.. _Basic_Linear_Transform:

Changing the contrast and brightness of an image!
***************************************************

Goal
=====

In this tutorial you will learn how to:

.. container:: enumeratevisibleitemswithsquare

   + Access pixel values 

   + Initialize a matrix with zeros

   + Learn what :saturate_cast:`saturate_cast <>` does and why it is useful

   + Get some cool info about pixel transformations

Cool Theory
=================
 
.. note::
   The explanation below belongs to the book `Computer Vision: Algorithms and Applications <http://szeliski.org/Book/>`_  by Richard Szeliski 

Image Processing
--------------------

* A general image processing operator is a function that takes one or more input images and produces an output image. 

* Image transforms can be seen as:

  * Point operators (pixel transforms)
  * Neighborhood (area-based) operators


Pixel Transforms
^^^^^^^^^^^^^^^^^

* In this kind of image processing transform, each output pixel's value depends on only the corresponding input pixel value (plus, potentially, some globally collected information or parameters).

* Examples of such operators include *brightness and contrast adjustments* as well as color correction and transformations.

Brightness and contrast adjustments
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
* Two commonly used point processes are *multiplication* and *addition* with a constant:

  .. math::

     g(x) = \alpha f(x) + \beta

* The parameters :math:`\alpha > 0` and :math:`\beta` are often called the *gain* and *bias* parameters; sometimes these parameters are said to control *contrast* and *brightness* respectively.

* You can think of :math:`f(x)` as the source image pixels and :math:`g(x)` as the output image pixels. Then, more conveniently we can write the expression as:

  .. math::
   
     g(i,j) = \alpha \cdot f(i,j) + \beta
  
  where :math:`i` and :math:`j` indicates that the pixel is located in the *i-th* row and *j-th* column. 

Code
=====

* The following code performs the operation :math:`g(i,j) = \alpha \cdot f(i,j) + \beta`
* Here it is:

.. code-block:: cpp

   #include <cv.h>
   #include <highgui.h>
   #include <iostream>

   using namespace cv;

   double alpha; /**< Simple contrast control */
   int beta;  /**< Simple brightness control */

   int main( int argc, char** argv )
   {
    /// Read image given by user
    Mat image = imread( argv[1] );
    Mat new_image = Mat::zeros( image.size(), image.type() );

    /// Initialize values 
    std::cout<<" Basic Linear Transforms "<<std::endl;
    std::cout<<"-------------------------"<<std::endl;
    std::cout<<"* Enter the alpha value [1.0-3.0]: ";std::cin>>alpha;
    std::cout<<"* Enter the beta value [0-100]: "; std::cin>>beta;

    /// Do the operation new_image(i,j) = alpha*image(i,j) + beta
    for( int y = 0; y < image.rows; y++ )
       { for( int x = 0; x < image.cols; x++ )
            { for( int c = 0; c < 3; c++ )
                 {
         new_image.at<Vec3b>(y,x)[c] = 
            saturate_cast<uchar>( alpha*( image.at<Vec3b>(y,x)[c] ) + beta );
                }
       }
       }

    /// Create Windows
    namedWindow("Original Image", 1);
    namedWindow("New Image", 1);

    /// Show stuff
    imshow("Original Image", image);
    imshow("New Image", new_image);

    /// Wait until user press some key
    waitKey();
    return 0;
   }

Explanation
============

#. We begin by creating parameters to save :math:`\alpha` and :math:`\beta` to be entered by the user:

   .. code-block:: cpp

      double alpha;
      int beta;


#. We load an image using :imread:`imread <>` and save it in a Mat object:
   
   .. code-block:: cpp

      Mat image = imread( argv[1] );

#. Now, since we will make some transformations to this image, we need a new Mat object to store it. Also, we want this to have the following features:
   
   * Initial pixel values equal to zero
   * Same size and type as the original image
 
   .. code-block:: cpp

      Mat new_image = Mat::zeros( image.size(), image.type() ); 
 
   We observe that :mat_zeros:`Mat::zeros <>` returns a Matlab-style zero initializer based on *image.size()* and *image.type()*  

#. Now, to perform the operation :math:`g(i,j) = \alpha \cdot f(i,j) + \beta` we will access to each pixel in image. Since we are operating with RGB images, we will have three values per pixel (R, G and B), so we will also access them separately. Here is the piece of code:

   .. code-block:: cpp
 
      for( int y = 0; y < image.rows; y++ )
         { for( int x = 0; x < image.cols; x++ )
              { for( int c = 0; c < 3; c++ )
                   { new_image.at<Vec3b>(y,x)[c] = 
                               saturate_cast<uchar>( alpha*( image.at<Vec3b>(y,x)[c] ) + beta ); }
         }
         }
 
   Notice the following:

   * To access each pixel in the images we are using this syntax: *image.at<Vec3b>(y,x)[c]* where *y* is the row, *x* is the column and *c* is R, G or B (0, 1 or 2). 

   * Since the operation :math:`\alpha \cdot p(i,j) + \beta` can give values out of range or not integers (if :math:`\alpha` is float), we use :saturate_cast:`saturate_cast <>` to make sure the values are valid.


#. Finally, we create windows and show the images, the usual way.

   .. code-block:: cpp
   
      namedWindow("Original Image", 1);
      namedWindow("New Image", 1);

      imshow("Original Image", image);
      imshow("New Image", new_image);

      waitKey(0);

.. note::
  
   Instead of using the **for** loops to access each pixel, we could have simply used this command:
  
   .. code-block:: cpp

      image.convertTo(new_image, -1, alpha, beta);

   where :convert_to:`convertTo <>` would effectively perform *new_image = a*image + beta*. However, we wanted to show you how to access each pixel. In any case, both methods give the same result.

Result
=======

* Running our code and using :math:`\alpha = 2.2` and :math:`\beta = 50`

  .. code-block:: bash

     $ ./BasicLinearTransforms lena.jpg
     Basic Linear Transforms
     -------------------------
     * Enter the alpha value [1.0-3.0]: 2.2
     * Enter the beta value [0-100]: 50

* We get this:

.. image:: images/Basic_Linear_Transform_Tutorial_Result_0.jpg
   :alt: Basic Linear Transform - Final Result
   :align: center 