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Soft Computing
Published in: Soft Computing 14/2018

01-06-2017 | Methodologies and Application

Aggregated distance functions and their application in image processing

Authors: Ljubo Nedović, Nebojša M. Ralević, Ivan Pavkov

Published in: Soft Computing | Issue 14/2018

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Abstract

In this paper, we propose a new method for construction of distance functions and metrics, by applying aggregation operators on some given distance functions and metrics. For some types and examples of aggregation operators, we analyze which properties of the given distance functions and metrics are preserved by such construction. We also present one possible application of the distance functions constructed in such way in image segmentation by fuzzy c-means algorithm. Other similar applications in image processing are also possible.
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Footnotes
1
Could be considered as functions whose codomain is \([0,\infty ]\) also.
 
2
Or distance function.
 
Literature
Bezdek JC, Ehrlich R, Full W (1984) Fcm: the fuzzy c-means clustering algorithm. Comput Geosci 10(2–3):191–203CrossRef
Chang HH, Zhuang AH, Valentino DJ, Chu WC (2009) Performance measure characterization for evaluating neuroimage segmentation algorithms. NeuroImage 47(1):122–135CrossRef
Grabish M, Marichal JL, Mesiar R, Pap E (2009) Aggregation functions. Cambridge University Press, CambridgeCrossRefMATH
Klement EP, Mesiar R, Pap E (2000) Triangular norms. Springer, Netherlands
Klir GJ, Yuan B (1995) Fuzzy sets and fuzzy logic, theory and applications. Prentice Hall, New JerseyMATH
Martin D, Fowlkes C, Tal D, Malik J (2001) A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: Proceedings of the 8th international conference on computer vision, vol 2, pp 416–423
Metadata
Title
Aggregated distance functions and their application in image processing
Authors
Ljubo Nedović
Nebojša M. Ralević
Ivan Pavkov
Publication date
01-06-2017
Publisher
Springer Berlin Heidelberg
Published in
Soft Computing / Issue 14/2018
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-017-2657-9

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