Advertisement

Computational Visual Media

, Volume 1, Issue 1, pp 27–35 | Cite as

Least-squares images for edge-preserving smoothing

  • Hui Wang
  • Junjie Cao
  • Xiuping LiuEmail author
  • Jianmin Wang
  • Tongrang Fan
  • Jianping Hu
Open Access
Research Article

Abstract

In this paper, we propose least-squares images (LS-images) as a basis for a novel edge-preserving image smoothing method. The LS-image requires the value of each pixel to be a convex linear combination of its neighbors, i.e., to have zero Laplacian, and to approximate the original image in a least-squares sense. The edge-preserving property inherits from the edge-aware weights for constructing the linear combination. Experimental results demonstrate that the proposed method achieves high quality results compared to previous state-of-the-art works. We also show diverse applications of LS-images, such as detail manipulation, edge enhancement, and clip-art JPEG artifact removal.

Keywords

feature-preserving image enhancement image smoothing least-squares images (LS-images) 

References

  1. [1]
    Perona, P.; Malik, J. Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence Vol. 12, No. 7, 629–639, 1990.CrossRefGoogle Scholar
  2. [2]
    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.CrossRefzbMATHGoogle Scholar
  3. [3]
    Tomasi, C.; Manduchi, R. Bilateral filtering for gray and color images. In: Sixth International Conference on Computer Vision, 839–846, 1998.Google Scholar
  4. [4]
    Comaniciu, D.; Meer, P. Mean shift: A robust approach toward feature space analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence Vol. 24, No. 5, 603–619, 2002.CrossRefGoogle Scholar
  5. [5]
    Farbman, Z.; Fattal, R.; Lischinski, D.; Szeliski, R. Edge-preserving decompositions for multi-scale tone and detail manipulation. ACM Transactions on Graphics Vol. 27, No. 3, Article No. 67, 2008.CrossRefGoogle Scholar
  6. [6]
    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.CrossRefGoogle Scholar
  7. [7]
    Fattal, R. Edge-avoiding wavelets and their applications. ACM Transactions on Graphics Vol. 28, No. 3, Article No. 22, 2009.CrossRefGoogle Scholar
  8. [8]
    Farbman, Z.; Fattal, R.; Lischinski, D. Diffusion maps for edge-aware image editing. ACM Transactions on Graphics Vol. 29, No. 6, Article No. 145, 2010.CrossRefGoogle Scholar
  9. [9]
    Xu, L.; Lu, C.; Xu, Y.; Jia, J. Image smoothing via L0 gradient minimization. ACM Transactions on Graphics Vol. 30, No. 6, Article No. 174, 2011.Google Scholar
  10. [10]
    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.CrossRefGoogle Scholar
  11. [11]
    He, K.; Sun, J.; Tang, X. Guided image filtering. IEEE Transactions on Pattern Analysis and Machine Intelligence Vol. 35, No. 6, 1397–1409, 2013.CrossRefGoogle Scholar
  12. [12]
    Cheng, X.; Zeng, M.; Liu, X. Feature-preserving filtering with L0 gradient minimization. Computers & Graphics Vol. 38, 150–157, 2014.CrossRefGoogle Scholar
  13. [13]
    Levin, A.; Lischinski, D.; Weiss, Y. Colorization using optimization. ACM Transactions on Graphics Vol. 23, No. 3, 689–694, 2004.CrossRefGoogle Scholar
  14. [14]
    Grady, L. Random walks for image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence Vol. 28, No. 11, 1768–1783, 2006.CrossRefGoogle Scholar
  15. [15]
    Sorkine, O.; Cohen- Or, D. Least-squares meshes. In: Proceedings of the Shape Modeling International, 191–199, 2004.Google Scholar
