--- /dev/null
+.. _Pyramids:
+
+Image Pyramids
+***************
+
+Goal
+=====
+
+In this tutorial you will learn how to:
+
+* Use the OpenCV functions :pyr_up:`pyrUp <>` and :pyr_down:`pyrDown <>` to downsample or upsample a given image.
+
+Cool 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 (:resize:`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.
+
+ .. image:: images/Pyramids_Tutorial_Pyramid_Theory.png
+ :alt: Pyramid figure
+ :align: center
+
+* Every layer is numbered from bottom to top, so layer :math:`(i+1)` (denoted as :math:`G_{i+1}` is smaller than layer :math:`i` (:math:`G_{i}`).
+
+* To produce layer :math:`(i+1)` in the Gaussian pyramid, we do the following:
+
+ * Convolve :math:`G_{i}` with a Gaussian kernel:
+
+ .. math::
+
+ \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}
+
+ * 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 :math:`G_{0}` (original image) produces the entire pyramid.
+
+* The procedure above was useful to downsample an image. What if we want to make it bigger?:
+
+ * First, upsize the image to twice the original in each dimension, wit the new even rows and columns filled with zeros (:math:`0`)
+
+ * 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 :pyr_up:`pyrUp <>` and :pyr_down:`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://code.ros.org/svn/opencv/trunk/opencv/samples/cpp/tutorial_code/Image_Processing/Pyramids.cpp>`_
+
+.. code-block:: cpp
+
+ #include "opencv2/imgproc/imgproc.hpp"
+ #include "opencv2/highgui/highgui.hpp"
+ #include <math.h>
+ #include <stdlib.h>
+ #include <stdio.h>
+
+ using namespace cv;
+
+ /// Global variables
+ Mat src, dst, tmp;
+ char* window_name = "Pyramids Demo";
+
+
+ /**
+ * @function main
+ */
+ int main( int argc, char** argv )
+ {
+ /// General instructions
+ printf( "\n Zoom In-Out demo \n " );
+ printf( "------------------ \n" );
+ printf( " * [u] -> Zoom in \n" );
+ printf( " * [d] -> Zoom out \n" );
+ printf( " * [ESC] -> Close program \n \n" );
+
+ /// Test image - Make sure it s divisible by 2^{n}
+ src = imread( "../images/chicky_512.png" );
+ if( !src.data )
+ { printf(" No data! -- Exiting the program \n");
+ return -1; }
+
+ tmp = src;
+ dst = tmp;
+
+ /// Create window
+ namedWindow( window_name, CV_WINDOW_AUTOSIZE );
+ imshow( window_name, dst );
+
+ /// Loop
+ 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;
+ }
+ return 0;
+ }
+
+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-block:: cpp
+
+ /// Test image - Make sure it s divisible by 2^{n}
+ src = imread( "../images/chicky_512.png" );
+ if( !src.data )
+ { printf(" No data! -- Exiting the program \n");
+ return -1; }
+
+ * Create a Mat object to store the result of the operations (*dst*) and one to save temporal results (*tmp*).
+
+ .. code-block:: cpp
+
+ Mat src, dst, tmp;
+ /* ... */
+ tmp = src;
+ dst = tmp;
+
+
+
+ * Create a window to display the result
+
+ .. code-block:: cpp
+
+ namedWindow( window_name, CV_WINDOW_AUTOSIZE );
+ imshow( window_name, dst );
+
+ * Perform an infinite loop waiting for user input.
+
+ .. code-block:: 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;
+ }
+
+
+ Our program exits if the user presses *ESC*. Besides, it has two options:
+
+ * **Perform upsampling (after pressing 'u')**
+
+ .. code-block:: cpp
+
+ pyrUp( tmp, dst, Size( tmp.cols*2, tmp.rows*2 )
+
+ We use the function :pyr_up:`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, :pyr_up:`pyrUp <>` expects a size double than the input image (in this case *tmp*).
+
+ * **Perform downsampling (after pressing 'd')**
+
+ .. code-block:: cpp
+
+ pyrDown( tmp, dst, Size( tmp.cols/2, tmp.rows/2 )
+
+ Similarly as with :pyr_up:`pyrUp <>`, we use the function :pyr_down:`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, :pyr_down:`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-block:: cpp
+
+ tmp = dst;
+
+
+
+Results
+========
+
+* After compiling the code above we can test it. The program calls an image **chicky_512.png** that comes in the *tutorial_code/image* folder. Notice that this image is :math:`512 \times 512`, hence a downsample won't generate any error (:math:`512 = 2^{9}`). The original image is shown below:
+
+ .. image:: images/Pyramids_Tutorial_Original_Image.png
+ :alt: Pyramids: Original image
+ :align: center
+
+* First we apply two successive :pyr_down:`pyrDown <>` operations by pressing 'd'. Our output is:
+
+ .. image:: images/Pyramids_Tutorial_PyrDown_Result.png
+ :alt: Pyramids: PyrDown Result
+ :align: center
+
+* 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 :pyr_up:`pyrUp <>` twice (by pressing 'u'). Our output is now:
+
+ .. image:: images/Pyramids_Tutorial_PyrUp_Result.png
+ :alt: Pyramids: PyrUp Result
+ :align: center
+
+
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