Flexible Rotation Invariant Bases from Orthogonal Moments

Abstract

Rotation transformation is a basic but fundamental geometric distortion. Design of rotation invariants is an indispensable part in researches on moment invariants. Due to better numerical stability and efficient invariant development, Gaussian-Hermite moments become powerful tools in field of pattern recognition. The existing rotation invariants of Gaussian-Hermite moments are constructed either with special constraints or for special patterns. The invariant bases neither contain all possible rotation invariants; nor are they available for all images. In this paper, we propose the flexible rotation invariant bases from Gaussian-Hermite moments. The invariants generated from such bases are available for any image and they are complete and exact representations of all rotation invariants of Gaussian-Hermite moments. The inherent properties, such as rotation invariance, completeness and independence of such flexible rotation bases are proven. Rotation invariance is verified by real data. The experiments with respect to template matching and image recognition show that the invariants generated by such flexible bases have better feature representation ability and numerical stability in comparison with traditional complex moment invariants.