The 2-Orthogonal and Orthogonal Radial Shape Moments for Image Representation and Recognition

Images recognition require an extraction technique of feature vectors of these images. These vectors must be invariant to the three geometric transformations: rotation, translation and scaling. In this context, there are several authors who used the theory of orthogonal moments, which are become an indispensable tool in a wide range of pattern recognition applications. In this paper, we generalize the notions of orthogonality and orthogonal moments by introducing the property «p-orthogonality» and «p-orthogonal moments». We show that a p-orthogonal set of functions is composed of p orthogonal subsets. We prove that the set of linear shape functions or hat functions, used in the finite element method (FEM), is 2-orthogonal. Based in these functions we present four types of moments: the set of 2-orthogonal radial shape moments (2ORSMs), the set of orthogonal radial shape moments (1ORSMs) for gray-level images, the set of multi-channel 2-orthogonal radial shape moments (2MRSMs) and the set of multi-channel orthogonal radial shape moments (1MRSMs) for color images. Invariants to translation, scaling and rotation (TSR) of the four proposed moments are derived for image representation and recognition. We present a set of numerical experiments in the field of classification and pattern recognition to evaluate the performance of the proposed invariant moments. From a comparative study with the recent invariant moments, we conclude that our approach is very promising in the pattern recognition field and image analysis.