Application of Smooth Fuzzy Model in Image Denoising and Edge Detection

In this paper, the bounded variation property of fuzzy models with smooth compositions have been studied, and they have been compared with the standard fuzzy composition (e.g., min–max). Moreover, the contribution of the bounded variation of the smooth fuzzy model for the noise removal and edge pres...

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Bibliographic Details
Published in:Mathematics (Basel) 2022-07, Vol.10 (14), p.2421
Main Authors: Sadjadi, Ebrahim Navid, Sadrian Zadeh, Danial, Moshiri, Behzad, García Herrero, Jesús, Molina López, Jose Manuel, Fernández, Roemi
Format: Article
Language:English
Subjects:
Algorithms
bounded variation function
Composition
Digital imaging
Edge detection
fuzzy models
Mathematics
Methods
Noise
noise reduction
Performance indices
smooth compositions
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Summary:In this paper, the bounded variation property of fuzzy models with smooth compositions have been studied, and they have been compared with the standard fuzzy composition (e.g., min–max). Moreover, the contribution of the bounded variation of the smooth fuzzy model for the noise removal and edge preservation of the digital images has been investigated. Different simulations on the test images have been employed to verify the results. The performance index related to the detected edges of the smooth fuzzy models in the presence of both Gaussian and Impulse (also known as salt-and-pepper noise) noises of different densities has been found to be higher than the standard well-known fuzzy models (e.g., min–max composition), which demonstrates the efficiency of smooth compositions in comparison to the standard composition.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10142421