Edge-guided second-order total generalized variation for Gaussian noise removal from depth map.
Shuaihao Li, Bin Zhang, Xinfeng Yang, Weiping Zhu
Author Information
Shuaihao Li: Research Center for International Business and Economy, Sichuan International Studies University, Chongqing, 400031, China. lishuaihao@whu.edu.cn.
Bin Zhang: Department of Computer Science, City University of Hong Kong, Hong Kong, 999077, China.
Xinfeng Yang: School of Computer Science, Wuhan University, Wuhan, 430072, China.
Weiping Zhu: School of Computer Science, Wuhan University, Wuhan, 430072, China.
Total generalized variation models have recently demonstrated high-quality denoising capacity for single image. In this paper, we present an accurate denoising method for depth map. Our method uses a weighted second-order total generalized variational model for Gaussian noise removal. By fusing an edge indicator function into the regularization term of the second-order total generalized variational model to guide the diffusion of gradients, our method aims to use the first or second derivative to enhance the intensity of the diffusion tensor. We use the first-order primal-dual algorithm to minimize the proposed energy function and achieve high-quality denoising and edge preserving result for depth maps with high -intensity noise. Extensive quantitative and qualitative evaluations in comparison to bench-mark datasets show that the proposed method provides significant higher accuracy and visual improvements than many state-of-the-art denoising algorithms.
References
Tomasi, C. & Manduchi, R. Bilateral filtering for gray and color images. In Proceedings of IEEE Conference Computer Vision. (ICCV). Bombay, India, Vol. 846, 839–846 (1998).
Dabov, K., Foi, A., Katkovnik, V. & Egiazarian, K. Image denoising by sparse 3-D transform-domain collaborative filtering. IEEE Trans. Image Process. 16, 2080–2095 (2007).
[DOI: 10.1109/TIP.2007.901238]
Li, S. H., Zhu, W. P., Zhang, B., Yang, X. F. & Chen, M. Depth map denoising using a bilateral filter and a progressive CNN. J. Opt. Technol. 87, 361–364 (2020).
[DOI: 10.1364/JOT.87.000361]
Koenderink, J. J. The structure of images. Biol. Cybern. 50, 363–370 (1984).
[DOI: 10.1007/BF00336961]
Witkin, A. P. Scale-space filtering. Read. Comput. Vis. 42, 329–332 (1987).
Gu, S., Zhang, L., Zuo, W. & Feng X. Weighted nuclear norm minimization with application to image denoising. In Proceedings of IEEE Conference Computer Vision Pattern Recognition. (CVPR) , 2862–2869 (Columbus, Ohio, USA, 2014).
Aharon, M., Elad, M. & Bruckstein, A. K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans. Signal Process. 54, 4311–4322 (2006).
[DOI: 10.1109/TSP.2006.881199]
Elad, M. & Aharon, M. Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans. Image Process. 15, 3736–3745 (2006).
[DOI: 10.1109/TIP.2006.881969]
Mahmoudi, M. & Sapiro, G. Sparse representations for range data restoration. IEEE Trans. Image Process. 21, 2909–2915 (2012).
[DOI: 10.1109/TIP.2012.2185940]
Hong, Y. & Zhu, W. P. Learning visual codebooks for image classification using spectral clustering. Soft Comput. 22, 1–10 (2017).
Hong, Y. & Zhu, W. P. Spatial co-training for semi-supervised image classification. Pattern Recognit. Lett. 63, 59–65 (2015).
[DOI: 10.1016/j.patrec.2015.06.017]
Burger, H. C., Schuler, C. J. & Harmeling, S. Image denoising: Can plain neural networks compete with BM3D? In Proceedings of IEEE Conference Computer Vision Pattern Recognition (CVPR) 2392–2399 (Providence, Rhode, USA, 2012).
Chen, Y. & Pock, T. Trainable nonlinear reaction diffusion: A flexible framework for fast and effective image restoration. IEEE Trans. Pattern Anal. Mach. Intell. 39, 1256–1272 (2017).
[DOI: 10.1109/TPAMI.2016.2596743]
Schmidt, U. & Roth, S. Shrinkage fields for effective image restoration. In Proceedings of IEEE Conference Computer Vision Pattern Recognition (CVPR) 2774–2781 (Columbus, Ohio, USA, 2014).
