# 2D moment invariants from the point of view of the classical invariant theory

arXiv: https://arxiv.org/abs/1908.08927 · HTML: https://mlsanity.com/paper/1908.08927/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Aug 2019.

## Built on by (most cited first, 1 of 1)

- [MSIQ: Moment-based Scale-Invariant Quality Measure for Single Image Super-Resolution](https://mlsanity.com/paper/2605.17588/) (2026)

## Abstract (arXiv)

Invariants allow to classify images up to the action of a group of transformations. In this paper we introduce notions of the algebras of simultaneous polynomial and rational 2D moment invariants and prove that they are isomorphic to the algebras of joint polynomial and rational SO(2)-invariants of binary forms. Also, to simplify the calculating of invariants we pass from an action of Lie group SO(2) to an action of its Lie algebra mathfrakso2. This allow us to reduce the problem to standard problems of the classical invariant theory.