Image reconstruction from a complete set of similarity invariants extracted from complex moments

Various types of moments have been used to recognize image patterns in a number of applications. However, only few works have paid attention to the completeness property of the invariant descriptor set, which is of fundamental importance from the theoretical as well as the practical points of views. This paper proposes a systematic method to extract a complete set of similarity invariants (translation, rotation and scale), by means of some linear combinations of complex moments. The problem of image reconstruction from a finite set of its moment invariants is then examined by exploiting the link between the discrete Fourier transform of an image and its complex moments. Experimental results are presented that confirm theoretical properties as well as numerical effectiveness of the method.