Fast algorithm for the computation of moment invariants
Pattern Recognition
A method for working out the moments of a polygon using an integration technique
Pattern Recognition Letters
A bit level systolic array for real-time two-dimensional moment generation
Systolic array processors
Simple and fast computation of moments
Pattern Recognition
Fast computation of moment invariants
Pattern Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Faster optimal parallel prefix circuits: New algorithmic construction
Journal of Parallel and Distributed Computing
Fast and scalable computations of 2D image moments
Image and Vision Computing
Computation-efficient parallel prefix
AIC'06 Proceedings of the 6th WSEAS International Conference on Applied Informatics and Communications
Two families of parallel prefix algorithms for multicomputers
TELE-INFO'08 Proceedings of the 7th WSEAS International Conference on Telecommunications and Informatics
Parallel prefix algorithms on the multicomputer
WSEAS Transactions on Computer Research
New parallel prefix algorithms
AIC'09 Proceedings of the 9th WSEAS international conference on Applied informatics and communications
New families of computation-efficient parallel prefix algorithms
WSEAS Transactions on Computers
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Moments of images are widely used in pattern recognition, because in suitable form they can be made invariant to variations in translation, rotation and size. However the computation of discrete moments by their definition requires many multiplications which limits the speed of computation. In this paper we express the moments as a linear combination of higher order prefix sums, obtained by iterating the prefix sum computation on previous prefix sums, starting with the original function values. Thus the p′th moment m_p=\sum^N_{x=1}x^pf(x) can be computed by O (N · p) additions followed by p multiply-adds. The prefix summations can be realized in time O(N) using p + 1 simple adders, and in time O(p log N) using parallel prefix computation and O(N) adders. The prefix sums can also be used in the computation of two-dimensional moments for any intensity function f(x,y). Using a simple bit-serial addition architecture, it is sufficient with 13 full adders and some shift registers to realize the 10 order 3 image moment computations (m_00, m_01, m_10, m_02, m_20, m_12, m_21, m_03, m_30) for a 512 × 512 size image at the TV rate. In 1986 Hatamian published a computationally equivalent algorithm, based on a cascade of filters performing the summations. Our recursive derivation allows for explicit expressions and recursive equations for the coefficients used in the final moment calculation. Thus a number of alternative forms for the moment computation can be derived, based on different sets of prefix sums. It is also shown that similar expressions can be obtained for the moments introduced by Liao and Pawlak in 1996, forming better approximations to the exact geometric moments, at no extra computational cost.