For our color based stereo application, we are interested by using grey level image attributes which are invariant with respect to some important group of transformations as the group of orthogonal and affine transformations. In this article, we will mainly consider the case of orthogonal transformation of image coordinates and affine transformation of image intensities. As it has been shown by Hilbert [8], any invariant of finite order can be expressed as a polynomial function of a set of irreducible invariants. Considering a scalar image, these invariants form the fundamental set of image primitives that have to be used in order to describe all local intrinsic properties. This set is well known for first and second properties [4], [14] and is better expressed in a system of coordinates, no more linked to the rotation as the well known Gauge coordinate as follows:
where 
is the unit vector given by 
and 
(Note that within this system of coordinate, we
have 
). Sets of higher order are increasingly more
complicated.
If one would like to use these attributes in any matching process, it is
worthwhile to note that it could be better, from a geometrical and/or
numerical point of view, to consider some other combinaison of
these 5 invariants rather than just considering the ones given by
(1). For example, the 5 following invariants
used at several scales
perform quite well for matching two gray level images:
Considering a set of color image R,G,B and the group of rotation
(specified by just one parameter i.e the rotation angle), the set
of invariants for first and second order will include 
17 invariants. These may include the fifth invariants for each color
channel, and two additional invariants that may be chosen from the
following set:
