorphTypes{
 enum MorphShapes {
     MORPH_RECT    = 0, //!< a rectangular structuring element:  \f[E_{ij}=1\f]
     MORPH_CROSS   = 1, //!< a cross-shaped structuring element:
-                       //!< \f[E_{ij} =  \fork{1}{if i=\texttt{anchor.y} or j=\texttt{anchor.x}}{0}{otherwise}\f]
+                       //!< \f[E_{ij} = \begin{cases} 1 & \texttt{if } {i=\texttt{anchor.y } {or } {j=\texttt{anchor.x}}} \\0 & \texttt{otherwise} \end{cases}\f]
     MORPH_ELLIPSE = 2 //!< an elliptic structuring element, that is, a filled ellipse inscribed
                       //!< into the rectangle Rect(0, 0, esize.width, 0.esize.height)
 };
@@ -1457,7 +1457,7 @@ The function smooths an image using the kernel:
 
 where
 
-\f[\alpha = \fork{\frac{1}{\texttt{ksize.width*ksize.height}}}{when \texttt{normalize=true}}{1}{otherwise}\f]
+\f[\alpha = \begin{cases} \frac{1}{\texttt{ksize.width*ksize.height}} & \texttt{when } \texttt{normalize=true}  \\1 & \texttt{otherwise}\end{cases}\f]
 
 Unnormalized box filter is useful for computing various integral characteristics over each pixel
 neighborhood, such as covariance matrices of image derivatives (used in dense optical flow
@@ -1531,7 +1531,7 @@ according to the specified border mode.
 
 The function does actually compute correlation, not the convolution:
 
-\f[\texttt{dst} (x,y) =  \sum _{ \stackrel{0\leq x' < \texttt{kernel.cols},}{0\leq y' < \texttt{kernel.rows}} }  \texttt{kernel} (x',y')* \texttt{src} (x+x'- \texttt{anchor.x} ,y+y'- \texttt{anchor.y} )\f]
+\f[\texttt{dst} (x,y) =  \sum _{ \substack{0\leq x' < \texttt{kernel.cols}\\{0\leq y' < \texttt{kernel.rows}}}}  \texttt{kernel} (x',y')* \texttt{src} (x+x'- \texttt{anchor.x} ,y+y'- \texttt{anchor.y} )\f]
 
 That is, the kernel is not mirrored around the anchor point. If you need a real convolution, flip
 the kernel using #flip and set the new anchor to `(kernel.cols - anchor.x - 1, kernel.rows -
diff --git a/modules/video/include/opencv2/video/tracking.hpp b/modules/video/include/opencv2/video/tracking.hpp
index e8566faa3a..9f344be225 100644
--- a/modules/video/include/opencv2/video/tracking.hpp
+++ b/modules/video/include/opencv2/video/tracking.hpp
@@ -308,7 +308,7 @@ Default values are shown in the declaration above.
 The function estimates the optimum transformation (warpMatrix) with respect to ECC criterion
 (@cite EP08), that is
 
-\f[\texttt{warpMatrix} = \texttt{warpMatrix} = \arg\max_{W} \texttt{ECC}(\texttt{templateImage}(x,y),\texttt{inputImage}(x',y'))\f]
+\f[\texttt{warpMatrix} = \arg\max_{W} \texttt{ECC}(\texttt{templateImage}(x,y),\texttt{inputImage}(x',y'))\f]
 
 where