research-article

Image smoothing via L₀ gradient minimization

Authors:

Jiaya JiaAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 30, Issue 6

Pages 1 - 12

https://doi.org/10.1145/2070781.2024208

Published: 12 December 2011 Publication History

Abstract

We present a new image editing method, particularly effective for sharpening major edges by increasing the steepness of transition while eliminating a manageable degree of low-amplitude structures. The seemingly contradictive effect is achieved in an optimization framework making use of L₀ gradient minimization, which can globally control how many non-zero gradients are resulted in to approximate prominent structure in a sparsity-control manner. Unlike other edge-preserving smoothing approaches, our method does not depend on local features, but instead globally locates important edges. It, as a fundamental tool, finds many applications and is particularly beneficial to edge extraction, clip-art JPEG artifact removal, and non-photorealistic effect generation.

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References

[1]

Arbelaez, P., Maire, M., Fowlkes, C., and Malik, J. 2011. Contour detection and hierarchical image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 33, 898--916.

Digital Library

[2]

Bae, S., and Durand, F. 2007. Defocus magnification. Comput. Graph. Forum 26, 3, 571--579.

[3]

Bae, S., Paris, S., and Durand, F. 2006. Two-scale tone management for photographic look. ACM Trans. Graph. 25, 3, 637--645.

Digital Library

[4]

Baek, J., and Jacobs, D. E. 2010. Accelerating spatially varying gaussian filters. ACM Trans. Graph..

Digital Library

[5]

Black, M. J., Sapiro, G., Marimont, D. H., and Heeger, D. 1998. Robust anisotropic diffusion. IEEE Transactions on Image Processing 7, 3, 421--432.

Digital Library

[6]

Blake, A., and Zisserman, A. 1987. Visual reconstruction. The MIT Press.

Digital Library

[7]

Boykov, Y., Veksler, O., and Zabih, R. 2001. Fast approximate energy minimization via graph cuts. IEEE Trans. Pattern Anal. Mach. Intell. 23, 11, 1222--1239.

Digital Library

[8]

Chen, J., Paris, S., and Durand, F. 2007. Real-time edge-aware image processing with the bilateral grid. ACM Trans. Graph. 26, 3, 103.

Digital Library

[9]

Choudhury, P., and Tumblin, J. 2003. The trilateral filter for high contrast images and meshes. In Rendering Techniques, 186--196.

Digital Library

[10]

Comaniciu, D., and Meer, P. 2002. Mean shift: A robust approach toward feature space analysis. IEEE Trans. Pattern Anal. Mach. Intell. 24, 5, 603--619.

Digital Library

[11]

Criminisi, A., Sharp, T., Rother, C., and Pérez, P. 2010. Geodesic image and video editing. ACM Trans. Graph. 29, 5, 134.

Digital Library

[12]

Dabov, K., Foi, A., Katkovnik, V., and Egiazarian, K. O. 2007. Image denoising by sparse 3-d transform-domain collaborative filtering. IEEE Transactions on Image Processing 16, 8, 2080--2095.

Digital Library

[13]

DeCarlo, D., and Santella, A. 2002. Stylization and abstraction of photographs. ACM Trans. Graph. 21, 3, 769--776.

Digital Library

[14]

Donoho, D. 2006. Compressed sensing. IEEE Transactions on Information Theory 52, 4, 1289--1306.

Digital Library

[15]

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

Digital Library

[16]

Farbman, Z., Fattal, R., Lischinski, D., and Szeliski, R. 2008. Edge-preserving decompositions for multi-scale tone and detail manipulation. ACM Trans. Graph. 27, 3.

Digital Library

[17]

Farbman, Z., Fattal, R., and Lischinski, D. 2010. Diffusion maps for edge-aware image editing. ACM Trans. Graph..

Digital Library

[18]

Fattal, R., Agrawala, M., and Rusinkiewicz, S. 2007. Multiscale shape and detail enhancement from multi-light image collections. ACM Trans. Graph. 26, 3, 51.

