Basic mathematical representation
Mathematics for the treatment and analysis of grey-scale images

Spatial support, denoted D, is made up of the spatial locations on which gray-scale images are defined. These spatial locations are called pixels (a contraction of picture elements). The spatial support is a part of the spatial domain ( ${\mathbb{D}}^n$ ). The integer n designates the Euclidean dimension of the spatial domain, and therefore of the spatial support D. It will be equal to 1, 2 or 3 in this article (linear, planar or volumetric image).

In the continuous case, the spatial domain ${\mathbb{D}}^n$...