Morphological structuring element decomposition
Computer Vision, Graphics, and Image Processing
Image Analysis Using Mathematical Morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
Decomposition of Arbitrarily Shaped Morphological Structuring Elements
IEEE Transactions on Pattern Analysis and Machine Intelligence
The applications of interval-valued fuzzy numbers and interval-distribution numbers
Fuzzy Sets and Systems
Connections between binary, gray-scale and fuzzy mathematical morphologies
Fuzzy Sets and Systems
On the relationship between some extensions of fuzzy set theory
Fuzzy Sets and Systems - Theme: Basic notions
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Classification of Fuzzy Mathematical Morphologies Based on Concepts of Inclusion Measure and Duality
Journal of Mathematical Imaging and Vision
IEEE Transactions on Fuzzy Systems
Permutation-based finite implicative fuzzy associative memories
Information Sciences: an International Journal
On the construction of interval-valued fuzzy morphological operators
Fuzzy Sets and Systems
Mathematical morphology on bipolar fuzzy sets: general algebraic framework
International Journal of Approximate Reasoning
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Interval-valued fuzzy mathematical morphology is an extension of classical fuzzy mathematical morphology, which is in turn one of the extensions of binary morphology to greyscale morphology. The uncertainty that may exist concerning the grey value of a pixel due to technical limitations or bad recording circumstances, is taken into account by mapping the pixels in the image domain onto an interval to which the pixel's grey value is expected to belong instead of one specific value. Such image representation corresponds to the representation of an interval-valued fuzzy set and thus techniques from interval-valued fuzzy set theory can be applied to extend greyscale mathematical morphology. In this paper, we study the decomposition of the interval-valued fuzzy morphological operators. We investigate in which cases the [驴 1,驴 2]-cuts of these operators can be written or approximated in terms of the corresponding binary operators. Such conversion into binary operators results in a reduction of the computation time and is further also theoretically interesting since it provides us a link between interval-valued fuzzy and binary morphology.