Image Invariants

A pre-processing technique for image features extraction is presented in the paper. It is based on algebraic properties of image transform ψ that are invariant to a given geometrical transformation of an image. A vector space H of digital images is introduced. Image invariant is represented by a family of linear maps R. A linear transform ψ defined on a space of images H pertained to a given image invariant R is constructed. The main idea of this paper is contained in a property of map ψ, that maps all images sharing the same feature described by a family R into a single point. Gained information of the digital image extracted by the transform ψ is suitable for further analysis of image features. Some examples of families R are presented. An example of an introduced transform ψ pertained to a given family R is described.