Add OpenCV parallel_for_ tutorial.

doc/tutorials/core/how_to_use_OpenCV_parallel_for_/how_to_use_OpenCV_parallel_for_.markdown

+How to use the OpenCV parallel_for_ to parallelize your code {#tutorial_how_to_use_OpenCV_parallel_for_}
+==================================================================
+
+Goal
+----
+
+The goal of this tutorial is to show you how to use the OpenCV `parallel_for_` framework to easily
+parallelize your code. To illustrate the concept, we will write a program to draw a Mandelbrot set
+exploiting almost all the CPU load available.
+The full tutorial code is [here](https://github.com/opencv/opencv/blob/master/samples/cpp/tutorial_code/core/how_to_use_OpenCV_parallel_for_/how_to_use_OpenCV_parallel_for_.cpp).
+If you want more information about multithreading, you will have to refer to a reference book or course as this tutorial is intended
+to remain simple.
+
+Precondition
+----
+
+The first precondition is to have OpenCV built with a parallel framework.
+In OpenCV 3.2, the following parallel frameworks are available in that order:
+1.   Intel Threading Building Blocks (3rdparty library, should be explicitly enabled)
+2.   C= Parallel C/C++ Programming Language Extension (3rdparty library, should be explicitly enabled)
+3.   OpenMP (integrated to compiler, should be explicitly enabled)
+4.   APPLE GCD (system wide, used automatically (APPLE only))
+5.   Windows RT concurrency (system wide, used automatically (Windows RT only))
+6.   Windows concurrency (part of runtime, used automatically (Windows only - MSVC++ >= 10))
+7.   Pthreads (if available)
+
+As you can see, several parallel frameworks can be used in the OpenCV library. Some parallel libraries
+are third party libraries and have to be explictly built and enabled in CMake (e.g. TBB, C=), others are
+automatically available with the platform (e.g. APPLE GCD) but chances are that you should be enable to
+have access to a parallel framework either directly or by enabling the option in CMake and rebuild the library.
+
+The second (weak) precondition is more related to the task you want to achieve as not all computations
+are suitable / can be adatapted to be run in a parallel way. To remain simple, tasks that can be splitted
+into multiple elementary operations with no memory dependency (no possible race condition) are easily
+parallelizable. Computer vision processing are often easily parallelizable as most of the time the processing of
+one pixel does not depend to the state of other pixels.
+
+Simple example: drawing a Mandelbrot set
+----
+
+We will use the example of drawing a Mandelbrot set to show how from a regular sequential code you can easily adapt
+the code to parallize the computation.
+
+Theory
+-----------
+
+The Mandelbrot set definition has been named in tribute to the mathematician Benoit Mandelbrot by the mathematician
+Adrien Douady. It has been famous outside of the mathematics field as the image representation is an example of a
+class of fractals, a mathematical set that exhibits a repeating pattern displayed at every scale (even more, a
+Mandelbrot set is self-similar as the whole shape can be repeatedly seen at different scale). For a more in-depth
+introduction, you can look at the corresponding [Wikipedia article](https://en.wikipedia.org/wiki/Mandelbrot_set).
+Here, we will just introduce the formula to draw the Mandelbrot set (from the mentioned Wikipedia article).
+
