Eigenmoments

Moments and functions of moments are powerful general tools in a vast number of fields, and particularly in the field of image signal processing. In this paper, we present a method for obtaining a set of orthogonal, noise-robust, transformation invariant and distribution sensitive moments, which we call Eigenmoments (EM). EM are obtained by performing eigen analysis in the moment space generated by geometric moments (GM). This is done by transforming the moment space into the feature space where the signal-to-noise ratio (SNR) is maximized. This is equivalent to solving a generalized eigenvalue problem related to a Rayleigh quotient which characterize the SNR. The generalized eigenvalue problem can be decomposed into two eigenvalue problems. In the first eigenvalue problem, the moment space is transformed into the noise space where the noise components are removed. In the second eigenvalue problem a second transformation is performed to find the most expressive components. Experiments are performed to gauge the performance of EM and comparisons are made with some well known feature descriptors such as GM, DCT, Legendre moments and Tchebichef moments. The results show that EM give significant improvements in terms of accuracy and noise robustness as predicted by the theoretical framework.