Image analysis by Gaussian–Hermite moments

Abstract

Orthogonal moments are powerful tools in pattern recognition and image processing applications. In this paper, the Gaussian–Hermite moments based on a set of orthonormal weighted Hermite polynomials are extensively studied. The rotation and translation invariants of Gaussian–Hermite moments are derived algebraically. It is proved that the construction forms of geometric moment invariants are valid for building the Gaussian–Hermite moment invariants. The paper also discusses the computational aspects of Gaussian–Hermite moment, including the recurrence relation and symmetrical property. Just as the other orthogonal moments, an image can be easily reconstructed from its Gaussian–Hermite moments thanks to the orthogonality of the basis functions. Some reconstruction tests with binary and gray-level images (without and with noise) were performed and the obtained results show that the reconstruction quality from Gaussian–Hermite moments is better than that from known Legendre, discrete Tchebichef and Krawtchouk moments. This means Gaussian–Hermite moment has higher image representation ability. The peculiarity of image reconstruction algorithm from Gaussian–Hermite moments is also discussed in the paper. The paper offers an example of classification using Gaussian–Hermite moment invariants as pattern feature and the result demonstrates that Gaussian–Hermite moment invariants perform significantly better than Hu's moment invariants under both noise-free and noisy conditions.