Explain a simple Image Formation Model.

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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:

  1. The amount of source illumination incident on the scene being


  1. 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.

Raju Singhaniya
Oct 15, 2021
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