Image Noise Reduction by Means of Bootstrapping-Based Fuzzy Numbers
Source abstract
Abstract
Removing or reducing noise in color images is one of the most important functions of image processing, which is used in many sciences. In many cases, nonlinear methods significantly reduce the noise in the image and are widely used today. One of these methods is the use of fuzzy logic. In this paper, we want to introduce a fuzzy filter by using the fuzzy metric for fuzzy sets. For this purpose, we define fuzzy color pixels by using the mean of neighborhoods. Due to the noise in the image, we use the bootstrap resampling method to reduce the effect of outliers. The concept of the strong law of large numbers for the bootstrap mean in fuzzy metric space helps us to use the resampling method.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Fuzzy Systems and Optimization · Multi-Criteria Decision Making · Fixed Point Theorems Analysis
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Statistics, Payame Noor University (PNU), Tehran 193953697, Iran
Instituto de Matemática Pura y Aplicada, Universitat Politécnica de Valéncia, 46022 Valencia, Spain
Department of Statistics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood 3619995161, Iran
Funding
Generalitat Valenciana
References (25)
Show source-provided references
1. Fuzzy metrics and statistical metric spaces
2. Statistical metrics10.1073/pnas.28.12.535 ↗
3. On some results in fuzzy metric spaces10.1016/0165-0114(94)90162-7 ↗
4. A fast impulsive noise color image filter using fuzzy metrics10.1016/j.rti.2005.06.007 ↗
5. Fuzzy peer groups for reducing mixed gaussian-impulse noise from color images10.1109/TIP.2009.2019305 ↗
6. Fuzzy analysis for detection of inconsistent data in experimental datasets employed at the development of the ciede2000 colour-difference formula10.1080/09500340902944038 ↗
7. Some questions in fuzzy metric spaces10.1016/j.fss.2011.12.008 ↗
8. Examples of fuzzy metrics and applications10.1016/j.fss.2010.10.019 ↗
9. Fuzzy averaging filter for impulse noise reduction in colour images with a correction step10.1016/j.jvcir.2018.06.025 ↗
10. A hybrid fuzzy filtering-fuzzy thresholding technique for region of interest detection in noisy images10.1007/s10489-019-01551-z ↗
11. Fuzzy metric and its applications in removing the image noise10.1007/s00500-019-03762-5 ↗
12. Strong law for the bootstrap10.1016/0167-7152(83)90063-9 ↗
13. Laws of large numbers for bootstrappedU-statistics10.1016/0378-3758(84)90019-3 ↗
14. Strong Law of Large Numbers for Fuzzy Random Variables in Fuzzy Metric Space10.5391/IJFIS.2020.20.4.278 ↗
15. Morillas, S., Gregori, V., Peris-Fajarnes, G., and Sapena, A. (2007). New adaptive vector filter using fuzzy metrics. J. Electron. Imaging, 16.10.1117/1.2767335 ↗
16. Statistical metric spaces10.2140/pjm.1960.10.313 ↗
17. Klement, E.P., Mesiar, R., and Pap, E. (2000). Triangular Norms, Kluwer Academic Publishers.10.1007/978-94-015-9540-7 ↗
18. Fuzzy sets10.1016/S0019-9958(65)90241-X ↗
19. Fuzzy pseudo-metric spaces10.1016/0022-247X(82)90255-4 ↗
20. On fuzzy metric spaces10.1016/0165-0114(84)90069-1 ↗
21. Metric spaces in fuzzy set theory10.1016/0022-247X(79)90189-6 ↗
22. Some results on fuzzy banach spaces10.1007/BF02936069 ↗
23. Efron, B. (1992). Bootstrap Methods: Another Look at the Jackknife Breakthroughs in Statistics, Springer.10.1007/978-1-4612-4380-9_41 ↗
24. On the law of large numbers for the bootstrap mean10.1016/0167-7152(92)90203-H ↗
25. Limit theorems for fuzzy random variables