Digital Library

[19]

Fattal, R. 2009. Edge-avoiding wavelets and their applications. ACM Trans. Graph. 28, 3.

Digital Library

[20]

Kass, M., and Solomon, J. 2010. Smoothed local histogram filters. ACM Trans. Graph. 29, 4.

Digital Library

[21]

Levin, A., Lischinski, D., and Weiss, Y. 2004. Colorization using optimization. ACM Trans. Graph. 23, 3, 689--694.

Digital Library

[22]

Levin, A., Fergus, R., Durand, F., and Freeman, W. T. 2007. Image and depth from a conventional camera with a coded aperture. ACM Trans. Graph. 26, 3, 70.

Digital Library

[23]

Li, Y., Sun, J., Tang, C.-K., and Shum, H.-Y. 2004. Lazy snapping. ACM Trans. Graph. 23, 3, 303--308.

Digital Library

[24]

Li, Y., Sharan, L., and Adelson, E. H. 2005. Compressing and companding high dynamic range images with subband architectures. ACM Trans. Graph. 24, 3, 836--844.

Digital Library

[25]

Lischinski, D., Farbman, Z., Uyttendaele, M., and Szeliski, R. 2006. Interactive local adjustment of tonal values. ACM Trans. Graph. 25, 3, 646--653.

Digital Library

[26]

Liu, J., Sun, J., and Shum, H.-Y. 2009. Paint selection. ACM Trans. Graph. 28, 3.

Digital Library

[27]

Mairal, J., Bach, F., Ponce, J., Sapiro, G., and Zisserman, A. 2009. Non-local sparse models for image restoration. In ICCV, 2272--2279.

[28]

Maji, S., Vishnoi, N., and Malik, J. 2011. Biased normalized cuts. In CVPR.

Digital Library

[29]

Paris, S., and Durand, F. 2006. A fast approximation of the bilateral filter using a signal processing approach. In ECCV (4), 568--580.

Digital Library

[30]

Paris, S., Hasinoff, S. W., and Kautz, J. 2011. Local laplacian filters: Edge-aware image processing with a laplacian pyramid. ACM Trans. Graph..

Digital Library

[31]

Perona, P., and Malik, J. 1990. Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12, 7, 629--639.

Digital Library

[32]

Rother, C., Kolmogorov, V., and Blake, A. 2004. "grab-cut": interactive foreground extraction using iterated graph cuts. ACM Trans. Graph. 23, 3, 309--314.

Digital Library

[33]

Rudin, L., Osher, S., and Fatemi, E. 1992. Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena 60, 1--4, 259--268.

Digital Library

[34]

Subr, K., Soler, C., and Durand, F. 2009. Edge-preserving multiscale image decomposition based on local extrema. ACM Trans. Graph. 28, 5.

Digital Library

[35]

Tomasi, C., and Manduchi, R. 1998. Bilateral filtering for gray and color images. In ICCV, 839--846.

Digital Library

[36]

Tumblin, J., and Turk, G. 1999. Lcis: A boundary hierarchy for detail-preserving contrast reduction. In SIGGRAPH, 83--90.

Digital Library

[37]

Wang, Z., Bovik, A. C., Sheikh, H. R., and Simoncelli, E. P. 2004. Image quality assessment: from error visibility to structural similarity. IEEE Transactions on Image Processing 13, 4, 600--612.

Digital Library

[38]

Wang, G., Wong, T.-T., and Heng, P.-A. 2006. Deringing cartoons by image analogies. ACM Trans. Graph. 25, 4, 1360--1379.

Digital Library

[39]

Wang, Y., Yang, J., Yin, W., and Zhang, Y. 2008. A new alternating minimization algorithm for total variation image reconstruction. SIAM J. Imaging Sciences 1, 3, 248--272.

Digital Library

[40]

Weiss, B. 2006. Fast median and bilateral filtering. ACM Trans. Graph. 25, 3, 519--526.

Digital Library

[41]

Winnemöller, H., Olsen, S. C., and Gooch, B. 2006. Realtime video abstraction. ACM Trans. Graph. 25, 3, 1221--1226.

