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Fast bilateral filter with spatial subsampling

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Abstract

The bilateral filter is a non-linear edge-preserving filter that can be adopted in a variety of tasks in computer photography. However, the naive bilateral filter is computationally expensive. Existing researches on the acceleration of bilateral filter mostly concentrate on range approximation. Nevertheless, the range kernel has more impact on the bilateral filter than the spatial kernel. Range approximation would have more side effects. In this paper, we propose a novel approximation of the bilateral filter with spatial subsampling, where the affinity matrix is estimated from a subset of it. We show that the main computational burden of our approximation is a large linear system, for which we propose an efficient iterative algorithm to solve. We have carried out both quantitative and qualitative experiments to evaluate our fast bilateral filter. Experimental results suggest that the proposed filter outperforms the state-of-the-art methods in approximation accuracy. The proposed filter is highly efficient; under a moderate sampling rate, i.e., \((1/5)\times (1/5)\), it needs 0.29s to process a color image with 1 megapixel on an Intel i7-9700 CPU.

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References

  1. Adams, A., Baek, J., Davis, M.A.: Fast high-dimensional filtering using the permutohedral lattice. Comput. Graph. Forum 29(2), 753–762 (2010)

    Article  Google Scholar 

  2. Anand Swamy, A.S., Shylashree, N.: Multiscale decomposition of hdr images using the edge-preserving filters. In: Microelectronics, Communication Systems, Machine Learning and Internet of Things, pp. 573–600. Springer Nature Singapore (2022)

  3. Bhargava, G.U., Sivakumar, V.G.: FPGA implementation of modified recursive box filter-based fast bilateral filter for image denoising. Circuits Syst. Signal Process. 40(3), 1438–1457 (2021)

    Article  Google Scholar 

  4. Chaudhury, K.N., Dabhade, S.D.: Fast and provably accurate bilateral filtering. IEEE Trans. Image Process. 25(6), 2519–2528 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chen, Q., Xu, J., Koltun, V.: Fast image processing with fully-convolutional networks. In: International Conference on Computer Vision, pp. 2516–2525 (2017)

  6. Dang-Nguyen, D., Pasquini, C., Conotter, V., Boato, G.: RAISE: a raw images dataset for digital image forensics. In: Proceedings of the 6th ACM Multimedia Systems Conference, MMSys, pp. 219–224 (2015)

  7. Durand, F., Dorsey, J.: Fast bilateral filtering for the display of high-dynamic-range images. ACM Trans. Graph. 21(3), 257–266 (2002)

    Article  Google Scholar 

  8. Feng, Y., Deng, S., Yan, X., Yang, X., Wei, M., Liu, L.: Easy2hard: Learning to solve the intractables from a synthetic dataset for structure-preserving image smoothing. IEEE Trans. Neural Netw. Learn. Syst. 1–14 (2021). https://doi.org/10.1109/TNNLS.2021.3084473

  9. Fowlkes, C.C., Belongie, S.J., Chung, F.R.K., Malik, J.: Spectral grouping using the nyström method. IEEE Trans. Pattern Anal. Mach. Intell. 26(2), 214–225 (2004)

    Article  Google Scholar 

  10. Gastal, E.S.L., Oliveira, M.M.: Adaptive manifolds for real-time high-dimensional filtering. ACM Trans. Graph. 31(4), 33:1-33:13 (2012)

    Article  Google Scholar 

  11. Gavaskar, R.G., Chaudhury, K.N.: Fast adaptive bilateral filtering. IEEE Trans. Image Process. 28(2), 779–790 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  12. Ghosh, S., Chaudhury, K.N.: On fast bilateral filtering using fourier kernels. IEEE Signal Process. Lett. 23(5), 570–573 (2016)

    Article  Google Scholar 

  13. Ghosh, S., Nair, P., Chaudhury, K.N.: Optimized fourier bilateral filtering. IEEE Signal Process. Lett. 25(10), 1555–1559 (2018)

    Article  Google Scholar 

  14. Jia, H., Wang, L., Song, H., Mao, Q., Ding, S.: An efficient nyström spectral clustering algorithm using incomplete cholesky decomposition. Expert Syst. Appl. 186, 115813 (2021)

