Abstract
Single image rain streak removal is a well-explored topic in the field of computer vision. The de-raining problem is modeled as an image decomposition task where a rainy image is decomposed into rain-free background image and rain streek map. Unlike most of the existing de-raining methods, this paper attempts to decompose the rainy image in the frequency domain. The idea is inspired by pseudo-periodic characteristics of the noise signal (here the rain streaks) which leave some traces in the frequency domain, and the same can be utilized to predict the noise signal. In this paper, a deep learning-based rain streak prediction model is proposed which learns in discrete Fourier transform Oppenheim and Schafer (Discrete-TimeSignal Processing, Prentice Hall, Upper Saddle River, 1989) domain. To the best of our knowledge, this is the first approach where compressed domain coefficients are directly used as input to a deep convolutional neural network. The proposed model has been tested on publicly available synthetic datasets Fu et al. (in: 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017. https://doi.org/10.1109/CVPR.2017.186, Yang et al. (in: 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017. https://doi.org/10.1109/CVPR.2017.183), Yeh et al. (in: 2015 IEEE International Conference on Consumer Electronics-Taiwan, 2015. https://doi.org/10.1109/ICCE-TW.2015.7216999) and results are found to be comparable with the state of the art methods in the spatial domain. The presented analysis and study have an obvious indication to extend transform domain input to train the deep learning architecture especially image de-noising like problems.
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Notes
DFT : Discrete Fourier Transformation.
The quantitative analysis has been given in Appendix 6.1.
Rain-streaks in this test-set may contradict with the real-rain.
References
Abadi, M., Agarwal, A., Barham, P., Brevdo, E., Chen, Z., Citro, C., Corrado, G.S., Davis, A., Dean, J., Devin, M., Ghemawat, S., Goodfellow, I., Harp, A., Irving, G., Isard, M., Jia, Y., Jozefowicz, R., Kaiser, L., Kudlur, M., Levenberg, J., Mané, D., Monga, R., Moore, S., Murray, D., Olah, C., Schuster, M., Shlens, J., Steiner, B., Sutskever, I., Talwar, K., Tucker, P., Vanhoucke, V., Vasudevan, V., Viégas, F., Vinyals, O., Warden, P., Wattenberg, M., Wicke, M., Yu, Y., Zheng, X.: TensorFlow: large-scale machine learning on heterogeneous systems (2015). URL https://www.tensorflow.org/, software available from tensorflow.org
Arbelaez, P., Maire, M., Fowlkes, C., Malik, J.: Contour detection and hierarchical image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 33(5), 898–916 (2011). https://doi.org/10.1109/TPAMI.2010.161
Chang, Y., Yan, L., Zhong, S.: Transformed low-rank model for line pattern noise removal. In: 2017 IEEE International Conference on Computer Vision (ICCV), pp 1735–1743 (2017). https://doi.org/10.1109/ICCV.2017.191
Chen, D.Y., Chen, C.C., Kang, L.W.: Visual depth guided color image rain streaks removal using sparse coding. IEEE Trans. Circuits Syst. Video Technol. 24(8), 1430–1455 (2014). https://doi.org/10.1109/TCSVT.2014.2308627
Chen, Q., Yi, X., Ni, B., Shen, Z., Yang, X.: Rain removal via residual generation cascading. In: 2017 IEEE Visual Communications and Image Processing (VCIP), pp 1–4 (2017). https://doi.org/10.1109/VCIP.2017.8305092
Davis, C.: The norm of the schur product operation. Numer. Math. 4(1), 343–344 (1962). https://doi.org/10.1007/BF01386329
Dunham, W.: Euler: the Master of Us All. No. v. 22 in Dolciani Mathematical Expositions, Mathematical Association of America (1999). https://books.google.co.in/books?id=uKOVNvGOkhQC
Fu, X., Huang, J., Ding, X., Liao, Y., Paisley, J.: Clearing the skies: a deep network architecture for single-image rain removal. IEEE Trans. Image Process. 26(6), 2944–2956 (2017). https://doi.org/10.1109/TIP.2017.2691802
Fu, X., Huang, J., Zeng, D., Huang, Y., Ding, X., Paisley, J.: Removing rain from single images via a deep detail network. In: 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp 1715–1723 (2017). https://doi.org/10.1109/CVPR.2017.186
Goodfellow, I., Bengio, Y., Courville, A.: Deep Learning. MIT Press, Cambridge (2016)
