Abstract
It is challenging to consistently smooth natural images, yet smoothing results determine the quality of a broad range of applications in computer vision. To achieve consistent smoothing, we propose a novel optimization model making use of the redundancy of natural images, by defining a nonlocal concentration regularization term on the gradient. This nonlocal constraint is carefully combined with a gradient-sparsity constraint, allowing details throughout the whole image to be removed automatically in a data-driven manner. As variations in gradient between similar patches can be suppressed effectively, the new model has excellent edge preserving, detail removal, and visual consistency properties. Comparisons with state-of-the-art smoothing methods demonstrate the effectiveness of the new method. Several applications, including edge manipulation, image abstraction, detail magnification, and image resizing, show the applicability of the new method.
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References
Arnheim R. Art and Visual Perception: A Psychology of the Creative Eye. University of California Press, 1954.
Tomasi, C.; Manduchi R. Bilateral filtering for gray and color images. In: Proceedings of the Sixth International Conference on Computer Vision, 839, 1998.
He, K.; Sun, J.; Tang X. Guided image filtering. Lecture Notes in Computer Science Vol. 6311, 1–14, 2010.
Paris, S.; Hasinoff S. W.; Kautz J. Local Laplacian filters: Edge-aware image processing with a Laplacian pyramid. ACM Transactions on Graphics Vol. 30, No. 4, Article No. 68, 2011.
Rudin L. I.; Osher, S.; Fatemi E. Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena Vol. 60, Nos. 1–4, 259–268, 1992.
Farbman, Z.; Fattal, R.; Lischinski, D.; Szeliski R. Edgepreserving decompositions for multi-scale tone and detail manipulation. ACM Transactions on Graphics Vol. 27, No. 3, Article No. 67, 2008.
Xu, L.; Lu, C.; Xu, Y.; Jia J. Image smoothing via L gradient minimization. ACM Transactions on Graphics Vol. 30, No. 6, Article No. 174, 2011.
Subr, K.; Soler, C.; Durand F. Edge-preserving multiscale image decomposition based on local extrema. ACM Transactions on Graphics Vol. 28, No. 5, Article No. 147, 2009.
Steidl, G.; Teuber T. Anisotropic smoothing using double orientations. Lecture Notes in Computer Science Vol. 5567, 477–489, 2009.
Kyprianidis J. E.; Kang H. Image and video abstraction by coherence-enhancing filtering. Computer Graphics Forum Vol. 30, No. 2, 593–602, 2011.
Xu, L.; Yan, Q.; Xia, Y.; Jia J. Structure extraction from texture via relative total variation. ACM Transactions on Graphics Vol. 31, No. 6, Article No. 139, 2012.
Karacan, L.; Erdem, E.; Erdem A. Structure-preserving image smoothing via region covariances. ACM Transactions on Graphics Vol. 32, No. 6, Article No. 176, 2013.
Su, Z.; Luo, X.; Artusi A. A novel image decomposition approach and its applications. The Visual Computer Vol. 29, No. 10, 1011–1023, 2013.
Li, X.-Y.; Gu, Y.; Martin R. R.; Hu S.-M. Mixed-domain edge-aware image manipulation. IEEE Transactions on Image Processing Vol. 22, No. 5, 1915–1925, 2013.
Bao, L.; Song, Y.; Yang, Q.; Yuan, H.; Wang G. Tree filtering: Efficient structure-preserving smoothing with a minimum spanning tree. IEEE Transactions on Image Processing Vol. 23, No. 2, 555–569, 2014.
Zhang, Q.; Shen, X.; Xu, L.; Jia J. Rolling guidance filter. Lecture Notes in Computer Science Vol. 8691, 815–830, 2014.
Zang, Y.; Huang, H.; Zhang L. Efficient structure-aware image smoothing by local extrema on space-filling curve. IEEE Transactions on Visualization and Computer Graphics Vol. 20, No. 9, 1253–1265, 2014.
Buades, A.; Coll, B.; Morel J.-M. A non-local algorithm for image denoising. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Vol. 2, 60–65, 2005.
Wang, Y.; Yang, J.; Yin, W.; Zhang Y. A new alternating minimization algorithm for total variation image reconstruction. SIAM Journal on Imaging Sciences Vol. 1, No. 3, 248–272, 2008.
Zhang, S.-H.; Li, X.-Y.; Hu, S.-M.; Martin R. R. Online video stream abstraction and stylization. IEEE Transactions on Multimedia Vol. 13, No. 6, 1286–1294, 2011.
Wong F. J.; Takahashi S. Abstracting images into continuousline artistic styles. The Visual Computer Vol. 29, Nos. 6–8, 729–738, 2013.
Avidan, S.; Shamir A. Seam carving for content-aware image resizing. ACM Transactions on Graphics Vol. 26, No. 3, Article No. 10, 2007.
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Qian Liu is currently a Ph.D. candidate in the School of Computer Science and Technology at Shandong University, China. She received the bachelor’s degree from the same institution in 2010. Her research interests include image processing, computer vision, and machine learning
Caiming Zhang is a professor and doctoral supervisor of the School of Computer Science and Technology in Shandong University. He received B.S. and M.E. degrees in computer science from Shandong University in 1982 and 1984, respectively, and a Dr.Eng. degree in computer science from Tokyo Institute of Technology, Japan, in 1994. From 1997 to 2000, Dr. Zhang held visiting position at University of Kentucky, USA. His research interests include CAGD, CG, information visualization, and medical image processing
Qiang Guo is currently an associate professor in the School of Computer Science and Technology at Shandong University of Finance and Economics, China. He received the B.S. degree in information and computing science from Shandong University of Technology, China, in 2002, and the M.S. and Ph.D. degrees in computer science from Shanghai University, China, in 2005 and 2010, respectively. His research interests include image restoration, sparse representation, and defect detection.
Yuanfeng Zhou is currently an associate professor in the School of Computer Science and Technology, Shandong University. He received his master’s degree and doctor’s degree in the Department of Computer Science and Technology at Shandong University in 2005 and 2009, respectively. He worked as a post-doctor at the Department of Computer Science of the University of Hong Kong from 2009 to 2011. His interested research fields include geometric modeling, information visualization, and image processing. He has published more than 20 papers on high level conferences and journals such as Graphical Models, Computer Animation and Virtual Worlds, Computer Graphics Forum, and Pacific Graphics.
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Liu, Q., Zhang, C., Guo, Q. et al. A nonlocal gradient concentration method for image smoothing. Comp. Visual Media 1, 197–209 (2015). https://doi.org/10.1007/s41095-015-0012-6
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DOI: https://doi.org/10.1007/s41095-015-0012-6