  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, definition
extension, and application. 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.
