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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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References

  1. Tomasi, C., & Manduchi, R. (1998). Bilateral filtering for gray and color images. In Proceedings on IEEE 6th ICCV, 98(1), 839–846.

  2. Paris, S., Kornprobst, P., Tumblin, J., Durand, F., et al. (2009). Bilateral filtering: Theory and applications. Foundations and Trends in Computer Graphics and Vision, 4(1), 1–73.

    Article  Google Scholar 

  3. Knaus, C., & Zwicker, M. (2014). Progressive image denoising. IEEE Transactions on Image Processing, 23(7), 3114–3125.

    Article  MathSciNet  Google Scholar 

  4. Chaudhury, K. N., & Rithwik, K., (2015). Image denoising using optimally weighted bilateral filters: A sure and fast approach. in Proceedings on IEEE ICIP. IEEE, pp. 108–112.

  5. Zhang, J., Lin, G., Wu, L., Wang, C., & Cheng, Y. (2015). Wavelet and fast bilateral filter based de-speckling method for medical ultrasound images. Biomedical Signal Processing and Control, 18, 1–10.

    Article  Google Scholar 

  6. Cho, H., Lee, H., Kang, H., & Lee, S. (2014). Bilateral texture filtering. ACM Trans. Graph., 33(4), 128.

    Article  Google Scholar 

  7. Akar, S. A. (2016). Determination of optimal parameters for bilateral filter in brain mr image denoising. Applied Soft Computing, 43, 87–96.

    Article  Google Scholar 

  8. Zhang, M., Gunturk, B. K. (2009). Compression artifact reduction with adaptive bilateral filtering, in Proceedings on SPIE, Visual Communication Image Process, 7257, 72571A.

  9. Elhoseny, M., & Shankar, K. (2019). Optimal bilateral filter and convolutional neural network based denoising method of medical image measurements. Measurement, 143, 125–135.

    Article  Google Scholar 

  10. Chen, B. H., Cheng, H. Y., Tseng, Y. S., & Yin, J. L. (2021). Two-pass bilateral smooth filtering for remote sensing imagery. IEEE Geoscience and Remote Sensing Letters.

  11. D’Hondt, O., Guillaso, S., & Hellwich, O. (2013). Iterative bilateral filtering of polarimetric sar data. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 6(3), 1628–1639.

    Article  Google Scholar 

  12. Dong, G., & Acton, S. T. (2007). On the convergence of bilateral filter for edge-preserving image smoothing. IEEE Signal Processing Letters, 14(9), 617–620.

    Article  Google Scholar 

  13. Chaudhury, K. N. (2013). Acceleration of the shiftable \(\mathcal O\mathcal(\mathcal1\mathcal)\) algorithm for bilateral filtering and nonlocal means. IEEE Transactions on Image Processing, 22(4), 1291–1300.

    Article  MathSciNet  Google Scholar 

  14. Chaudhury, K. N., & Dabhade, S. D. (2016). Fast and provably accurate bilateral filtering. IEEE Transactions on Image Processing, 25(6), 2519–2528.

    Article  MathSciNet  Google Scholar 

  15. Chen, Y., & Shu, Y. (2014). Optimization of bilateral filter parameters via chi-square unbiased risk estimate. IEEE Signal Processing Letter, 21(1), 97–100.

    Article  Google Scholar 

  16. Ghosh, S., & Chaudhury, K. N. (2016). On fast bilateral filtering using Fourier kernels. IEEE Signal Processing Letters, 23(5), 570–573.

    Article  Google Scholar 

  17. Papari, G., Idowu, N., & Varslot, T. (2016). Fast bilateral filtering for denoising large 3D images. IEEE Transactions on Image Processing, 26(1), 251–261.

    Article  MathSciNet  Google Scholar 

  18. Chen, B. H., Tseng, Y. S., & Yin, J. L. (2020). Gaussian-adaptive bilateral filter. IEEE Signal Processing Letters, 27, 1670–1674.

    Article  Google Scholar 

  19. Zhang, B., & Allebach, J. P. (2008). Adaptive bilateral filter for sharpness enhancement and noise removal. IEEE Transactions on Image Processing, 17(5), 664–678.

    Article  MathSciNet  Google Scholar 

  20. Chaudhury, K. N., Sage, D., & Unser, M. (2011). Fast \(\cal{O}(1)\) bilateral filtering using trigonometric range kernels. IEEE Transactions on Image Processing, 20(12), 3376–3382.

