An efficient method for the computation of Legendre moments

Legendre moments are continuous moments, hence, when applied to discrete-space images, numerical approximation is involved and error occurs. This paper proposes a method to compute the exact values of the moments by mathematically integrating the Legendre polynomials over the corresponding intervals...

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Bibliographic Details
Published in:IEEE transactions on pattern analysis and machine intelligence 2005-12, Vol.27 (12), p.1996-2002
Main Authors: Pew-Thian Yap, Paramesran, R.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Approximation
Artificial Intelligence
Computation
Computer science
control theory
systems
Error analysis
Errors
Exact sciences and technology
Face recognition
feature representation
Image analysis
Image Enhancement - methods
Image Interpretation, Computer-Assisted - methods
Image reconstruction
Image sampling
Imaging, Three-Dimensional - methods
Index Terms- Moments
Indexing
Intelligence
Kernel
Mathematical analysis
Mathematical models
Numerical Analysis, Computer-Assisted
Pattern analysis
Pattern recognition
Pattern Recognition, Automated - methods
Pattern recognition. Digital image processing. Computational geometry
Pixel
Polynomials
Signal Processing, Computer-Assisted
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Summary:Legendre moments are continuous moments, hence, when applied to discrete-space images, numerical approximation is involved and error occurs. This paper proposes a method to compute the exact values of the moments by mathematically integrating the Legendre polynomials over the corresponding intervals of the image pixels. Experimental results show that the values obtained match those calculated theoretically, and the image reconstructed from these moments have lower error than that of the conventional methods for the same order. Although the same set of exact Legendre moments can be obtained indirectly from the set of geometric moments, the computation time taken is much longer than the proposed method.
ISSN:0162-8828
1939-3539
DOI:10.1109/TPAMI.2005.232