
4.2
Sampling
Using
Orthonormal
Functions
93
4.2 SAMPLING USING ORTHONORMAL FUNCTIONS
The aim of sampling is to represent a picture by a finite string or array of
numbers. As long as it is possible to reconstruct a picture from these numbers,
the samples need not correspond to gray levels on a sampling lattice in the
picture plane. In this section, we will show that if we expand a picture function
in terms of a set of orthonormal functions, we may take the coefficients of the
expansion as the picture samples.
4.2.1 Orthonormal Expansions
Let f(x,y) be a real function defined over a region of the *j>-plane.
The function f(x, y) is assumed to