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176 lines
6.8 KiB
Markdown
176 lines
6.8 KiB
Markdown
Image Pyramids {#tutorial_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 @ref cv::pyrUp and @ref cv::pyrDown to downsample or upsample a given
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image.
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Theory
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------
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@note 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
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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
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image (@ref cv::resize , which we will show in a future tutorial), in this section we analyze
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first the use of **Image Pyramids**, which are widely applied in a huge range of vision
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applications.
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### Image Pyramid
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- An image pyramid is a collection of images - all arising from a single original image - that are
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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
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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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- Imagine the pyramid as a set of layers in which the higher the layer, the smaller the size.
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- Every layer is numbered from bottom to top, so layer \f$(i+1)\f$ (denoted as \f$G_{i+1}\f$ is smaller
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than layer \f$i\f$ (\f$G_{i}\f$).
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- To produce layer \f$(i+1)\f$ in the Gaussian pyramid, we do the following:
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- Convolve \f$G_{i}\f$ with a Gaussian kernel:
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\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]
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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
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predecessor. Iterating this process on the input image \f$G_{0}\f$ (original image) produces the
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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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columns filled with zeros (\f$0\f$)
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- First, upsize the image to twice the original in each dimension, wit the new even rows and
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- Perform a convolution with the same kernel shown above (multiplied by 4) to approximate the
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values of the "missing pixels"
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- These two procedures (downsampling and upsampling as explained above) are implemented by the
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OpenCV functions @ref cv::pyrUp and @ref cv::pyrDown , as we will see in an example with the
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code below:
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@note 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
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[here](https://github.com/Itseez/opencv/tree/master/samples/cpp/tutorial_code/ImgProc/Pyramids.cpp)
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@include samples/cpp/tutorial_code/ImgProc/Pyramids.cpp
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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
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as an argument)
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@code{.cpp}
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/// Test image - Make sure it s divisible by 2^{n}
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src = imread( "../images/chicky_512.jpg" );
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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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@endcode
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- Create a Mat object to store the result of the operations (*dst*) and one to save temporal
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results (*tmp*).
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@code{.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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@endcode
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- Create a window to display the result
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@code{.cpp}
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namedWindow( window_name, WINDOW_AUTOSIZE );
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imshow( window_name, dst );
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@endcode
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- Perform an infinite loop waiting for user input.
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@code{.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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@endcode
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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{.cpp}
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pyrUp( tmp, dst, Size( tmp.cols*2, tmp.rows*2 )
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@endcode
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We use the function @ref cv::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
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input image)
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- *Size( tmp.cols*2, tmp.rows\*2 )\* : The destination size. Since we are upsampling,
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@ref cv::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{.cpp}
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pyrDown( tmp, dst, Size( tmp.cols/2, tmp.rows/2 )
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@endcode
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Similarly as with @ref cv::pyrUp , we use the function @ref cv::pyrDown with 03
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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
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image)
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- *Size( tmp.cols/2, tmp.rows/2 )* : The destination size. Since we are upsampling,
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@ref cv::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
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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
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subsequent operations are performed on it.
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@code{.cpp}
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tmp = dst;
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@endcode
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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.jpg**
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that comes in the *tutorial_code/image* folder. Notice that this image is \f$512 \times 512\f$,
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hence a downsample won't generate any error (\f$512 = 2^{9}\f$). The original image is shown below:
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- First we apply two successive @ref cv::pyrDown operations by pressing 'd'. Our output is:
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- Note that we should have lost some resolution due to the fact that we are diminishing the size
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of the image. This is evident after we apply @ref cv::pyrUp twice (by pressing 'u'). Our output
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is now:
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