An image is represented by two-dimensional functions of the form f(x, y). The value or amplitude of f at spatial coordinates (x, y) is a positive scalar quantity whose physical meaning is determined by the source of the image. When an image is generated from a physical process, its values are proportional to energy radiated by a physical source (e.g., electromagnetic waves). As a consequence, f(x, y) must be nonzero and finite; that is,
0 < f (x, y) < ∞ …. (1) The function f(x, y) may be characterized by two components:
- The amount of source illumination incident on the scene being
- The amount of illumination reflected by the objects in the
Appropriately, these are called the illumination and reflectance components and are denoted by i (x, y) and r (x, y), respectively. The two functions combine as a product to form f (x, y).
f (x, y) = i (x, y) r (x, y) …. (2)
0 < i (x, y) < ∞ …. (3)
0 < r (x, y) < 1 …. (4)
Equation (4) indicates that reflectance is bounded by 0 (total absorption) and 1 (total reflectance).The nature of i (x, y) is determined by the illumination source, and r (x, y) is determined by the characteristics of the imaged objects. It is noted that these expressions also are applicable to images formed via transmission of the illumination through a medium, such as a chest X-ray.