Moment invariants under similarity transformation

•We present a method for constructing moment invariant under similarity transformation.•Our method can be used for deriving moment invariants of arbitrary dimension and order.•Our invariants are algebraically independent and complete.•We present some explicit formulas for computing invariant sets׳ dimensions.

This paper presents a method of deriving moment invariants under similarity transformation. The invariants sets are algebraically independent and complete. The method can be adopted for arbitrary dimension and order. This paper also presents some explicit formulas for computing invariant sets׳ dimension, which reveals how the number of invariants increases with moments׳ order and dimension elevating.