* 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.
* 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.
* 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:
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>`_
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*).
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.
* 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:
* 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:
