2D moment invariants from the point of view of the classical invariant theory
This work addresses image classification challenges in computer vision by providing a theoretical framework for invariants, though it appears incremental as it builds on classical invariant theory.
The paper tackles the problem of classifying images under group transformations by introducing algebras of 2D moment invariants and proving they are isomorphic to algebras of joint SO(2)-invariants of binary forms, simplifying calculations by shifting to Lie algebra actions.
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 $\mathfrak{so}_2$. This allow us to reduce the problem to standard problems of the classical invariant theory.