The Gaussian Pyramid is a hierarchy of low-pass filtered versions of the original image, such that successive levels correspond to lower frequencies.

The low-pass filtering is done using convolution with a Gaussian filter kernel.
Where the filter overhangs the image edges we reflect the image about its edge.
Since the lowest frequencies have been removed, the full-size image contains
redundant pixels. One may define the
REDUCE operator which is a filtering followed by elimination of unnessesary pixels.
For a filter kernel *w*[*i*,*j*] of dimension and reduction factor 4 we have:

There is a corresponding EXPAND operator which will reconstruct the low-pass filtered image by interpolating between pixels in the reduced image.

A Gaussian pyramid *G*(*I*) is defined on image *I* as:

Tue Jun 20 08:41:17 METDST 2000