Sketch simplification guided by complex agglomeration

  • Yue Liu
  • Xuemei LiEmail author
  • Pengbo Bo
  • Xifeng Gao
Research Paper


We propose a novel method for vector sketch simplification based on the simplification of the geometric structure that is extracted from the input vector graph, which can be referred to as a base complex. Unlike the sets of strokes, which are treated in the existing approaches, a base complex is considered to be a collection of various geometric primitives. Guided by the shape similarity metrics that are defined for the base complex, an agglomeration procedure is proposed to simplify the base complex by iteratively merging a pair of geometric primitives that exhibit the minimum cost into a new one. This simplified base complex is finally converted into a simplified vector graph. Our algorithm is computationally efficient and is able to retain a large amount of useful shape information from the original vector graph, thereby achieving a tradeoff between efficiency and geometric fidelity. Furthermore, the level of simplification of the input vector graph can be easily controlled using a single threshold in our method. We make comparisons with some existing methods using the datasets that have been provided in the corresponding studies as well as using different styles of sketches drawn by artists. Thus, our experiments demonstrate the computational efficiency of our method and its capability for producing the desirable results.


sketch simplification base complex iterative merging 



This work was partly supported by National Natural Science Foundation of China (Grant Nos. 61572292, 6160227, 61672187), NSFC Joint Fund with Guangdong (Grant No. U1609218), and Shandong Provincial Key Research and Development Project (Grant No. 2018GGX103038).


