3-D moment forms: their construction and application to object identification and positioning

The 3-D moment method is applied to object identification and positioning. A general theory of deriving 3-D moments invariants is proposed. The notion of complex moments is introduced. Complex moments are defined as linear combinations of moments with complex coefficients and are collected into multiplets such that each multiplet transforms irreducibly under 3-D rotations. The application of the 3-D moment method to motion estimation is also discussed. Using group-theoretic techniques, various invariant scalars are extracted from compounds of complex moments via Clebsch-Gordon expansion. Twelve moment invariants consisting of the second-order and third-order moments are explicitly derived. Based on a perturbation formula, it is shown that the second-order moment invariants can be used to predict whether the estimation using noisy data is reliable or not. The new derivation of vector forms also facilities the calculation of motion estimation in a tensor approach. Vectors consisting of the third-order moments can be derived in a similar manner