You, C. et al. Structurally-sensitive multi-scale deep neural network for low-dose CT denoising. IEEE Access. 6, 41839–41855 (2018).
[DOI: 10.1109/ACCESS.2018.2858196]
You, C. et al. CT super-resolution GAN constrained by the identical, residual, and cycle learning ensemble (GAN-CIRCLE). IEEE Trans. Med. Imaging. 39, 188–203 (2019).
[DOI: 10.1109/TMI.2019.2922960]
Guha, I. et al. Deep learning-based high-resolution reconstruction of trabecular bone microstructures from low-resolution CT scans using GAN-CIRCLE. InProceedings of SPIE—The International Society for Optical Engineering Vol. 11317. https://doi.org/10.1117/12.2549318 (2020).
You, C., Yang, L., Zhang, Y. & Wang, G. Low-dose CT via deep CNN with skip connection and network-in-network.InProceedings of SPIE in Developments in X-ray Tomography XII Vol.11113 (2019). https://doi.org/10.1117/12.2534960 .
Lyu, Q., You, C., Shan, H., Zhang, Y. & Wang, G. Super-resolution MRI and CT through GAN-circle. InProceedings of SPIE in Developments in X-Ray Tomography XII Vol. 11113 (2019). https://doi.org/10.1117/12.2530592
Li, S. H., Zhang, B., Yang, X. F., He, Y. X. & Chen, M. Depth image super resolution for 3D reconstruction of oil reflnery buildings. Chem Tech Fuels Oil+ 55, 491–496 (2019).
[DOI: 10.1007/s10553-019-01055-z]
Sun, L. et al. A novel weighted cross total variation method for hyperspectral image mixed denoising. IEEE Access. 5, 27172–27188 (2017).
[DOI: 10.1109/ACCESS.2017.2768580]
Rudin, L. I., Osher, S. & Fatemi, E. Nonlinear total variation-based noise removal algorithms. Physica D 60, 259–268 (1992).
[DOI: 10.1016/0167-2789(92)90242-F]
Ranftl, R., Bredies, K. & Pock, T. Non-local total generalized variation for optical flow estimation. In Proceedings of European Conference on Computer Vision (ECCV)439–454 (Springer, Cham, 2014).
Bredies, K., Kunisch, K. & Pock, T. Total generalized variation. Slam J Imaging Sci. 3, 492–526 (2010).
[DOI: 10.1137/090769521]
Chambolle, A. & Pock, T. A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40, 120–145 (2011).
[DOI: 10.1007/s10851-010-0251-1]
Rockafellar, R. T. & Zagrodny, D. A derivative-coderivative inclusion in second-order non-smooth analysis. Set Valued Anal. 5, 89–105 (1997).
[DOI: 10.1023/A]
Bredies, K., Dong, Y. & Hintermüller, M. Spatially dependent regularization parameter selection in total generalized variation models for image restoration. Int. J. Comput. Math. 90, 109–123 (2013).
[DOI: 10.1080/00207160.2012.700400]
Canny, J. A computational approach to edge detection.IEEE Trans. Pattern Anal. Mach. Intell. PAMI-8, 679–698 (1986).
Bertsekas, D. Convex analysis and optimization. Athena Sci. 129, 420–432 (2010).
Bredies, K., Kunisch, K. & Pock, T. Total generalized variation. SIAM J. Imaging Sci. 3, 492–526 (2010).
[DOI: 10.1137/090769521]
Scharstein, D. & Szeliski, R. High-accuracy stereo depth maps using structured light. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition 195–202 (Madison, WI, 2003).
Hirschmuller, H. & Scharstein, D. Evaluation of cost functions for stereo matching. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. (CVPR)1–8 (Minneapolis, MN, 2007).
Grants
61772573/the Nature Science Foundation of China
SIDT20170101/the National Mapping and Geographic Information Bureau of China
SIDT20170101/the National Mapping and Geographic Information Bureau of China
2016YFB1101702/the National Key Research and Development Program of China
2018YFC1604000/the National Key Research and Development Program of China
