3D geometric moment invariants from the point of view of the classical invariant theory

The aim of this paper is to clear up the problem connection between 3D geometric moments invariants and invariant theory, considering a describing as classical theory.Using remarkable fact that complex groups $SO(3,\mathbb{C})$ $SL(2,\mathbb{C})$ are locally isomorphic, we reduced deriving well-known theory.
 We give precise statement computation, intro\-ducing notions algebras simultaneous moment invariants, prove they isomorphic joint $SL(2,\mathbb{C})$-invariants several binary forms. To simplify calculating proceed from an action Lie group equivalent algebra $\mathfrak{sl}_2$. author hopes results will be useful researchers in thefields image analysis pattern recognition.