Paper Info
Title
On Geometric And Orthogonal Moments
Abstract
Moments are widely used in pattern recognition, image processing, computer vision and multiresolution analysis. To clarify and to guide the use of different types of moments, we present in this paper a study on the different moments and compare their behavior. After an introduction to geometric, Legendre, Hermite and Gaussian-Hermite moments and their calculation, we analyze at first their behavior in spatial domain. Our analysis shows orthogonal moment base functions of different orders having different number of zero-crossings and very different shapes, therefore they can better separate image features based on different modes, which is very interesting for pattern analysis and shape classification. Moreover, Gaussian-Hermite moment base functions are much more smoothed, they are thus less sensitive to noise and avoid the artifacts introduced by window function discontinuity. We then analyze the spectral behavior of moments in frequency domain. Theoretical and numerical analyses show that orthogonal Legendre and Gaussian-Hermite moments of different orders separate different frequency bands more effectively It is also shown that Gaussian-Hermite moments present an approach to construct orthogonal features from the results of wavelet analysis. The orthogonality equivalence theorem is also presented. Our analysis is confirmed by numerical results, which are then reported.
Year
DOI
Venue
2000
10.1142/S0218001400000581
INTERNATIONAL JOURNAL OF PATTERN RECOGNITION AND ARTIFICIAL INTELLIGENCE
Keywords
Field
DocType
image characterization, classification, moments, orthogonal moments, behavior analysis, frequency analysis, orthogonality equivalence
Orthogonal functions,Mathematical analysis,Legendre polynomials,Multiresolution analysis,Orthogonality,Artificial intelligence,Geometry,Velocity Moments,Hermite interpolation,Frequency domain,Pattern recognition,Mathematics,Shape analysis (digital geometry)
Journal
Volume
Issue
ISSN
14
7
0218-0014
Citations 
PageRank 
References 
32
2.34
8
Authors
3
Name
Order
Citations
PageRank
Jun Shen135358.94
Wei Shen25110.11
Danfei Shen3362.78