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Bilateral Filters with Adaptive Generalized Kernels Generated via Riemann-Lebesgue Theorem

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Abstract

This paper introduces families of bilateral filters for image denoising and sharpness enhancements, JPEG deblocking, and texture filtering. While the Gaussian distribution dictates the application of the bilateral filters, we introduce a wide variety of kernels based on Riemann-Lebesgue’s theorem. The derivation of the bilateral filters are established in both adaptive and non-adaptive approaches. The adaptation of the filters is adjusted via computing the variances (inflection points) using different methods based on applications. For image denoising and sharpness, the variance estimated using Laplacian-of-Gaussian filter followed by affine mapping. The variance is computed as a proportion of intensity differences across the boundary in JPEG deblocking. In texture filtering, the variance is calculated form modified relative variations. We carry out extensive experiments in three different applications and compare the results using different bilateral filters. The proposed filters are giving better results, compared with standard bilateral and adaptive bilateral filters.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Cairo University, Giza, P.O. Box 12613, Egypt

    M. H. Annaby

  2. Systems and Computer Engineering, Carleton University, Ottawa, Canada

    E. A. Nehary

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  1. M. H. Annaby
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  2. E. A. Nehary
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Correspondence to M. H. Annaby.

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Annaby, M.H., Nehary, E.A. Bilateral Filters with Adaptive Generalized Kernels Generated via Riemann-Lebesgue Theorem. J Sign Process Syst 93, 1301–1322 (2021). https://doi.org/10.1007/s11265-021-01707-6

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  • DOI: https://doi.org/10.1007/s11265-021-01707-6

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