Image Pyramids {#tutorial_pyramids}
==============

Goal
----

In this tutorial you will learn how to:

-   Use the OpenCV functions @ref cv::pyrUp and @ref cv::pyrDown to downsample or upsample a given
    image.

Theory
------

@note The explanation below belongs to the book **Learning OpenCV** by Bradski and Kaehler.

-   Usually we need to convert an image to a size different than its original. For this, there are
    two possible options:
    -#  *Upsize* the image (zoom in) or
    -#  *Downsize* it (zoom out).
-   Although there is a *geometric transformation* function in OpenCV that -literally- resize an
    image (@ref cv::resize , which we will show in a future tutorial), in this section we analyze
    first the use of **Image Pyramids**, which are widely applied in a huge range of vision
    applications.

### Image Pyramid

-   An image pyramid is a collection of images - all arising from a single original image - that are
    successively downsampled until some desired stopping point is reached.
-   There are two common kinds of image pyramids:
    -   **Gaussian pyramid:** Used to downsample images
    -   **Laplacian pyramid:** Used to reconstruct an upsampled image from an image lower in the
        pyramid (with less resolution)
-   In this tutorial we'll use the *Gaussian pyramid*.

#### Gaussian Pyramid

-   Imagine the pyramid as a set of layers in which the higher the layer, the smaller the size.

    ![](images/Pyramids_Tutorial_Pyramid_Theory.png)

-   Every layer is numbered from bottom to top, so layer \f$(i+1)\f$ (denoted as \f$G_{i+1}\f$ is smaller
    than layer \f$i\f$ (\f$G_{i}\f$).
-   To produce layer \f$(i+1)\f$ in the Gaussian pyramid, we do the following:
    -   Convolve \f$G_{i}\f$ with a Gaussian kernel:

        \f[\frac{1}{16} \begin{bmatrix} 1 & 4 & 6 & 4 & 1  \\ 4 & 16 & 24 & 16 & 4  \\ 6 & 24 & 36 & 24 & 6  \\ 4 & 16 & 24 & 16 & 4  \\ 1 & 4 & 6 & 4 & 1 \end{bmatrix}\f]

    -   Remove every even-numbered row and column.

-   You can easily notice that the resulting image will be exactly one-quarter the area of its
    predecessor. Iterating this process on the input image \f$G_{0}\f$ (original image) produces the
    entire pyramid.
-   The procedure above was useful to downsample an image. What if we want to make it bigger?:
    columns filled with zeros (\f$0\f$)
    -   First, upsize the image to twice the original in each dimension, wit the new even rows and
    -   Perform a convolution with the same kernel shown above (multiplied by 4) to approximate the
        values of the "missing pixels"
-   These two procedures (downsampling and upsampling as explained above) are implemented by the
    OpenCV functions @ref cv::pyrUp and @ref cv::pyrDown , as we will see in an example with the
    code below:

@note When we reduce the size of an image, we are actually *losing* information of the image.

Code
----

This tutorial code's is shown lines below. You can also download it from
[here](https://github.com/Itseez/opencv/tree/master/samples/cpp/tutorial_code/ImgProc/Pyramids.cpp)

@include samples/cpp/tutorial_code/ImgProc/Pyramids.cpp

Explanation
-----------

Let's check the general structure of the program:

-   Load an image (in this case it is defined in the program, the user does not have to enter it
    as an argument)
    @code{.cpp}
    /// Test image - Make sure it s divisible by 2^{n}
    src = imread( "../images/chicky_512.jpg" );
    if( !src.data )
      { printf(" No data! -- Exiting the program \n");
        return -1; }
    @endcode

-   Create a Mat object to store the result of the operations (*dst*) and one to save temporal
    results (*tmp*).
    @code{.cpp}
    Mat src, dst, tmp;
    /* ... */
    tmp = src;
    dst = tmp;
    @endcode

-   Create a window to display the result
    @code{.cpp}
    namedWindow( window_name, WINDOW_AUTOSIZE );
    imshow( window_name, dst );
    @endcode

-   Perform an infinite loop waiting for user input.
    @code{.cpp}
    while( true )
    {
      int c;
      c = waitKey(10);

      if( (char)c == 27 )
        { break; }
      if( (char)c == 'u' )
        { pyrUp( tmp, dst, Size( tmp.cols*2, tmp.rows*2 ) );
          printf( "** Zoom In: Image x 2 \n" );
        }
      else if( (char)c == 'd' )
       { pyrDown( tmp, dst, Size( tmp.cols/2, tmp.rows/2 ) );
         printf( "** Zoom Out: Image / 2 \n" );
       }

      imshow( window_name, dst );
      tmp = dst;
    }
    @endcode
    Our program exits if the user presses *ESC*. Besides, it has two options:

    -   **Perform upsampling (after pressing 'u')**
        @code{.cpp}
        pyrUp( tmp, dst, Size( tmp.cols*2, tmp.rows*2 )
        @endcode
        We use the function @ref cv::pyrUp with 03 arguments:

        -   *tmp*: The current image, it is initialized with the *src* original image.
        -   *dst*: The destination image (to be shown on screen, supposedly the double of the
            input image)
        -   *Size( tmp.cols*2, tmp.rows\*2 )\* : The destination size. Since we are upsampling,
            @ref cv::pyrUp expects a size double than the input image (in this case *tmp*).
    -   **Perform downsampling (after pressing 'd')**
        @code{.cpp}
        pyrDown( tmp, dst, Size( tmp.cols/2, tmp.rows/2 )
        @endcode
        Similarly as with @ref cv::pyrUp , we use the function @ref cv::pyrDown with 03
        arguments:

        -   *tmp*: The current image, it is initialized with the *src* original image.
        -   *dst*: The destination image (to be shown on screen, supposedly half the input
            image)
        -   *Size( tmp.cols/2, tmp.rows/2 )* : The destination size. Since we are upsampling,
            @ref cv::pyrDown expects half the size the input image (in this case *tmp*).
    -   Notice that it is important that the input image can be divided by a factor of two (in
        both dimensions). Otherwise, an error will be shown.
    -   Finally, we update the input image **tmp** with the current image displayed, so the
        subsequent operations are performed on it.
        @code{.cpp}
        tmp = dst;
        @endcode

Results
-------

-   After compiling the code above we can test it. The program calls an image **chicky_512.jpg**
    that comes in the *tutorial_code/image* folder. Notice that this image is \f$512 \times 512\f$,
    hence a downsample won't generate any error (\f$512 = 2^{9}\f$). The original image is shown below:

    ![](images/Pyramids_Tutorial_Original_Image.jpg)

-   First we apply two successive @ref cv::pyrDown operations by pressing 'd'. Our output is:

    ![](images/Pyramids_Tutorial_PyrDown_Result.jpg)

-   Note that we should have lost some resolution due to the fact that we are diminishing the size
    of the image. This is evident after we apply @ref cv::pyrUp twice (by pressing 'u'). Our output
    is now:

    ![](images/Pyramids_Tutorial_PyrUp_Result.jpg)