257 lines
8.4 KiB
ReStructuredText
257 lines
8.4 KiB
ReStructuredText
.. _Pyramids:
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Image Pyramids
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***************
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Goal
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=====
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In this tutorial you will learn how to:
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* Use the OpenCV functions :pyr_up:`pyrUp <>` and :pyr_down:`pyrDown <>` to downsample or upsample a given image.
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Theory
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=======
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.. note::
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The explanation below belongs to the book **Learning OpenCV** by Bradski and Kaehler.
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* Usually we need to convert an image to a size different than its original. For this, there are two possible options:
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* *Upsize* the image (zoom in) or
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* *Downsize* it (zoom out).
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* 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.
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Image Pyramid
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--------------
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* 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.
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* There are two common kinds of image pyramids:
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* **Gaussian pyramid:** Used to downsample images
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* **Laplacian pyramid:** Used to reconstruct an upsampled image from an image lower in the pyramid (with less resolution)
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* In this tutorial we'll use the *Gaussian pyramid*.
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Gaussian Pyramid
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^^^^^^^^^^^^^^^^^
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* Imagine the pyramid as a set of layers in which the higher the layer, the smaller the size.
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.. image:: images/Pyramids_Tutorial_Pyramid_Theory.png
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:alt: Pyramid figure
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:align: center
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* 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}`).
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* To produce layer :math:`(i+1)` in the Gaussian pyramid, we do the following:
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* Convolve :math:`G_{i}` with a Gaussian kernel:
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.. math::
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\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}
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* Remove every even-numbered row and column.
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* 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.
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* The procedure above was useful to downsample an image. What if we want to make it bigger?:
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* First, upsize the image to twice the original in each dimension, wit the new even rows and columns filled with zeros (:math:`0`)
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* Perform a convolution with the same kernel shown above (multiplied by 4) to approximate the values of the "missing pixels"
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* 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:
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.. note::
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When we reduce the size of an image, we are actually *losing* information of the image.
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Code
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======
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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/ImgProc/Pyramids.cpp>`_
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.. code-block:: cpp
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#include "opencv2/imgproc/imgproc.hpp"
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#include "opencv2/highgui/highgui.hpp"
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#include <math.h>
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#include <stdlib.h>
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#include <stdio.h>
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using namespace cv;
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/// Global variables
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Mat src, dst, tmp;
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char* window_name = "Pyramids Demo";
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/**
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* @function main
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*/
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int main( int argc, char** argv )
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{
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/// General instructions
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printf( "\n Zoom In-Out demo \n " );
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printf( "------------------ \n" );
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printf( " * [u] -> Zoom in \n" );
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printf( " * [d] -> Zoom out \n" );
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printf( " * [ESC] -> Close program \n \n" );
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/// Test image - Make sure it s divisible by 2^{n}
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src = imread( "../images/chicky_512.png" );
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if( !src.data )
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{ printf(" No data! -- Exiting the program \n");
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return -1; }
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tmp = src;
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dst = tmp;
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/// Create window
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namedWindow( window_name, CV_WINDOW_AUTOSIZE );
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imshow( window_name, dst );
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/// Loop
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while( true )
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{
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int c;
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c = waitKey(10);
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if( (char)c == 27 )
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{ break; }
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if( (char)c == 'u' )
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{ pyrUp( tmp, dst, Size( tmp.cols*2, tmp.rows*2 ) );
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printf( "** Zoom In: Image x 2 \n" );
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}
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else if( (char)c == 'd' )
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{ pyrDown( tmp, dst, Size( tmp.cols/2, tmp.rows/2 ) );
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printf( "** Zoom Out: Image / 2 \n" );
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}
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imshow( window_name, dst );
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tmp = dst;
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}
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return 0;
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}
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Explanation
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=============
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#. Let's check the general structure of the program:
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* Load an image (in this case it is defined in the program, the user does not have to enter it as an argument)
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.. code-block:: cpp
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/// Test image - Make sure it s divisible by 2^{n}
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src = imread( "../images/chicky_512.png" );
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if( !src.data )
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{ printf(" No data! -- Exiting the program \n");
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return -1; }
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* Create a Mat object to store the result of the operations (*dst*) and one to save temporal results (*tmp*).
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.. code-block:: cpp
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Mat src, dst, tmp;
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/* ... */
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tmp = src;
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dst = tmp;
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* Create a window to display the result
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.. code-block:: cpp
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namedWindow( window_name, CV_WINDOW_AUTOSIZE );
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imshow( window_name, dst );
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* Perform an infinite loop waiting for user input.
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.. code-block:: cpp
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while( true )
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{
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int c;
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c = waitKey(10);
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if( (char)c == 27 )
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{ break; }
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if( (char)c == 'u' )
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{ pyrUp( tmp, dst, Size( tmp.cols*2, tmp.rows*2 ) );
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printf( "** Zoom In: Image x 2 \n" );
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}
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else if( (char)c == 'd' )
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{ pyrDown( tmp, dst, Size( tmp.cols/2, tmp.rows/2 ) );
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printf( "** Zoom Out: Image / 2 \n" );
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}
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imshow( window_name, dst );
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tmp = dst;
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}
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Our program exits if the user presses *ESC*. Besides, it has two options:
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* **Perform upsampling (after pressing 'u')**
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.. code-block:: cpp
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pyrUp( tmp, dst, Size( tmp.cols*2, tmp.rows*2 )
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We use the function :pyr_up:`pyrUp <>` with 03 arguments:
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* *tmp*: The current image, it is initialized with the *src* original image.
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* *dst*: The destination image (to be shown on screen, supposedly the double of the input image)
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* *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*).
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* **Perform downsampling (after pressing 'd')**
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.. code-block:: cpp
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pyrDown( tmp, dst, Size( tmp.cols/2, tmp.rows/2 )
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Similarly as with :pyr_up:`pyrUp <>`, we use the function :pyr_down:`pyrDown <>` with 03 arguments:
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* *tmp*: The current image, it is initialized with the *src* original image.
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* *dst*: The destination image (to be shown on screen, supposedly half the input image)
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* *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*).
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* 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.
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* Finally, we update the input image **tmp** with the current image displayed, so the subsequent operations are performed on it.
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.. code-block:: cpp
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tmp = dst;
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Results
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========
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* 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:
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.. image:: images/Pyramids_Tutorial_Original_Image.png
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:alt: Pyramids: Original image
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:align: center
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* First we apply two successive :pyr_down:`pyrDown <>` operations by pressing 'd'. Our output is:
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.. image:: images/Pyramids_Tutorial_PyrDown_Result.png
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:alt: Pyramids: PyrDown Result
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:align: center
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* 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:
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.. image:: images/Pyramids_Tutorial_PyrUp_Result.png
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:alt: Pyramids: PyrUp Result
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:align: center
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