Systematic generation of moment invariant bases for 2D and 3D tensor fields

Abstract

Moment invariants have been successfully applied to pattern detection tasks in 2D and 3D scalar, vector, and matrix valued data. However so far no flexible basis of invariants exists, i.e., no set that is optimal in the sense that it is complete and independent for every input pattern.In this paper, we prove that a basis of moment invariants can be generated that consists of tensor contractions of not more than two different moment tensors each under the conjecture of the set of all possible tensor contractions to be complete.This result allows us to derive the first generator algorithm that produces flexible bases of moment invariants with respect to orthogonal transformations by selecting a single non-zero moment to pair with all others in these two-factor products. Since at least one non-zero moment can be found in every non-zero pattern, this approach always generates a complete set of descriptors.