Algebraic representation of size functions

In this paper we show that size functions, a class of shape descriptors, can be represented as countable collections of points and lines of the real plane with multiplicities, i.e. as particular formal series. This algebraic approach allows to reduce the information storage necessary to work with size functions. Some further applications are discussed. Namely, the possibility ofdefining new pseudo-distances between size functions and the possibility of emphasizing the part of information considered more important from the shape recognition viewpoint in order to make recognition more efficient