Migrating orthogonal rotation-invariant moments from continuous to discrete space

Orthogonality and rotation invariance are important feature properties in digital signal processing. Orthogonality enables a target to be represented by a compact number of features, while rotation invariance results in unique features for a target with different orientations. The orthogonal, rotation-invariant moments (ORIMs), such as Zernike, Pseudo-Zernike, and Orthogonal Fourier-Melling moments, are defined in continuous space. These ORIMs have been digitized and have been demonstrated effectively for some digital imagery applications. However, digitization compromises the orthogonality of the moments, and hence, reduces their precision. Therefore, digital ORIMs are incapable of representing the fine details of images. In this paper, we propose a numerical optimization technique to improve the orthogonality of the digital ORIMs. Simulation results show that our optimized digital ORIMs can be used to reproduce subtle details of images.