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Improved adaptive type-2 fuzzy filter with exclusively two fuzzy membership function for filtering salt and pepper noise

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Abstract

Image denoising is one of the preliminary steps in image processing methods in which the presence of noise can deteriorate image quality. This paper presents an improved two-stage fuzzy filter for filtering salt and pepper noise from the images to enhance the image quality. In the first stage, the pixels in the image are categorized as good or noisy based on adaptive thresholding using type-2 fuzzy logic with exclusively two different membership functions in the filter window. In the second stage, the noisy pixels are denoised using modified ordinary fuzzy logic in the respective filter window. The proposed filter is validated on standard images with various noise levels. The proposed filter removes the noise and preserves beneficial image characteristics, i.e., edges and corners at higher noise levels. The performance of the proposed filter is compared with the various state-of-the-art methods in terms of peak signal-to-noise ratio and computation time. The average PSNR values for the noise percentage 20%, 50% and 80% are the 37%, 31% and 27%. To show the effectiveness of statistical filter tests, i.e., the Friedman test and Bonferroni−Dunn (BD) test are also carried out, which ascertain that the proposed filter outperforms in comparison to various filtering approaches.

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Data Availability

The datasets analysed during the current study are available in the USC-SIPI Image Database repository, https://sipi.usc.edu/database/, and cited in [50].

Abbreviations

SAP :

Salt and Pepper

MF :

Membership Function

PSNR :

Peak Signal-to-Noise Ratio

LMF :

Lower Membership Function

UMF :

Upper Membership Function

BD :

Bonferroni-Dunn

CD :

Critical Difference

\(\boldsymbol {\tilde {\mu }}\) :

Membership value matrix

\(\boldsymbol {P}^{H}_{ij}\) :

Fuzzy set

χ 2 :

Friedman statistic

\(\mu _{\boldsymbol {P}^{H}_{ij}}\) :

Primary membership value

\(\mu _{\tilde {\boldsymbol {P}}_{ij}^{H}}\) :

Secondary membership value

σ :

Variance in a filter window

\(\tilde {\boldsymbol {P}}_{ij}^{H}\) :

Type-2 fuzzy set

F F :

Fisher distribution

H :

Half filter window size

I :

Collection of pixels in an image

l :

Number of methods

M :

Number of dataset

m 1,m 2 :

Different means in a filter window

N :

Number of elements in a filter window

p i j :

Pixel values of ith row and jth column

R z :

Average rank of zth method

T h :

Adaptive threshold

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  1. Indian Institute of Technology Kanpur, Kanpur, India

    Vikas Singh, Pooja Agrawal, Teena Sharma & Nishchal K Verma

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Singh, V., Agrawal, P., Sharma, T. et al. Improved adaptive type-2 fuzzy filter with exclusively two fuzzy membership function for filtering salt and pepper noise. Multimed Tools Appl 82, 20015–20037 (2023). https://doi.org/10.1007/s11042-022-14248-2

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