3-D moment forms: their construction and application to objectidentification and positioning
Lo, C.-H.
Don, H.-S.
Dept. of Electr. Eng., State Univ. of New York, Stony Brook, NY;
This paper appears in: Pattern Analysis and Machine Intelligence, IEEE Transactions on
Publication Date: Oct 1989
Volume: 11,
Issue: 10
On page(s): 1053-1064
ISSN: 0162-8828
References Cited: 21
CODEN: ITPIDJ
INSPEC Accession Number: 3562017
Digital Object Identifier: 10.1109/34.42836
Current Version Published: 2002-08-06
Abstract
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
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