    Article  Google Scholar 

  15. Kaur, M., Singh, D., Kumar, V., Sun, K.: Color image dehazing using gradient channel prior and guided \(L_{0}\) filter. Inf. Sci. 521, 326–342 (2020)

    Article  MATH  Google Scholar 

  16. Khan, S., Singh, Y.V., Rai, A.K.: An efficient edge preserving universal noise removal algorithm using kernel ridge regression. Multim. Tools Appl. 81(14), 19863–19877 (2022)

    Article  Google Scholar 

  17. Kim, B., Ponce, J., Ham, B.: Deformable kernel networks for joint image filtering. Int. J. Comput. Vis. 129(2), 579–600 (2021)

    Article  Google Scholar 

  18. Koh, P.W., Liang, P.: Understanding black-box predictions via influence functions. In: International Conference on Machine Learning, vol. 70, pp. 1885–1894 (2017)

  19. Kornprobst, P., Tumblin, J., Durand, F.: Bilateral filtering: Theory and applications. Found. Trends Comput. Graph. Vis. 4(1), 1–74 (2009)

    MATH  Google Scholar 

  20. Li, J., Qin, K., Xu, R., Ji, H.: Deep scale-aware image smoothing. In: IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2022, Virtual and Singapore, 23–27 May 2022, pp. 2105–2109 (2022)

  21. Lin, F., Xie, H., Liu, C., Zhang, Y.: Bilateral temporal re-aggregation for weakly-supervised video object segmentation. IEEE Trans. Circuits Syst. Video Technol. 32(7), 4498–4512 (2022)

    Article  Google Scholar 

  22. Liu, W., Zhang, P., Chen, X., Shen, C., Huang, X., Yang, J.: Embedding bilateral filter in least squares for efficient edge-preserving image smoothing. IEEE Trans. Circuits Syst. Video Technol. 30(1), 23–35 (2020)

    Article  Google Scholar 

  23. Lv, H., Shan, P., Shi, H., Zhao, L.: An adaptive bilateral filtering method based on improved convolution kernel used for infrared image enhancement. Signal Image Video Process. 15(6), 1075–1080 (2022)

    Google Scholar 

  24. Nair, P., Chaudhury, K.N.: Fast high-dimensional bilateral and nonlocal means filtering. IEEE Trans. Image Process. 28(3), 1470–1481 (2019)

    Article  MathSciNet  Google Scholar 

  25. Nair, P., Chaudhury, K.N.: Fast high-dimensional kernel filtering. IEEE Signal Process. Lett. 26(2), 377–381 (2019)

    Article  Google Scholar 

  26. Nair, P., Gavaskar, R.G., Chaudhury, K.N.: Compressive adaptive bilateral filtering. In: IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 2078–2082. IEEE (2020)

  27. Nair, P., Popli, A., Chaudhury, K.N.: A fast approximation of the bilateral filter using the discrete fourier transform. Image Process. Line 7, 115–130 (2017)

    Article  Google Scholar 

  28. Paris, S., Durand, F.: A fast approximation of the bilateral filter using a signal processing approach. Int. J. Comput. Vis. 81(1), 24–52 (2009)

    Article  Google Scholar 

  29. Porikli, F.: Constant time O(1) bilateral filtering. In: IEEE Conference on Computer Vision and Pattern Recognition (2008)

  30. Rajalingam, B., Al-Turjman, F., Santhoshkumar, R., Rajesh, M.: Intelligent multimodal medical image fusion with deep guided filtering. Multim. Syst. (2020). https://doi.org/10.1007/s00530-020-00706-0

  31. Sheng, J., Lv, G., Xue, Z., Wu, L., Feng, Q.: Mixed noise removal by bilateral weighted sparse representation. Circuits Syst. Signal Process. 40(9), 4490–4515 (2021)

    Article  Google Scholar 

  32. Sugimoto, K., Fukushima, N., Kamata, S.: 200 FPS constant-time bilateral filter using SVD and tiling strategy. In: IEEE International Conference on Image Processing, ICIP, pp. 190–194 (2019)

  33. Sugimoto, K., Kamata, S.: Compressive bilateral filtering. IEEE Trans. Image Process. 24(11), 3357–3369 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  34. Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In: International Conference on Computer Vision, pp. 839–846 (1998)

