Image analysis by Gaussian-Hermite moments

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.