Images and two-dimensional signals

The function f(x, y) describes intensity or luminance at location (x, y) within an image. Therefore, one says that a function of two independent variables f(x, y) models an image, or one says that an image is two-dimensional signal as it is modeled by a function of two independent variables.

From the mathematical point of view, one may consider function f(x, y) where the two spatial variables x and y are real. In such a case one would speak about a two-dimensional continuous function.

Continuous signals may be sampled by considering the function values in some isolated points only. Sampled signal is a discrete signal. A two-dimensional discrete signal is modeled by a function f(n_x,n_y),where n_x,n_y are integer variables obtained by sampling of x and y.