For rotation-invariant Hamiltonian systems, canonical angular momentum is conserved. In beam optics, this statement is known as Busch’s theorem. This theorem can be generalized to symplectic mappings; two generalizations are presented in this paper. The first one states that a group of rotation-invariant mappings is identical to a group of the angular-momentum preserving mappings, assuming both...

This paper presents a theoretically very simple yet efficient approach for gray scale and rotation invariant texture classification based on local binary patterns and nonparametric discrimination of sample and prototype distributions. The proposed approach is very robust in terms of gray scale variations, since the operators are by definition invariant against any monotonic transformation of th...

Texture retrieval is a vital branch of content-based image retrieval. Rotation-invariant texture retrieval plays a key role in texture retrieval. This paper addresses three major issues in rotation-invariant texture retrieval: how to select the texture measurement methods, how to alleviate the influence of rotation for texture retrieval and how to apply the proper multi-scale analysis theory fo...