Merge branch 4.x

doc/tutorials/gpu/gpu-thrust-interop/gpu_thrust_interop.markdown

@@ -10,7 +10,7 @@ Goal
 ----
 
 Thrust is an extremely powerful library for various cuda accelerated algorithms.  However thrust is designed
-to work with vectors and not pitched matricies.  The following tutorial will discuss wrapping cv::cuda::GpuMat's
+to work with vectors and not pitched matrices.  The following tutorial will discuss wrapping cv::cuda::GpuMat's
 into thrust iterators that can be used with thrust algorithms.
 
 This tutorial should show you how to:

doc/tutorials/imgproc/erosion_dilatation/erosion_dilatation.markdown

@@ -129,6 +129,7 @@ receives three arguments:
     -   Rectangular box: MORPH_RECT
     -   Cross: MORPH_CROSS
     -   Ellipse: MORPH_ELLIPSE
+    -   Diamond: MORPH_DIAMOND
 
     Then, we just have to specify the size of our kernel and the *anchor point*. If not
     specified, it is assumed to be in the center.
@@ -256,6 +257,7 @@ receives two arguments and returns the processed image:
     -   Rectangular box: MORPH_RECT
     -   Cross: MORPH_CROSS
     -   Ellipse: MORPH_ELLIPSE
+    -   Diamond: MORPH_DIAMOND
 
 Then, we just have to specify the size of our kernel and the *anchor point*. If the anchor point not
 specified, it is assumed to be in the center.

doc/tutorials/imgproc/histograms/histogram_comparison/histogram_comparison.markdown

@@ -25,7 +25,7 @@ Theory
 
 -   To compare two histograms ( \f$H_{1}\f$ and \f$H_{2}\f$ ), first we have to choose a *metric*
     (\f$d(H_{1}, H_{2})\f$) to express how well both histograms match.
--   OpenCV implements the function @ref cv::compareHist to perform a comparison. It also offers 4
+-   OpenCV implements the function @ref cv::compareHist to perform a comparison. It also offers 6
     different metrics to compute the matching:
     -#  **Correlation ( cv::HISTCMP_CORREL )**
         \f[d(H_1,H_2) =  \frac{\sum_I (H_1(I) - \bar{H_1}) (H_2(I) - \bar{H_2})}{\sqrt{\sum_I(H_1(I) - \bar{H_1})^2 \sum_I(H_2(I) - \bar{H_2})^2}}\f]
@@ -36,12 +36,18 @@ Theory
     -#  **Chi-Square ( cv::HISTCMP_CHISQR )**
         \f[d(H_1,H_2) =  \sum _I  \frac{\left(H_1(I)-H_2(I)\right)^2}{H_1(I)}\f]
 
-    -#  **Intersection ( method=cv::HISTCMP_INTERSECT )**
+    -#  **Intersection ( cv::HISTCMP_INTERSECT )**
         \f[d(H_1,H_2) =  \sum _I  \min (H_1(I), H_2(I))\f]
 
     -#  **Bhattacharyya distance ( cv::HISTCMP_BHATTACHARYYA )**
         \f[d(H_1,H_2) =  \sqrt{1 - \frac{1}{\sqrt{\bar{H_1} \bar{H_2} N^2}} \sum_I \sqrt{H_1(I) \cdot H_2(I)}}\f]
 
+    -#  **Alternative Chi-Square ( cv::HISTCMP_CHISQR_ALT )**
+        \f[d(H_1,H_2) =  2 * \sum _I  \frac{\left(H_1(I)-H_2(I)\right)^2}{H_1(I)+H_2(I)}\f]
+
+    -#  **Kullback-Leibler divergence ( cv::HISTCMP_KL_DIV )**
+        \f[d(H_1,H_2) =  \sum _I H_1(I) \log \left(\frac{H_1(I)}{H_2(I)}\right)\f]
+
 Code
 ----
 
@@ -123,7 +129,7 @@ Explanation
     @snippet samples/python/tutorial_code/Histograms_Matching/histogram_comparison/compareHist_Demo.py Convert to HSV half
     @end_toggle
 
--   Initialize the arguments to calculate the histograms (bins, ranges and channels H and S ).
+-   Initialize the arguments to calculate the histograms (bins, ranges and channels H and S).
 
