  Image representation is an important topic in computer vision and pattern
recognition. It plays a fundamental role in a range of applications towards
understanding visual contents. Moment-based image representation has been
reported to be effective in satisfying the core conditions of semantic
description due to its beneficial mathematical properties, especially geometric
invariance and independence. This paper presents a comprehensive survey of the
orthogonal moments for image representation, covering recent advances in
fast/accurate calculation, robustness/invariance optimization, and definition
extension. We also create a software package for a variety of widely-used
orthogonal moments and evaluate such methods in a same base. The presented
theory analysis, software implementation, and evaluation results can support
the community, particularly in developing novel techniques and promoting
real-world applications.
