Image pyramids

Pyramids are multiple copies of the same images that differ in their sizes. They are represented as layers, as shown in the following figure. Each level in the pyramid is obtained by reducing the rows and columns by half. Thus, effectively, we make the image's size one quarter of its original size:

Relative sizes of pyramids

Pyramids intrinsically define reduce and expand as their two operations. Reduce refers to a reduction in the image's size, whereas expand refers to an increase in its size.

Note

We will use a convention that lower levels in a pyramid mean downsized images and higher levels mean upsized images.

Gaussian pyramids

In the reduce operation, the equation that we use to successively find levels in pyramids, while using a 5x5 sliding window, has been written as follows. Notice that the size of the image reduces to a quarter of its original size:

The elements of the weight kernel, w, should add up to 1. We use a 5x5 Gaussian kernel for this task. This operation...