6. Operators and functions

In mathematics, an operator (not to be confused with an operation) is an application between two spaces of functions or sets. A functional is an application of a space of functions or sets in the body of scalar numbers (generally real and often positive). In binary imaging, there are two main categories of operators and functionals:

• those acting on binary images ;

• those concerning binary objects.

Operators act on one or more binary images (or objects) as input and produce one or more other binary images (or objects) as output. They model image transformations (for example, spatial rotation of an image or skeletonization). Functionals act as inputs on one or more binary images (or objects) and provide one or more quantitative information. They model image measurements. Operators...