Pyramids refer to rescaling a photograph either increasing the resolution or decreasing it. These are often used to increase the computation efficiency of computer vision algorithms such as image matching in a huge database. In such cases, image matching is computed on a downsampled image and later on the search is iteratively refined for a higher resolution of the image.

The downsampling and upsampling often depend on the pixel selection process. One of the simplest processes is selecting alternative rows and column pixel values to create a downsampled version of the photo as follows:

However, if we try to upsample from the rightmost picture in the previous figure, the results look as follows:

It can easily be seen that the rightmost picture above is not the same as the original one that we started with. This is due to the fact that we lose information during...