+> The Mandelbrot set is the set of values of \f$ c \f$ in the complex plane for which the orbit of 0 under iteration
+> of the quadratic map
+> \f[\begin{cases} z_0 = 0 \\ z_{n+1} = z_n^2 + c \end{cases}\f]
+> remains bounded.
+> That is, a complex number \f$ c \f$ is part of the Mandelbrot set if, when starting with \f$ z_0 = 0 \f$ and applying
+> the iteration repeatedly, the absolute value of \f$ z_n \f$ remains bounded however large \f$ n \f$ gets.
+> This can also be represented as
+> \f[\limsup_{n\to\infty}|z_{n+1}|\leqslant2\f]
+
+Pseudocode
+-----------
+
+A simple algorithm to generate a representation of the Mandelbrot set is called the
+["escape time algorithm"](https://en.wikipedia.org/wiki/Mandelbrot_set#Escape_time_algorithm).
+For each pixel in the rendered image, we test using the recurrence relation if the complex number is bounded or not
+under a maximum number of iterations. Pixels that do not belong to the Mandelbrot set will escape quickly whereas
+we assume that the pixel is in the set after a fixed maximum number of iterations. A high value of iterations will
+produce a more detailed image but the computation time will increase accordingly. We use the number of iterations
+needed to "escape" to depict the pixel value in the image.
+
+```
+For each pixel (Px, Py) on the screen, do:
+{
+  x0 = scaled x coordinate of pixel (scaled to lie in the Mandelbrot X scale (-2, 1))
+  y0 = scaled y coordinate of pixel (scaled to lie in the Mandelbrot Y scale (-1, 1))
+  x = 0.0
+  y = 0.0
+  iteration = 0
+  max_iteration = 1000
+  while (x*x + y*y < 2*2  AND  iteration < max_iteration) {
+    xtemp = x*x - y*y + x0
+    y = 2*x*y + y0
+    x = xtemp
+    iteration = iteration + 1
+  }
+  color = palette[iteration]
+  plot(Px, Py, color)
+}
+```
+
+To relate between the pseudocode and the theory, we have:
+*   \f$ z = x + iy \f$
+*   \f$ z^2 = x^2 + i2xy - y^2 \f$
+*   \f$ c = x_0 + iy_0 \f$
+
+![](images/how_to_use_OpenCV_parallel_for_640px-Mandelset_hires.png)
+
+On this figure, we recall that the real part of a complex number is on the x-axis and the imaginary part on the y-axis.
+You can see that the whole shape can be repeatedly visible if we zoom at particular locations.
+
+Implementation
+-----------
+
+Escape time algorithm implementation
+--------------------------
+
+@snippet how_to_use_OpenCV_parallel_for_.cpp mandelbrot-escape-time-algorithm
+
+Here, we used the [`std::complex`](http://en.cppreference.com/w/cpp/numeric/complex) template class to represent a
+complex number. This function performs the test to check if the pixel is in set or not and returns the "escaped" iteration.
+
+Sequential Mandelbrot implementation
+--------------------------
+
+@snippet how_to_use_OpenCV_parallel_for_.cpp mandelbrot-sequential
+
+In this implementation, we sequentially iterate over the pixels in the rendered image to perform the test to check if the
+pixel is likely to belong to the Mandelbrot set or not.
+
+Another thing to do is to transform the pixel coordinate into the Mandelbrot set space with:
+
+@snippet how_to_use_OpenCV_parallel_for_.cpp mandelbrot-transformation
+
+Finally, to assign the grayscale value to the pixels, we use the following rule:
+*   a pixel is black if it reaches the maximum number of iterations (pixel is assumed to be in the Mandelbrot set),
+*   otherwise we assign a grayscale value depending on the escaped iteration and scaled to fit the grayscale range.
+