    Article  MathSciNet  Google Scholar 

  21. Dai, L., Yuan, M., & Zhang, X. (2016). Speeding up the bilateral filter: A joint acceleration way. IEEE Transactions on Image Processing, 25(6), 2657–2672.

    Article  MathSciNet  Google Scholar 

  22. Sugimoto, K., & Kamata, S. I. (2015). Compressive bilateral filtering. IEEE Transactions on Image Processing, 24(11), 3357–3369.

    Article  MathSciNet  Google Scholar 

  23. Ghosh, S., Nair, P., & Chaudhury, K. N. (2018). Optimized Fourier bilateral filtering. IEEE Signal Processing Letter, 25(10), 1555–1559.

    Article  Google Scholar 

  24. Chandrasekharan, K. (1989). Classical Fourier Transforms. Berlin: Springer.

    Book  Google Scholar 

  25. Gunturk, B. K. (2011). Fast bilateral filter with arbitrary range and domain kernels. IEEE Transactions on Image Processing, 20(9), 2690–2696.

    Article  MathSciNet  Google Scholar 

  26. Pan, S., An, X., & He, H. (2014). Optimal \(\cal{O} (1)\) bilateral filter with arbitrary spatial and range kernels using sparse approximation. Mathematical Problems in Engineering, 2014.

  27. Annaby, M. H., & Tharwat, M. M. (2007). Sinc-based computations of eigenvalues of dirac systems. BIT Numerical Mathematics, 47(4), 699–713.

    Article  MathSciNet  Google Scholar 

  28. —. (2019). Sinc-regularized techniques to compute eigenvalues of Schrödinger operators on \({L}^2({I})\oplus {C}^2\). Numerical Algorithm, 80(3), 795–817.

  29. Higgins, J. R. (1996). Sampling Theory in Fourier and Signal Analysis: Foundations. Oxford: Oxford University Press.

    MATH  Google Scholar 

  30. Gibson, C. G. (2001). Elementary Geometry of Differentiable Curves: An Undergraduate Introduction. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  31. Truesdell, C. (1989). Maria Gaetana Agnesi. Archive for History of Exact Sciences, 40, 113–142.

    Article  MathSciNet  Google Scholar 

  32. Tolstov, G. P. (1962). Fourier Series. New York: Dover.

    Google Scholar 

  33. Wang, Z., Bovik, A. C., Sheikh, H. R., Simoncelli, E. P., et al. (2004). Image quality assessment: from error visibility to structural similarity. IEEE Transactions on Image Processing, 13(4), 600–612.

    Article  Google Scholar 

  34. Zhang, J., Xiong, R., Zhao, C., Zhang, Y., Ma, S., & Gao, W. (2016). CONCOLOR: Constrained non-convex low-rank model for image deblocking. IEEE Transactions on Image Processing, 25(3), 1246–1259.

    Article  MathSciNet  Google Scholar 

  35. Zhang, Q., Shen, X., Xu, L., & Jia, J. (2014). Rolling guidance filter. in Proceedings of European Conference in Computer Vision. Springer, pp. 815–830.

  36. Gavaskar, R. G., & Chaudhury, K. N. (2018). Fast adaptive bilateral filtering. IEEE Transactions on Image Processing, 28(2), 779–790.

    Article  MathSciNet  Google Scholar 

  37. Farbman, Z., Fattal, R., Lischinski, D., & Szeliski, R. (2008). Edge-preserving decompositions for multi-scale tone and detail manipulation. ACM Transanctions on Graphics (TOG), 27(3), 1–10.

    Article  Google Scholar 

  38. He, K., Sun, J., & Tang, X. (2012). Guided image filtering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 35(6), 1397–140.

  39. Ghosh, S., Gavaskar, R. G., Panda, D., & Chaudhury, K. N. (2019). Fast scale-adaptive bilateral texture smoothing. IEEE Transactions on Circuits and Systems for Video Technology, 30(7), 2015–2026.

    Google Scholar 

  40. Ono, S. (2017). \(L_0\) gradient projection. IEEE Transactions on Image Process, 26(4), 1554–1564.

  41. Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization. in Proceedings of ICNN’95-international conference on neural networks, 4, 1942–1948.

  42. Ghosh, S., & Chaudhury, K. N. (2019). Fast bright-pass bilateral filtering for low-light enhancement. in 2019 IEEE International Conference on Image Processing (ICIP), pp. 205–209.

  43. —. (2018). Color bilateral filtering using stratified fourier sampling. in 2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP), pp. 26–30.

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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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