Images can be characterized by a two dimensional spacial function of the form f(x,y) where x,y are the spacial coordinates and f is the intensity value proportional to the the radiated energy. Hence
The function ‘f’ can be decomposed into i(x,y) and r(x,y) where :
‘i’ is the measure of the amount of ‘illumination’.
‘r’ is the measure of ‘reflectance’.
Therefore the function f(x,y) = i(x,y)*r(x,y) such that:
0<r(x,y)<1 where r=0(total absorption) and r=1(total reflectance).
The intensity or gray level of a monochromatic image is given by l=f(x,y)
From the given conditions on ‘i’ and ‘r’ it can be concluded that ‘l’ lies within the range:
Lmin< l <Lmax
The interval [Lmin,Lmax] is called the ‘gray scale’. Generally the scale is shifted numerically to [0,L-1] where l=0 is black and l=L-1 is white and the intermediate values are various shades of gray.