Abstract
Edge-preserving image smoothing plays a vital role in the field of computational photography. In this paper, we propose a weighted and truncated \(L_1\)-regularized optimization model for image smoothing. We show that the weighted and truncated scheme significantly promotes the edge-preserving property. Furthermore, we propose a deep unsupervised learning-based filter based on the loss function defined by the proposed optimization model. The proposed filter leverages a U-Net structure, which fully exploits the spatially varying smoothing scales of the edge-preserving filtering. We have conducted extensive experiments to evaluate the proposed filter. The results suggest that our filter outperforms the state-of-the-art filters in image quality on various tasks, such as image smoothing, detail enhancing, HDR tone mapping, and edge detection. Meanwhile, our filter is extremely efficient. It is able to process 720P images in real-time (more than 16 frames per second) on a modern desktop with an Intel i7-8700K CPU, an NVIDIA GTX 1080 GPU and 16GB memory.
Similar content being viewed by others
Data Availability
Our source code, trained model, and data are available at https://github.com/dtz-dd/weighted-and-truncated-L1-smooth.
References
Xie, Z., Lau, R.W.H., Gui, Y., Chen, M., Ma, L.: A gradient-domain-based edge-preserving sharpen filter. Vis. Comput. 28(12), 1195–1207 (2012)
Tan, A., Liao, H., Zhang, B., Gao, M., Li, S., Bai, Y., et al.: Infrared image enhancement algorithm based on detail enhancement guided image filtering. Vis. Comput. (2022). https://doi.org/10.1007/s00371-022-02741-6
Durand, F., Dorsey, J.: Fast bilateral filtering for the display of high-dynamic-range images. ACM Trans. Graph. 21(3), 257–266 (2002)
Song, X., Huang, J., Cao, J., Song, D.: Feature spatial pyramid network for low-light image enhancement. Vis. Comput. 39, 489–499 (2022)
Wang, C., Zhang, H., Liu, L.: Total generalized variation-based Retinex image decomposition. Vis. Comput. 37(1), 77–93 (2021)
He, K., Sun, J., Tang, X.: Guided image filtering. IEEE Trans. Pattern Anal. Mach. Intell. 35(6), 1397–1409 (2013)
Xiao, C., Gan, J.: Fast image dehazing using guided joint bilateral filter. Vis. Comput. 28(6–8), 713–721 (2012)
Xu, L., Yan, Q., Xia, Y., Jia, J.: Structure extraction from texture via relative total variation. ACM Trans. Graph. 31(6), 139:1-139:10 (2012)
Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In: IEEE International Conference on Computer Vision, pp. 839–846 (1998)
Rao, S., Wang, H.: Optical flow estimation via weighted guided filtering with non-local steering kernel. Vis. Comput. 39(3), 835–845 (2023)
Gastal, E.S.L., Oliveira, M.M.: Domain transform for edge-aware image and video processing. ACM Trans. Graph. 30(4), 691–6911 (2011)
Yin, H., Gong, Y., Qiu, G.: Side window filtering. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 8758–8766 (2019)
Zhou, P., Xue, Y., Xue, M.: Adaptive side window joint bilateral filter. Vis. Comput. 39(4), 1533–1555 (2023)
Wang, H., Cao, J., Liu, X., Wang, J., Fan, T., Hu, J.: Least-squares images for edge-preserving smoothing. Comput. Vis. Media 1(1), 27–35 (2015)
Farbman, Z., Fattal, R., Lischinski, D., Szeliski, R.: Edge-preserving decompositions for multi-scale tone and detail manipulation. ACM Trans. Graph. 27(3), 67:1-67:10 (2008)
Xu, L., Lu, C., Xu, Y., Jia, J.: Image smoothing via L\({}_{0}\) gradient minimization. ACM Trans. Graph. 30(6), 174:1-174:11 (2011)
Bi, S., Han, X., Yu, Y.: An L\({}_{{1}}\) image transform for edge-preserving smoothing and scene-level intrinsic decomposition. ACM Trans. Graph. 34(4), 78:1-78:12 (2015)
Ma, X., Li, X., Zhou, Y., Zhang, C.: Image smoothing based on global sparsity decomposition and a variable parameter. Comput. Vis. Media 7(4), 483–497 (2021)
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. 33(12), 7223–7236 (2022)
Wu, H., Zheng, S., Zhang, J., Huang, K.: Fast end-to-end trainable guided filter. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 1838–1847 (2018)
Zhu, F., Liang, Z., Jia, X., Zhang, L., Yu, Y.: A benchmark for edge-preserving image smoothing. IEEE Trans. Image Process. 28(7), 3556–3570 (2019)
Chen, Q., Xu, J., Koltun, V.: Fast image processing with fully-convolutional networks. In: IEEE International Conference on Computer Vision, pp. 2516–2525 (2017)