Digital Library

Cited By

Nogami HKanetaka YNaganawa YMaeda YFukushima N(2024)Decomposed Multilateral Filtering for Accelerating Filtering with Multiple Guidance ImagesSensors10.3390/s2402063324:2(633)Online publication date: 19-Jan-2024
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Wang SMa XLi X(2024)A Parameter Adaptive Method for Image SmoothingTsinghua Science and Technology10.26599/TST.2023.901006829:4(1138-1151)Online publication date: Aug-2024
https://doi.org/10.26599/TST.2023.9010068
LIU GCHEN XGAO Z(2024)A Novel Double-Tail Generative Adversarial Network for Fast Photo AnimationIEICE Transactions on Information and Systems10.1587/transinf.2023EDP7061E107.D:1(72-82)Online publication date: 1-Jan-2024
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Index Terms

Image smoothing via L₀ gradient minimization
1. Computing methodologies
  1. Artificial intelligence
    1. Computer vision
      1. Computer vision tasks
  2. Computer graphics
    1. Image manipulation

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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 30, Issue 6

December 2011

678 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/2070781

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Copyright © 2011 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 12 December 2011

Published in TOG Volume 30, Issue 6

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Cited By

Nogami HKanetaka YNaganawa YMaeda YFukushima N(2024)Decomposed Multilateral Filtering for Accelerating Filtering with Multiple Guidance ImagesSensors10.3390/s2402063324:2(633)Online publication date: 19-Jan-2024
https://doi.org/10.3390/s24020633
Wang SMa XLi X(2024)A Parameter Adaptive Method for Image SmoothingTsinghua Science and Technology10.26599/TST.2023.901006829:4(1138-1151)Online publication date: Aug-2024
https://doi.org/10.26599/TST.2023.9010068
LIU GCHEN XGAO Z(2024)A Novel Double-Tail Generative Adversarial Network for Fast Photo AnimationIEICE Transactions on Information and Systems10.1587/transinf.2023EDP7061E107.D:1(72-82)Online publication date: 1-Jan-2024
https://doi.org/10.1587/transinf.2023EDP7061
XIA ZLIU YWANG XZHANG FCHEN RJIANG W(2024)Infrared and Visible Image Fusion via Hybrid Variational ModelIEICE Transactions on Information and Systems10.1587/transinf.2023EDL8027E107.D:4(569-573)Online publication date: 1-Apr-2024
https://doi.org/10.1587/transinf.2023EDL8027
Yin HLi XLiu ZPeng WWang CYu W(2024) CT image restoration method via total variation and L 0 smoothing filter Journal of Inverse and Ill-posed Problems10.1515/jiip-2023-0052Online publication date: 30-Jan-2024
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Yang YQiu SZeng LPan Z(2024)Detail-preserving Joint Image UpsamplingACM Transactions on Multimedia Computing, Communications, and Applications10.1145/366524620:8(1-23)Online publication date: 13-Jun-2024
https://dl.acm.org/doi/10.1145/3665246
Xiong YYang YZeng LWang XPan ZJiang L(2024)Deep unsupervised nonconvex optimization for edge-preserving image smoothingJournal of Electronic Imaging10.1117/1.JEI.33.4.04300133:04Online publication date: 1-Jul-2024
https://doi.org/10.1117/1.JEI.33.4.043001
Liu QLu ZZhang JBu XHanajima N(2024)Cluster segmentation algorithm for enhancing edge informationJournal of Electronic Imaging10.1117/1.JEI.33.1.01304033:01Online publication date: 1-Jan-2024
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Xu RZhang LZhang F(2024)Intrinsic Omnidirectional Image Decomposition With Illumination Pre-ExtractionIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2024.336634330:7(4416-4428)Online publication date: 1-Jul-2024
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Zhang ZLi MZhao ZFang QFu X(2024)Practical Integer-Constrained Cone Construction for Conformal ParameterizationsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.328730330:8(5227-5239)Online publication date: Aug-2024
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