Dilation (morphology) - Grayscale Dilation

Grayscale Dilation

In grayscale morphology, images are functions mapping a Euclidean space or grid E into, where is the set of reals, is an element larger than any real number, and is an element smaller than any real number.

Grayscale structuring elements are also functions of the same format, called "structuring functions".

Denoting an image by f(x) and the structuring function by b(x), the grayscale dilation of f by b is given by

,

where "sup" denotes the supremum.