+@snippet how_to_use_OpenCV_parallel_for_.cpp mandelbrot-grayscale-value
+
+Using a linear scale transformation is not enough to perceive the grayscale variation. To overcome this, we will boost
+the perception by using a square root scale transformation (borrowed from Jeremy D. Frens in his
+[blog post](http://www.programming-during-recess.net/2016/06/26/color-schemes-for-mandelbrot-sets/)):
+\f$ f \left( x \right) = \sqrt{\frac{x}{\text{maxIter}}} \times 255 \f$
+
+![](images/how_to_use_OpenCV_parallel_for_sqrt_scale_transformation.png)
+
+The green curve corresponds to a simple linear scale transformation, the blue one to a square root scale transformation
+and you can observe how the lowest values will be boosted when looking at the slope at these positions.
+
+Parallel Mandelbrot implementation
+--------------------------
+
+When looking at the sequential implementation, we can notice that each pixel is computed independently. To optimize the
+computation, we can perform multiple pixel calculations in parallel, by exploiting the multi-core architecture of modern
+processor. To achieve this easily, we will use the OpenCV @ref cv::parallel_for_ framework.
+
+@snippet how_to_use_OpenCV_parallel_for_.cpp mandelbrot-parallel
+
+The first thing is to declare a custom class that inherits from @ref cv::ParallelLoopBody and to override the
+`virtual void operator ()(const cv::Range& range) const`.
+
+The range in the `operator ()` represents the subset of pixels that will be treated by an individual thread.
+This splitting is done automatically to distribuate equally the computation load. We have to convert the pixel index coordinate
+to a 2D `[row, col]` coordinate. Also note that we have to keep a reference on the mat image to be able to modify in-place
+the image.
+
+The parallel execution is called with:
+
+@snippet how_to_use_OpenCV_parallel_for_.cpp mandelbrot-parallel-call
+
+Here, the range represents the total number of operations to be executed, so the total number of pixels in the image.
+To set the number of threads, you can use: @ref cv::setNumThreads. You can also specify the number of splitting using the
+nstripes parameter in @ref cv::parallel_for_. For instance, if your processor has 4 threads, setting `cv::setNumThreads(2)`
+or setting `nstripes=2` should be the same as by default it will use all the processor threads available but will split the
+workload only on two threads.
+
+Results
+-----------
+
+You can find the full tutorial code [here](https://github.com/opencv/opencv/blob/master/samples/cpp/tutorial_code/core/how_to_use_OpenCV_parallel_for_/how_to_use_OpenCV_parallel_for_.cpp).
+The performance of the parallel implementation depends of the type of CPU you have. For instance, on 4 cores / 8 threads
+CPU, you can expect a speed-up of around 6.9X. There are many factors to explain why we do not achieve a speed-up of almost 8X.
+Main reasons should be mostly due to:
+*   the overhead to create and manage the threads,
+*   background processes running in parallel,
+*   the difference between 4 hardware cores with 2 logical threads for each core and 8 hardware cores.
+
+The resulting image produced by the tutorial code (you can modify the code to use more iterations and assign a pixel color
+depending on the escaped iteration and using a color palette to get more aesthetic images):
+![Mandelbrot set with xMin=-2.1, xMax=0.6, yMin=-1.2, yMax=1.2, maxIterations=500](images/how_to_use_OpenCV_parallel_for_Mandelbrot.png)