  35. User Benchmark: Comparison between intel i7-9700 and i7-8750h. https://cpu.userbenchmark.com/Compare/Intel-Core-i7-9700-vs-Intel-Core-i7-8750H/m816180vsm470418 (2022)

  36. Wagner, F., Thies, M., Gu, M., Huang, Y., Pechmann, S., Patwari, M., Ploner, S.B., Aust, O., Uderhardt, S., Schett, G., Christiansen, S.H., Maier, A.K.: Ultra low-parameter denoising: Trainable bilateral filter layers in computed tomography. CoRR arXiv:2201.10345 (2022)

  37. Wang, L., Wang, H., Fu, G.: Multi-nyström method based on multiple kernel learning for large scale imbalanced classification. Comput. Intell. Neurosci. 2021, 9911871:1-9911871:11 (2021)

    Google Scholar 

  38. Weiss, B.: Fast median and bilateral filtering. ACM Trans. Graph. 25(3), 519–526 (2006)

    Article  Google Scholar 

  39. Xu, J., Liu, Z., Hou, Y., Zhen, X., Shao, L., Cheng, M.: Pixel-level non-local image smoothing with objective evaluation. IEEE Trans. Multim. 23, 4065–4078 (2021)

    Article  Google Scholar 

  40. Xu, L., Ren, J.S.J., Yan, Q., Liao, R., Jia, J.: Deep edge-aware filters. In: International Conference on Machine Learning, vol. 37, pp. 1669–1678 (2015)

  41. Yang, Q., Tan, K., Ahuja, N.: Real-time O(1) bilateral filtering. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 557–564 (2009)

  42. Yang, Y., Hui, H., Zeng, L., Zhao, Y., Zhan, Y., Yan, T.: Edge-preserving image filtering based on soft clustering. IEEE Trans. Circuits Syst. Video Technol. 32(7), 4150–4162 (2022)

    Article  Google Scholar 

  43. Yang, Y., Zheng, H., Zeng, L., Shen, X., Zhan, Y.: L1-regularized reconstruction model for edge-preserving filtering. IEEE Trans. Multimed. pp. 1–1 (2022). https://doi.org/10.1109/TMM.2022.3171686

  44. Yin, H., Gong, Y., Qiu, G.: Fast and efficient implementation of image filtering using a side window convolutional neural network. Signal Process. 176, 107717 (2020)

    Article  Google Scholar 

  45. You, C., Yang, S.: A simple and effective multi-focus image fusion method based on local standard deviations enhanced by the guided filter. Displays 72, 102146 (2022)

    Article  Google Scholar 

  46. Zhong, G., Pun, C.: Revisiting nyström extension for hypergraph clustering. Neurocomputing 403, 247–256 (2020)

    Article  Google Scholar 

  47. Zhong, Z., Liu, X., Jiang, J., Zhao, D., Ji, X.: Deep attentional guided image filtering. CoRR arXiv:2112.06401 (2021)

  48. Zhou, P.C., Xue, Y., Xue, M.G.: Adaptive side window joint bilateral filter. Vis. Comput. (2022). https://doi.org/10.1007/s00371-022-02427-z

  49. Zhu, H., Peng, H., Xu, G., Deng, L., Cheng, Y., Song, A.: Bilateral weighted regression ranking model with spatial-temporal correlation filter for visual tracking. IEEE Trans. Multim. 24, 2098–2111 (2022)

    Article  Google Scholar 

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant No. 61902155, in part by the China Postdoctoral Science Foundation under Grant No. 2015M571688, and in part by the Jiangsu University under Grant No. 19JDG024.

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Authors and Affiliations

  1. Department of Computer Science, Jiangsu University, Zhenjiang, China

    Yang Yang, Yiwen Xiong, Yanqing Cao, Lanling Zeng, Yan Zhao & Yongzhao Zhan

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  1. Yang Yang
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Yang, Y., Xiong, Y., Cao, Y. et al. Fast bilateral filter with spatial subsampling. Multimedia Systems 29, 435–446 (2023). https://doi.org/10.1007/s00530-022-01004-7

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