Translation of a Digital Line into another according to various Digitization Processes

Abstract

We introduce unusual methods for the digitization process of a line. A square pixel of the computer screen is blackened when the line crosses a special part of this pixel, called the active pixel. The shape of this active pixel is discussed, in the following sense: can we obtain the new Freeman Code of the line, using of a mechanical transformation of the initial Freeman Code, which is the classical Cutting Sequence? Our choice is to limit mechanical transformations to the existence of a given transducer, so that everytime we put in (a power of) the classical Freeman Code of a line, the output recovers the new Freeman Code. Then we prove that such a transducer exists if and only if the active pixel is a polygon with rational vertices and big enough. The same result can be proved if we introduce several grey levels in the representation of the line. Then we get some antialising effects.