doc/tutorials/core/table_of_content_core.markdown

@@ -106,3 +106,10 @@ understanding how to manipulate the images on a pixel level.
     *Author:* Elena Gvozdeva
 
     You will see how to use the IPP Async with OpenCV.
+
+
+-   @subpage tutorial_how_to_use_OpenCV_parallel_for_
+
+    *Compatibility:* \>= OpenCV 2.4.3
+
+    You will see how to use the OpenCV parallel_for_ to easily parallelize your code.

samples/cpp/tutorial_code/core/how_to_use_OpenCV_parallel_for_/how_to_use_OpenCV_parallel_for_.cpp

+#include <iostream>
+#include <opencv2/core.hpp>
+#include <opencv2/imgcodecs.hpp>
+
+using namespace std;
+using namespace cv;
+
+namespace
+{
+//! [mandelbrot-escape-time-algorithm]
+int mandelbrot(const complex<float> &z0, const int max)
+{
+    complex<float> z = z0;
+    for (int t = 0; t < max; t++)
+    {
+        if (z.real()*z.real() + z.imag()*z.imag() > 4.0f) return t;
+        z = z*z + z0;
+    }
+
+    return max;
+}
+//! [mandelbrot-escape-time-algorithm]
+
+//! [mandelbrot-grayscale-value]
+int mandelbrotFormula(const complex<float> &z0, const int maxIter=500) {
+    int value = mandelbrot(z0, maxIter);
+    if(maxIter - value == 0)
+    {
+        return 0;
+    }
+
+    return cvRound(sqrt(value / (float) maxIter) * 255);
+}
+//! [mandelbrot-grayscale-value]
+
+//! [mandelbrot-parallel]
+class ParallelMandelbrot : public ParallelLoopBody
+{
+public:
+    ParallelMandelbrot (Mat &img, const float x1, const float y1, const float scaleX, const float scaleY)
+        : m_img(img), m_x1(x1), m_y1(y1), m_scaleX(scaleX), m_scaleY(scaleY)
+    {
+    }
+
+    virtual void operator ()(const Range& range) const
+    {
+        for (int r = range.start; r < range.end; r++)
+        {
+            int i = r / m_img.cols;
+            int j = r % m_img.cols;
+
+            float x0 = j / m_scaleX + m_x1;
+            float y0 = i / m_scaleY + m_y1;
+
+            complex<float> z0(x0, y0);
+            uchar value = (uchar) mandelbrotFormula(z0);
+            m_img.ptr<uchar>(i)[j] = value;
+        }
+    }
+
+    ParallelMandelbrot& operator=(const ParallelMandelbrot &) {
+        return *this;
+    };
+
+private:
+    Mat &m_img;
+    float m_x1;
+    float m_y1;
+    float m_scaleX;
+    float m_scaleY;
+};
+//! [mandelbrot-parallel]
+
+//! [mandelbrot-sequential]
+void sequentialMandelbrot(Mat &img, const float x1, const float y1, const float scaleX, const float scaleY)
+{
+    for (int i = 0; i < img.rows; i++)
+    {
+        for (int j = 0; j < img.cols; j++)
+        {
+            float x0 = j / scaleX + x1;
+            float y0 = i / scaleY + y1;
+
+            complex<float> z0(x0, y0);
+            uchar value = (uchar) mandelbrotFormula(z0);
+            img.ptr<uchar>(i)[j] = value;
+        }
+    }
+}
+//! [mandelbrot-sequential]
+}
+
+int main()
+{
+    //! [mandelbrot-transformation]
+    Mat mandelbrotImg(4800, 5400, CV_8U);
+    float x1 = -2.1f, x2 = 0.6f;
+    float y1 = -1.2f, y2 = 1.2f;
+    float scaleX = mandelbrotImg.cols / (x2 - x1);
+    float scaleY = mandelbrotImg.rows / (y2 - y1);
+    //! [mandelbrot-transformation]
+
+    double t1 = (double) getTickCount();
+    //! [mandelbrot-parallel-call]
+    ParallelMandelbrot parallelMandelbrot(mandelbrotImg, x1, y1, scaleX, scaleY);
+    parallel_for_(Range(0, mandelbrotImg.rows*mandelbrotImg.cols), parallelMandelbrot);
+    //! [mandelbrot-parallel-call]
+    t1 = ((double) getTickCount() - t1) / getTickFrequency();
+    cout << "Parallel Mandelbrot: " << t1 << " s" << endl;
+
+    Mat mandelbrotImgSequential(4800, 5400, CV_8U);
+    double t2 = (double) getTickCount();
+    sequentialMandelbrot(mandelbrotImgSequential, x1, y1, scaleX, scaleY);
+    t2 = ((double) getTickCount() - t2) / getTickFrequency();
+    cout << "Sequential Mandelbrot: " << t2 << " s" << endl;
+    cout << "Speed-up: " << t2/t1 << " X" << endl;
+
+    imwrite("Mandelbrot_parallel.png", mandelbrotImg);
+    imwrite("Mandelbrot_sequential.png", mandelbrotImgSequential);
+
+    return EXIT_SUCCESS;
+}