  1. 1.
    Barla P, Thollot J, Sillion F X. Geometric clustering for line drawing simplification. In: Proceedings of the 16th Eurographics Conference on Rendering Techniques, 2005. 183–3Google Scholar
  2. 2.
    Liu X, Wong T T, Heng P A. Closure-aware sketch simplification. ACM Trans Graph, 2015, 34: 1–10Google Scholar
  3. 3.
    Shesh A, Chen B Q. Efficient and dynamic simplification of line drawings. Comput Graph Forum, 2008, 27: 537–545CrossRefGoogle Scholar
  4. 4.
    Grabli S, Durand F, Sillion F X. Density measure for line-drawing simplification. In: Proceedings of the 12th Pacific Conference on Computer Graphics and Applications, 2004. 309–3Google Scholar
  5. 5.
    Pusch R, Samavati F, Nasri A, et al. Improving the sketch-based interface. Visual Comput, 2007, 23: 955–962CrossRefGoogle Scholar
  6. 6.
    Orbay G, Kara L B. Beautification of design sketches using trainable stroke clustering and curve fitting. IEEE Trans Visual Comput Graph, 2011, 17: 694–708CrossRefGoogle Scholar
  7. 7.
    Ogawa T, Matsui Y, Yamasaki T, et al. Sketch simplification by classifying strokes. In: Proceedings of the International Conference on Pattern Recognition, 2016. 1065–3Google Scholar
  8. 8.
    Simo-Serra E, Iizuka S, Sasaki K, et al. Learning to simplify: fully convolutional networks for rough sketch cleanup. ACM Trans Graph, 2016, 35: 1–11CrossRefGoogle Scholar
  9. 9.
    Bartolo A, Camilleri K P, Fabri S G, et al. Scribbles to vectors: preparation of scribble drawings for CAD interpretation. In: Proceedings of the 4th Eurographics Workshop on Sketch-Based Interfaces and Modeling, 2007. 123–3Google Scholar
  10. 10.
    Favreau J D, Lafarge F, Bousseau A. Fidelity vs. simplicity: a global approach to line drawing vectorization. ACM Trans Graph, 2016, 35: 1–10CrossRefGoogle Scholar
  11. 11.
    Parakkat A D, Pundarikaksha U B, Muthuganapathy R. A Delaunay triangulation based approach for cleaning rough sketches. Comput Graph, 2018, 74: 171–181CrossRefGoogle Scholar
  12. 12.
    Zou J J, Yan H. Cartoon image vectorization based on shape subdivision. In: Proceedings of the International Computer Graphics, 2001. 225–3Google Scholar
  13. 13.
    Bo P B, Luo G N, Wang K Q. A graph-based method for fitting planar B-spline curves with intersections. J Comput Des Eng, 2016, 3: 14–23Google Scholar
  14. 14.
    Wang Y T, Wang L Y, Deng Z G, et al. Sketch-based shape-preserving tree animations. In: Proceedings of the Computer Animation and Social Agents, 2018Google Scholar
  15. 15.
    Guo X K, Lin J C, Xu K, et al. CustomCut: on-demand extraction of customized 3D parts with 2D sketches. In: Proceeding of the Eurographics Symposium on Geometry Processing, 2016Google Scholar
  16. 16.
    Shesh A, Chen B. Smartpaper: an interactive and user friendly sketching system. In: Proceedings of the Computer Graphics Forum, 2004Google Scholar
  17. 17.
    Ku D C, Qin S F, Wright D K. Interpretation of overtracing freehand sketching for geometric shapes. In: Proceedings of the Computer Graphics, Visualization and Computer Vision, 2006. 263–3Google Scholar
  18. 18.
    Schmidt R, Wyvill B, Sousa M C, et al. Shapeshop: sketch-based solid modeling with blobtrees. In: Proceedings of the ACM SIGGRAPH, San Diego, 2007Google Scholar
  19. 19.
    Bae S H, Balakrishnan R, Singh K. ILoveSketch: as-natural-as-possible sketching system for creating 3D curve models. In: Proceedings of the ACM Symposium on User Interface Software and Technology, 2008. 151–3Google Scholar
  20. 20.
    Grimm C, Joshi P. Just DrawIt: a 3D sketching system. In: Proceedings of the International Symposium on Sketch-Based Interfaces and Modeling, 2012. 121–3Google Scholar
  21. 21.
    Schroeder W J, Zarge J A, Lorensen W E. Decimation of triangle meshes. In: Proceedings of the 19th Annual Conference on Computer Graphics and Interactive Techniques, 1992. 65–3Google Scholar
  22. 22.
    Hoppe H, DeRose T, Duchamp T, et al. Mesh optimization. In: Proceedings of the 20th Annual Conference on Computer Graphics and Interactive Techniques, 1993. 19–3Google Scholar
  23. 23.
    Guéziec A. Surface simplification with variable tolerance. In: Proceedings of the 2nd International Symposium on Medical Robotics and Computer Assisted Surgery, 1995. 132–3Google Scholar
  24. 24.
    Garland M, Heckbert P S. Surface simplification using quadric error metrics. In: Proceedings of the 24th International Conference on Computer Graphics and Interactive Techniques, 1997. 209–3Google Scholar
  25. 25.
    Cohen J, Manocha D, Olano M. Simplifying polygonal models using successive mappings. In: Proceedings of the Conference on Visualization, 1997. 395–3Google Scholar
  26. 26.
    Kobbelt L, Campagna S, Seidel H P. A general framework for mesh decimation. In: Proceedings of the Graphics Interface Conference, 1998. 43–3Google Scholar
  27. 27.
    Hoppe H. View-dependent refinement of progressive meshes. In: Proceedings of the 24th International Conference on Computer Graphics and Interactive Techniques, 1997. 189–3Google Scholar
  28. 28.
    Tarini M, Puppo E, Panozzo D, et al. Simple quad domains for field aligned mesh parametrization. ACM Trans Graph, 2011, 30: 1CrossRefGoogle Scholar
  29. 29.
    Gao X F, Deng Z G, Chen G N. Hexahedral mesh re-parameterization from aligned base-complex. ACM Trans Graph, 2015, 34: 142:1–142:10CrossRefzbMATHGoogle Scholar
  30. 30.
    Noris G, Hornung A, Sumner R W, et al. Topology-driven vectorization of clean line drawings. ACM Trans Graph, 2013, 32: 1–11CrossRefzbMATHGoogle Scholar
  31. 31.
    Kauppinen H, Seppanen T, Pietikainen M. An experimental comparison of autoregressive and Fourier-based descriptors in 2D shape classification. IEEE Trans Pattern Anal Mach Intell, 1995, 17: 201–207CrossRefGoogle Scholar
  32. 32.
    Loncaric S. A survey of shape analysis techniques. Pattern Recogn, 1998, 31: 983–1001CrossRefGoogle Scholar
  33. 33.
    Zhang D S, Lu G J. A comparative study on shape retrieval using Fourier descriptors with different shape signatures. In: Proceedings of Asian Conference on Computer Vision, 2002Google Scholar
  34. 34.
    Zhang D S, Lu G J. Study and evaluation of different Fourier methods for image retrieval. Image Vision Comput, 2005, 23: 33–49CrossRefGoogle Scholar
  35. 35.
    Glassner A. Graphics Gems. Orlando: Academic Press, 1990zbMATHGoogle Scholar
  36. 36.
    El-ghazal A, Basir O, Belkasim S. Farthest point distance: a new shape signature for Fourier descriptors. Signal Process-Image Commun, 2009, 24: 572–586CrossRefGoogle Scholar
  37. 37.
    Durand F. Where do people draw lines?: technical perspective. Commun ACM, 2012, 55: 106CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Computer Science and TechnologyShandong UniversityJinanChina
  2. 2.School of SoftwareShandong UniversityJinanChina
  3. 3.School of Computer Science and TechnologyHarbin Institute of TechnologyWeihaiChina
  4. 4.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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