Multivariate mathematical morphology based on fuzzy extremum estimation

The existing lexicographical ordering approaches respect the total ordering properties, thus making this approach a very robust solution for multivariate ordering. However, different marginal components derived from various representations of a colour image will lead to different results of multivar...

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Bibliographic Details
Published in:IET image processing 2014-09, Vol.8 (9), p.548-558
Main Authors: Lei, Tao, Wang, Yi, Wang, Guohua, Fan, Yangyu
Format: Article
Language:English
Subjects:
Applied sciences
colour image representations
Decomposition
Detection, estimation, filtering, equalization, prediction
Exact sciences and technology
FEEA
Fuzzy
fuzzy extremum estimation
fuzzy extremum estimation algorithm
fuzzy lexicographical ordering approach
Fuzzy logic
Fuzzy set theory
image colour analysis
Image processing
image representation
Information, signal and communications theory
marginal components
Mathematical analysis
mathematical morphology
multivariate image filtering
multivariate mathematical morphological operators
multivariate ordering
Operators
Order disorder
quaternion decomposition
Quaternions
Signal and communications theory
Signal processing
Signal, noise
Telecommunications and information theory
total ordering property
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Summary:The existing lexicographical ordering approaches respect the total ordering properties, thus making this approach a very robust solution for multivariate ordering. However, different marginal components derived from various representations of a colour image will lead to different results of multivariate ordering. Moreover, the output of lexicographical ordering only depends on the first component leading to the followed components taking no effect. To address these issues, three new marginal components are obtained by means of quaternion decomposition, and they are employed by fuzzy lexicographical ordering, and thus a new fuzzy extremum estimation algorithm (FEEA) based on quaternion decomposition is proposed in this study. The novel multivariate mathematical morphological operators are also defined according to FEEA. Comparing with the existing solutions, experimental results show that the proposed FEEA performs better results on multivariate extremum estimation, and the presented multivariate mathematical operators can be easily handled and can provide better results on multivariate image filtering.
ISSN:1751-9659
1751-9667
1751-9667
DOI:10.1049/iet-ipr.2013.0510