Goodfellow, I.J., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., Bengio, Y.: Generative adversarial nets. In: Proceedings of the 27th International Conference on Neural Information Processing Systems—Volume 2, MIT Press, Cambridge, MA, USA, NIPS’14, pp 2672–2680 (2014). http://dl.acm.org/citation.cfm?id=2969033.2969125
Gu, S., Meng, D., Zuo, W., Zhang, L.: Joint convolutional analysis and synthesis sparse representation for single image layer separation. In: 2017 IEEE International Conference on Computer Vision (ICCV), pp 1717–1725 (2017). https://doi.org/10.1109/ICCV.2017.189
Haar, A.: Zur theorie der orthogonalen funktionensysteme. Math Ann 69(3), 331–371 (1910). https://doi.org/10.1007/BF01456326
He, K., Sun, J., Tang, X.: Single image haze removal using dark channel prior. IEEE Trans. Pattern Anal. Mach. Intell. 33(12), 2341–2353 (2011). https://doi.org/10.1109/TPAMI.2010.168
He, K., Zhang, X., Ren, S., Sun, J.: Deep residual learning for image recognition (2015). arXiv:1512.03385
Hore, A., Ziou, D.: Image quality metrics: Psnr vs. ssim. In: Proceedings of the 2010 20th International Conference on Pattern Recognition, IEEE Computer Society, Washington, DC, USA, ICPR ’10, pp 2366–2369 (2010). https://doi.org/10.1109/ICPR.2010.579
Huang, D.A., Kang, L.W., Wang, Y.C.F., Lin, C.W.: Self-learning based image decomposition with applications to single image denoising. IEEE Trans. Multimed. 16(1), 83–93 (2014). https://doi.org/10.1109/TMM.2013.2284759
Kang, L.W., Lin, C.W., Fu, Y.H.: Automatic single-image-based rain streaks removal via image decomposition. IEEE Trans. Image Process. 21(4), 1742–1755 (2012). https://doi.org/10.1109/TIP.2011.2179057
Katznelson, Y.: An introduction to harmonic analysis. Cambridge Mathematical Library (1976)
Lee, J.H., Heo, M., Kim, K.R., Kim, C.S.: Single-image depth estimation based on Fourier domain analysis. In: The IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2018)
Li, Y., Tan, R.T., Guo, X., Lu, J., Brown, M.S.: Rain streak removal using layer priors. In: 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp 2736–2744 (2016). https://doi.org/10.1109/CVPR.2016.299
Li, Y., Tan, R.T., Guo, X., Lu, J., Brown, M.S.: Single image rain streak decomposition using layer priors. IEEE Trans. Image Process. 26(8), 3874–3885 (2017). https://doi.org/10.1109/TIP.2017.2708841
Luo, Y., Xu, Y., Ji, H.: Removing rain from a single image via discriminative sparse coding. In: 2015 IEEE International Conference on Computer Vision (ICCV), pp 3397–3405 (2015). https://doi.org/10.1109/ICCV.2015.388
Lian, N.-X., Zagorodnov, V., Tan, Y.-P.: Edge-preserving image denoising via optimal color space projection. IEEE Trans. Image Process. 15(9), 2575–2587 (2006)
Oppenheim, A.V., Schafer, R.W.: Discrete-Time Signal Processing. Prentice Hall, Upper Saddle River (1989)
Park, K., Yu, S., Jeong, J.: A contrast restoration method for effective single image rain removal algorithm. In: 2018 International Workshop on Advanced Image Technology (IWAIT), pp 1–4 (2018). https://doi.org/10.1109/IWAIT.2018.8369644
Pratt, H., Williams, B., Coenen, F., Zheng, Y.: Fcnn: Fourier convolutional neural networks. In: Ceci, M., Hollmén, J., Todorovski, L., Vens, C., Džeroski, S. (eds.) Machine Learning and Knowledge Discovery in Databases, pp. 786–798. Springer, Cham (2017)
Ren, W., Tian, J., Han, Z., Chan, A., Tang, Y.: Video desnowing and deraining based on matrix decomposition. In: 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp 2838–2847 (2017). https://doi.org/10.1109/CVPR.2017.303
Schaefer, G., Stich, M.: UCID: an uncompressed color image database. In: Yeung, M.M., Lienhart, R.W., Li, C.S. (eds.) Storage and Retrieval Methods and Applications for Multimedia 2004, vol 5307, pp 472–480 (2003). https://doi.org/10.1117/12.525375
Sharma, P.K., Jain, P., Sur, A.: Dual-domain single image de-raining using conditional generative adversarial network. In: 2019 IEEE International Conference on Image Processing (ICIP), pp 2796–2800 (2019). https://doi.org/10.1109/ICIP.2019.8803353
Shen, L., Yue, Z., Chen, Q., Feng, F., Ma, J.: Deep joint rain and haze removal from single images (2018). arXiv:1801.06769
Wang, T., Yang, X., Xu, K., Chen, S., Zhang, Q., Lau, R.W.: Spatial attentive single-image deraining with a high quality real rain dataset. In: The IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2019)
Wang, Y., Chen, C., Zhu, S., Zeng, B.: A framework of single-image deraining method based on analysis of rain characteristics. In: 2016 IEEE International Conference on Image Processing (ICIP), pp 4087–4091 (2016). https://doi.org/10.1109/ICIP.2016.7533128
Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. Trans. Image Proc. 13(4), 600–612 (2004). https://doi.org/10.1109/TIP.2003.819861
Yang, W., Tan, R.T., Feng, J., Liu, J., Guo, Z., Yan, S.: Deep joint rain detection and removal from a single image. In: 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp 1685–1694 (2017). https://doi.org/10.1109/CVPR.2017.183
Yeh, C.H., Liu, P.H., Yu, C.E., Lin, C.Y.: Single image rain removal based on part-based model. In: 2015 IEEE International Conference on Consumer Electronics—Taiwan, pp 462–463 (2015). https://doi.org/10.1109/ICCE-TW.2015.7216999
Yu, S., Ou, W., You, X., Mou, Y., Jiang, X., Tang, Y.: Single image rain streaks removal based on self-learning and structured sparse representation. In: 2015 IEEE China Summit and International Conference on Signal and Information Processing (ChinaSIP), pp 215–219 (2015). https://doi.org/10.1109/ChinaSIP.2015.7230394
Zhang, H., Patel, V.M.: Convolutional sparse and low-rank coding-based rain streak removal. In: 2017 IEEE Winter Conference on Applications of Computer Vision (WACV), pp 1259–1267 (2017). https://doi.org/10.1109/WACV.2017.145
Zhang, H., Patel, V.M.: Density-aware single image de-raining using a multi-stream dense network (2018). arXiv:1802.07412
Zhu, L., Fu, C.W., Lischinski, D., Heng, P.A.: Joint bi-layer optimization for single-image rain streak removal. In: 2017 IEEE International Conference on Computer Vision (ICCV), pp 2545–2553 (2017). https://doi.org/10.1109/ICCV.2017.276
Acknowledgements
Authors would like to thank the anonymous reviewers for their insightful comments and suggestions. Authors would also like to acknowledge the funding agency, Ministry of Human Resource Development, Government of India.
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Appendix
Appendix
1.1 Quantitative analysis of rain-streaks present in Y channel compared to Cb & Cr
Deep learning models for image restoration, in RGB color-space due to its highly correlated nature, may induce white pixel artifacts and color saturation, especially in the case of image de-raining [30]. YCbCr is a more suitable color-space for image restoration when the noise in an image exhibits linear or a pseudo-periodic nature [24, 30]. To quantify the noise present in the Y channel compared to chrominance channels, we have adopted the concept of sparsity and conducted the following experiment on the test-set TD- Zhang et al. that consists of 1200 rainy-clean image pairs.
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1.
We convert the rainy and clean images into YCbCr color-space.
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2.
Obtains the pixel-wise difference between corresponding Y Cb Cr channels of rainy and clean images.
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3.
Measure the sparsity ratio based on the following equation
$$\begin{aligned} \mathcal {S} = \frac{\text {No. of Zero-pixels}}{\text {Total No. of pixels}} \end{aligned}$$(19) -
4.
High sparsity indicates the low rain-noise present in the channel compared to its clean counterpart. We have obtained the following results. The same has been added in the appendix with qualitative results.
Metric
Y
Cr
Cb
\(\mathcal {S}\) (avg.)
0.0449
0.4481
0.4040
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5.
It can be observed that the Y channel has the lowest sparsity ratio that indicates the highest rain-streak noise present compared to other channels.
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6.
Although the values are test-set specific, it may obey for any rain-streak removal test-set.
1.2 Run-time comparison
We have implemented the proposed model using Tensorflow framework [1]. It takes \(\sim \) 0.56 s to test an image of size \(512 \times 512\) on an 8 GB GPU. We have also compared the proposed model with existing schemes based on the run-time per image, and results are shown in Table 5.
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Sharma, P.K., Basavaraju, S. & Sur, A. Deep learning-based image de-raining using discrete Fourier transformation. Vis Comput 37, 2083–2096 (2021). https://doi.org/10.1007/s00371-020-01971-w
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DOI: https://doi.org/10.1007/s00371-020-01971-w