Approximation by Shepard type pseudo-linear operators and applications to Image Processing

Recently, it has been shown that sum and product are not the only operations that can be used in order to define concrete approximation operators. Several other operations provided by fuzzy sets theory can be used. In the present paper, pseudo-linear approximation operators are investigated from the...

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Bibliographic Details
Published in:International Journal of Approximate Reasoning Vol. 50; no. 1; pp. 21 - 36
Main Authors: Bede, Barnabás, Schwab, Emil Daniel, Nobuhara, Hajime, Rudas, Imre J.
Format: Journal Article Conference Proceeding
Language:English
Japanese
Published: Amsterdam Elsevier Inc 2009
Elsevier BV
Elsevier
Subjects:
Applied Mathematics
Applied sciences
Approximation
Artificial Intelligence
Computer science; control theory; systems
Exact sciences and technology
Image Processing
Learning and adaptive systems
Pattern recognition. Digital image processing. Computational geometry
Pseudo-analysis
Pseudo-linear approximation
Shepard operators
Software
Theoretical Computer Science
Pseudo-analysis
Approximation
Shepard operators
Pseudo-linear approximation
Image Processing
Image processing
Linear approximation
Minimax method
Fuzzy set
Artificial intelligence
Linear operator
ISSN:0888-613X, 1873-4731
Online Access:Get full text
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Summary:Recently, it has been shown that sum and product are not the only operations that can be used in order to define concrete approximation operators. Several other operations provided by fuzzy sets theory can be used. In the present paper, pseudo-linear approximation operators are investigated from the practical point of view in Image Processing. We study max–min, max–product Shepard type approximation operators together with Shepard operators based on pseudo-operations generated by an increasing continuous generator. It is shown that in several cases these outperform classical approximation operators based on sum and product operations.
ISSN:0888-613X
1873-4731
DOI:10.1016/j.ijar.2008.01.007