     @add_toggle_cpp
     @snippet samples/cpp/tutorial_code/Histograms_Matching/compareHist_Demo.cpp Using 50 bins for hue and 60 for saturation
@@ -151,7 +157,7 @@ Explanation
     @snippet samples/python/tutorial_code/Histograms_Matching/histogram_comparison/compareHist_Demo.py Calculate the histograms for the HSV images
     @end_toggle
 
--   Apply sequentially the 4 comparison methods between the histogram of the base image (hist_base)
+-   Apply sequentially the 6 comparison methods between the histogram of the base image (hist_base)
     and the other histograms:
 
     @add_toggle_cpp
@@ -182,15 +188,17 @@ Results
     are from the same source. For the other two test images, we can observe that they have very
     different lighting conditions, so the matching should not be very good:
 
--#  Here the numeric results we got with OpenCV 3.4.1:
-      *Method*        |  Base - Base |  Base - Half |  Base - Test 1 |  Base - Test 2
-    ----------------- | ------------ | ------------ | -------------- | ---------------
-      *Correlation*   |  1.000000    |  0.880438    |  0.20457       |  0.0664547
-      *Chi-square*    |  0.000000    |  4.6834      |  2697.98       |  4763.8
-      *Intersection*  |  18.8947     |  13.022      |  5.44085       |  2.58173
-      *Bhattacharyya* |  0.000000    |  0.237887    |  0.679826      |  0.874173
+-#  Here the numeric results we got with OpenCV 4.12.0:
+      *Method*          |  Base - Base |  Base - Half |  Base - Test 1 |  Base - Test 2
+    ------------------- | ------------ | ------------ | -------------- | ---------------
+      *Correlation*     |  1.000000    |  0.880438    |  0.20457       |  0.065752
+      *Chi-square*      |  0.000000    |  0.328307    |  181.674       |  80.1494
+      *Intersection*    |  1.000000    |  0.75005     |  0.315061      |  0.0908022
+      *Bhattacharyya*   |  0.000000    |  0.237866    |  0.679825      |  0.873709
+      *Chi-Square alt.* |  0.000000    |  0.395046    |  2.31572       |  3.41024
+      *KL divergence*   |  0.000000    |  0.321064    |  2.6616        |  9.55412
+
     For the *Correlation* and *Intersection* methods, the higher the metric, the more accurate the
     match. As we can see, the match *base-base* is the highest of all as expected. Also we can observe
-    that the match *base-half* is the second best match (as we predicted). For the other two metrics,
-    the less the result, the better the match. We can observe that the matches between the test 1 and
-    test 2 with respect to the base are worse, which again, was expected.
+    that the match *base-half* is the second best match (as we predicted). For the other four metrics,
+    the less the result, the better the match.

doc/tutorials/objdetect/aruco_faq/aruco_faq.markdown

@@ -166,7 +166,7 @@ for `cv::aruco::Dictionary`. The data member of board classes are public and can
 - Alright, but how can I render a 3d model to create an augmented reality application?
 
 To do so, you will need to use an external rendering engine library, such as OpenGL. The aruco module
-only provides the functionality to obtain the camera pose, i.e. the rotation and traslation vectors,
+only provides the functionality to obtain the camera pose, i.e. the rotation and translation vectors,
 which is necessary to create the augmented reality effect. However, you will need to adapt the rotation
 and traslation vectors from the OpenCV format to the format accepted by your 3d rendering library.
 The original ArUco library contains examples of how to do it for OpenGL and Ogre3D.