3. A fundamental example

From a mathematical point of view, the natural representation of an image is a function f (x, y ) representing the light intensity, between 0 (black) and 1 (white), at the point (x, y ) of the "frame" [0, 1] × [0, 1]. In a digital context, the image is given in discretized form on a pixel grid, i.e. as an array f (k _x , k _y ). Such an image is visualized in figure 3 for discretization on a 512 × 512 pixel grid.

A particularly fruitful idea in digital image processing is that visual information is hierarchical across scales. Thus, starting from a discretized image, we can consider its approximations obtained by successively averaging light intensity over 2 × 2 pixel squares, then 4 × 4, 8...