  16. [16]
    Sorkine, O. Differential representations for mesh processing. Computer Graphics Forum Vol. 25, No. 4, 789–807, 2006.CrossRefGoogle Scholar
  17. [17]
    Sorkine, O.; Cohen- Or, D.; Irony, D.; Toledo, S. Geometry-aware bases for shape approximation. IEEE Transactions on Visualization and Computer Graphics Vol. 11, No. 2, 171–180, 2005.CrossRefGoogle Scholar
  18. [18]
    Chen, D.; Cohen- Or, D.; Sorkine, O.; Toledo, S. Algebraic analysis of high-pass quantization. ACM Transactions on Graphics Vol. 24, No. 4, 1259–1282, 2005.CrossRefGoogle Scholar
  19. [19]
    Chen, J.; Paris, S.; Durand, F. Real-time edge-aware image processing with the bilateral grid. ACM Transactions on Graphics Vol. 26, No. 3, Article No. 103, 2007.CrossRefGoogle Scholar
  20. [20]
    Yang, Q.; Tan, K.-H.; Ahuja, N. Real-time O(1) bilateral filtering. In: IEEE Conference on Computer Vision and Pattern Recognition, 557–564, 2009.Google Scholar
  21. [21]
    Gastal, E. S. L.; Oliveira, M. M. Adaptive manifolds for real-time high-dimensional filtering. ACM Transactions on Graphics Vol. 31, No. 4, Article No. 33, 2012.CrossRefGoogle Scholar
  22. [22]
    Cho, H.; Lee, H.; Kang, H.; Lee, S. Bilateral texture filtering. ACM Transactions on Graphics Vol. 33, No. 4, Article No. 128, 2014.CrossRefGoogle Scholar
  23. [23]
    Criminisi, A.; Sharp, T.; Rother, C.; Pérez, P. Geodesic image and video editing. ACM Transactions on Graphics Vol. 29, No. 5, Article No. 134, 2010.CrossRefGoogle Scholar
  24. [24]
    Gastal, E. S. L.; Oliveiral, M. M. Domain transform for edge-aware image and video processing. ACM Transactions on Graphics Vol. 30, No. 4, Article No. 69, 2011.CrossRefGoogle Scholar
  25. [25]
    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.CrossRefGoogle Scholar
  26. [26]
    Huang, S.-S.; Zhang, G.-X.; Lai, Y.-K.; Kopf, J.; Cohen- Or, D.; Hu, S.-M. Parametric meta-filter modeling from a single example pair. The Visual Computer Vol. 30, Nos. 6–8, 673–684, 2014.CrossRefGoogle Scholar
  27. [27]
    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.Google Scholar
  28. [28]
    Li, X.-Y.; Gu, Y.; Hu, S.-M.; Martin, R. R. Mixed-domain edge-aware image manipulation. IEEE Transactions on Image Processing Vol. 22, No. 5, 1915–1925, 2013.MathSciNetCrossRefGoogle Scholar
  29. [29]
    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.CrossRefGoogle Scholar
  30. [30]
    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.CrossRefGoogle Scholar
  31. [31]
    Kyprianidis, J. E.; Kang, H. Image and video abstraction by coherence-enhancing filtering. Computer Graphics Forum Vol. 30, No. 2, 593–602, 2011.CrossRefGoogle Scholar
  32. [32]
    Botsch, M.; Sorkine, O. On linear variational surface deformation methods. IEEE Transactions on Visualization and Computer Graphics Vol. 14, No. 1, 213–230, 2008.CrossRefGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Hui Wang
    • 1
  • Junjie Cao
    • 2
  • Xiuping Liu
    • 2
    Email author
  • Jianmin Wang
    • 1
  • Tongrang Fan
    • 1
  • Jianping Hu
    • 3
  1. 1.School of Information Science and TechnologyShijiazhuang Tiedao UniversityShijiazhuangChina
  2. 2.School of Mathematical SciencesDalian University of TechnologyDalianChina
  3. 3.School of SciencesNortheast Dianli UniversityJilinChina

Personalised recommendations