  In this paper, we propose a new mathematical model for image processing. It
is a logarithmical one. We consider the bounded interval (-1, 1) as the set of
gray levels. Firstly, we define two operations: addition <+> and real scalar
multiplication <x>. With these operations, the set of gray levels becomes a
real vector space. Then, defining the scalar product (.|.) and the norm || .
||, we obtain an Euclidean space of the gray levels. Secondly, we extend these
operations and functions for color images. We finally show the effect of
various simple operations on an image.