Xu, L., Ren, J.S.J., Yan, Q., Liao, R., Jia, J.: Deep edge-aware filters. In: International Conference on Machine Learning, pp. 1669–1678 (2015)
Zhang, Q., Xu, L., Jia, J.: 100+ times faster weighted median filter (WMF). In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 2830–2837 (2014)
Fattal, R.: Edge-avoiding wavelets and their applications. ACM Trans. Graph. 28(3), 22 (2009)
Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990)
Zhang, Q., Shen, X., Xu, L., Jia, J.: Rolling guidance filter. In: European Conference on Computer Vision, pp. 815–830 (2014)
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)
Dai, L., Tang, L., Tang, J.: Speed up bilateral filtering via sparse approximation on a learned cosine dictionary. IEEE Trans. Circuits Syst. Video Technol. 30(3), 603–617 (2020)
Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Phys. D 60, 259–268 (1992)
Yang, Y., Zheng, H., Zeng, L., Shen, X., Zhan, Y.: L1-regularized reconstruction model for edge-preserving filtering. IEEE Trans. Multimed. 25, 4148–4162 (2022)
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)
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)
Liu, W., Zhang, P., Lei, Y., Huang, X., Yang, J., Ng, M.: A generalized framework for edge-preserving and structure-preserving image smoothing. IEEE Trans. Pattern Anal. Mach. Intell. 44(10), 6631–6648 (2022)
Liu, W., Zhang, P., Huang, X., Yang, J., Shen, C., Reid, I.: Real-time image smoothing via iterative least squares. ACM Trans. Graph. 39(3), 28:1-28:24 (2020)
Fan, Q., Yang, J., Wipf, D.P., Chen, B., Tong, X.: Image smoothing via unsupervised learning. ACM Trans. Graph. 37(6), 259:1-259:14 (2018)
Gharbi, M., Chen, J., Barron, J.T., Hasinoff, S.W., Durand, F.: Deep bilateral learning for real-time image enhancement. ACM Trans. Graph. 36(4), 118:1-118:12 (2017)
Isola, P., Zhu, J., Zhou, T., Efros, A.A.: Image-to-image translation with conditional adversarial networks. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 5967–5976 (2017)
Liu, S., Pan, J., Yang, M.: Learning recursive filters for low-level vision via a hybrid neural network. In: European Conference on Computer Vision, pp. 560–576 (2016)
Ronneberger, O., Fischer, P., Brox, T.: U-Net: convolutional networks for biomedical image segmentation. Med. Image Comput. Comput. Assist. Interv. 9351, 234–241 (2015)
Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization. In: International Conference on Learning Representations (2015)
Xu, J., Liu, Z., Hou, Y., Zhen, X., Shao, L., Cheng, M.: Pixel-level non-local image smoothing with objective evaluation. IEEE Trans. Multimed. 23, 4065–4078 (2021)
Liu, W., Chen, X., Shen, C., Liu, Z., Yang, J.: Semi-global weighted least squares in image filtering. In: IEEE International Conference on Computer Vision, pp. 5862–5870 (2017)
Sun, Z., Han, B., Li, J., Zhang, J., Gao, X.: Weighted guided image filtering with steering kernel. IEEE Trans. Image Process. 29, 500–508 (2020)
Arbelaez, P., Maire, M., Fowlkes, C.C., Malik, J.: Contour detection and hierarchical image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 33(5), 898–916 (2011)
Rother, C., Kolmogorov, V., Blake, A.: GrabCut: interactive foreground extraction using iterated graph cuts. ACM Trans. Graph. 23(3), 309–314 (2004)
Ferrari, V., Fevrier, L., Jurie, F., Schmid, C.: Groups of adjacent contour segments for object detection. IEEE Trans. Pattern Anal. Mach. Intell. 30(1), 36–51 (2008)
Girshick, R.B., Donahue, J., Darrell, T., Malik, J.: Rich feature hierarchies for accurate object detection and semantic segmentation. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 580–587 (2014)
Canny, J.F.: A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. 8(6), 679–698 (1986)
DeCarlo, D., Santella, A.: Stylization and abstraction of photographs. ACM Trans. Graph. 21(3), 769–776 (2002)
Winnemöller, H., Olsen, S.C., Gooch, B.: Real-time video abstraction. ACM Trans. Graph. 25(3), 1221–1226 (2006)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Yang, Y., Wu, D., Tang, L. et al. Weighted and truncated \(L_1\) image smoothing based on unsupervised learning. Vis Comput (2023). https://doi.org/10.1007/s00371-023-03141-0
Accepted:
Published:
DOI: https://doi.org/10.1007/s00371-023-03141-0