Wavelets - Caltech Multi-Res Modeling Group

1 Scale
1.1 Image pyramids
I: Introduction
Alain FOURNIER
University of British Columbia
Analyzing, manipulating and generating data at various scales should be a familiar concept to anybody
involved in Computer Graphics. We will start with “image” pyramids 1 .
In pyramids such as a MIP map used for filtering, successive averages are built from the initial signal.
Figure I.1 shows a schematic representation of the operations and the results.
Figure I.1: Mean pyramid
Sum
Difference
Stored value
Addition
Subtraction
It is clear that it can be seen as the result of applying box filters scaled and translated over the signal. For n
initial values we have log 2 (n) stages, and 2n,1 terms in the result. Moreover because of the order we have
1 We will use the word “image” even though our examples in this section are for 1D signals.