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.. _Pyramids:
Image Pyramids
***************
Goal
=====
In this tutorial you will learn how to:
.. container:: enumeratevisibleitemswithsquare
* Use the OpenCV functions :pyr_up:`pyrUp <>` and :pyr_down:`pyrDown <>` to downsample or upsample a given image.
Theory
=======
.. note::
The explanation below belongs to the book **Learning OpenCV** by Bradski and Kaehler.
.. container:: enumeratevisibleitemswithsquare
* 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
--------------
.. container:: enumeratevisibleitemswithsquare
* 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://github.com/Itseez/opencv/tree/master/samples/cpp/tutorial_code/ImgProc/Pyramids.cpp>`_
.. code-block:: cpp
#include "opencv2/imgproc.hpp"
#include "opencv2/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.jpg" );
if( !src.data )
{ printf(" No data! -- Exiting the program \n");
return -1; }
tmp = src;
dst = tmp;
/// Create window
namedWindow( window_name, 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.jpg" );
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, 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.jpg** 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.jpg
: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.jpg
: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.jpg
:alt: Pyramids: PyrUp Result
:align: center
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