Skip to main content

Segment- and Arc-Based Vectorizations by Multi-scale/Irregular Tangential Covering

  • Conference paper
  • First Online:
Geometry and Vision (ISGV 2021)

Abstract

In this paper, we propose an original manner to employ a tangential cover algorithm - minDSS - in order to vectorize noisy digital contours. To do so, we exploit the representation of graphical objects by maximal primitives we have introduced in previous work. By calculating multi-scale and irregular isothetic representations of the contour, we obtained 1-D (one-dimensional) intervals, and achieved afterwards a decomposition into maximal line segments or circular arcs. By adapting minDSS to this sparse and irregular data of 1-D intervals supporting the maximal primitives, we are now able to reconstruct the input noisy objects into cyclic contours made of lines or arcs with a minimal number of primitives. We explain our novel complete pipeline in this work, and present its experimental evaluation by considering both synthetic and real image data.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    http://vision.lems.brown.edu/content/available-software-and-databases.

References

  1. Bessmeltsev, M., Solomon, J.: Vectorization of line drawings via polyvector fields. ACM Trans. Graph. 38(1), 12 p. (2019). https://doi.org/10.1145/3202661

  2. Damaschke, P.: The linear time recognition of digital arcs. Pattern Recogn. Lett. 16, 543–548 (1995)

    Article  Google Scholar 

  3. Dominici, E.A., Schertler, N., Griffin, J., Hoshyari, S., Sigal, L., Sheffer, A.: PolyFit: perception-aligned vectorization of raster clip-art via intermediate polygonal fitting. ACM Trans. Graph. (TOG) 39(4), 77-1 (2020)

    Article  Google Scholar 

  4. Egiazarian, V., et al.: Deep vectorization of technical drawings. In: Vedaldi, A., Bischof, H., Brox, T., Frahm, J.-M. (eds.) ECCV 2020. LNCS, vol. 12358, pp. 582–598. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-58601-0_35

    Chapter  Google Scholar 

  5. Faure, A., Feschet, F.: Multi-primitive analysis of digital curves. In: Wiederhold, P., Barneva, R.P. (eds.) IWCIA 2009. LNCS, vol. 5852, pp. 30–42. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10210-3_3

    Chapter  MATH  Google Scholar 

  6. Favreau, J.D., Lafarge, F., Bousseau, A.: Fidelity vs. simplicity: a global approach to line drawing vectorization. ACM Trans. Graph. 35(4), 120:1–120:10 (2016)

    Google Scholar 

  7. Feschet, F., Tougne, L.: On the min DSS problem of closed discrete curves. Discret. Appl. Math. 151(1), 138–153 (2005)

    Article  MathSciNet  Google Scholar 

  8. Kass, M., Witkin, A., Terzopoulos, D.: Snakes: active contour models. Int. J. Comput. Vision 1(4), 321–331 (1988). https://doi.org/10.1007/BF00133570

    Article  MATH  Google Scholar 

  9. Kerautret, B., Lachaud, J.: Meaningful scales detection along digital contours for unsupervised local noise estimation. IEEE Trans. Pattern Anal. Mach. Intell. 34(12), 2379–2392 (2012)

    Article  Google Scholar 

  10. Kerautret, B., Lachaud, J.: Meaningful scales detection: an unsupervised noise detection algorithm for digital contours. Image Process. On Line 4, 98–115 (2014)

    Article  Google Scholar 

  11. Kerautret, B., Ngo, P., Kenmochi, Y., Vacavant, A.: Greyscale image vectorization from geometric digital contour representations. In: Kropatsch, W.G., Artner, N.M., Janusch, I. (eds.) DGCI 2017. LNCS, vol. 10502, pp. 319–331. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66272-5_26

    Chapter  Google Scholar 

  12. Kim, B., Wang, O., Öztireli, A., Gross, M.: Semantic segmentation for line drawing vectorization using neural networks. In: Computer Graphics Forum, vol. 37, no. 2, pp. 329–338. Wiley Online Library (2018)

    Google Scholar 

  13. Lebrun, M., Colom, M., Buades, A., Morel, J.: Secrets of image denoising cuisine. Acta Numerica 21, 475–576 (2012)

    Article  MathSciNet  Google Scholar 

  14. Montanari, U.: Continuous skeletons from digitized images. J. ACM 16(4), 534–549 (1969)

    Article  Google Scholar 

  15. Nguyen, T.P., Debled-Rennesson, I.: Arc segmentation in linear time. In: Real, P., Diaz-Pernil, D., Molina-Abril, H., Berciano, A., Kropatsch, W. (eds.) CAIP 2011. LNCS, vol. 6854, pp. 84–92. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-23672-3_11

    Chapter  Google Scholar 

  16. Nguyen, T.P., Debled-Rennesson, I.: Decomposition of a curve into arcs and line segments based on dominant point detection. In: Heyden, A., Kahl, F. (eds.) SCIA 2011. LNCS, vol. 6688, pp. 794–805. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-21227-7_74

    Chapter  Google Scholar 

  17. Nguyen, T.P., Kerautret, B., Debled-Rennesson, I., Lachaud, J.-O.: Unsupervised, fast and precise recognition of digital arcs in noisy images. In: Bolc, L., Tadeusiewicz, R., Chmielewski, L.J., Wojciechowski, K. (eds.) ICCVG 2010. LNCS, vol. 6374, pp. 59–68. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15910-7_7

    Chapter  Google Scholar 

  18. Rodríguez, M., Largeteau-Skapin, G., Andres, E.: Adaptive pixel resizing for multiscale recognition and reconstruction. In: Wiederhold, P., Barneva, R.P. (eds.) IWCIA 2009. LNCS, vol. 5852, pp. 252–265. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10210-3_20

    Chapter  Google Scholar 

  19. Rosin, P., West, G.: Nonparametric segmentation of curves into various representations. IEEE Trans. Pattern Anal. Mach. Intell. 17(12), 1140–1153 (1995)

    Article  Google Scholar 

  20. Sharir, M., Welzl, E.: A combinatorial bound for linear programming and related problems. In: Finkel, A., Jantzen, M. (eds.) STACS 1992. LNCS, vol. 577, pp. 567–579. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-55210-3_213

    Chapter  Google Scholar 

  21. Vacavant, A.: Robust image processing: definition, algorithms and evaluation. Habilitation, Université Clermont Auvergne (2018)

    Google Scholar 

  22. Vacavant, A., Kerautret, B., Roussillon, T., Feschet, F.: Reconstructions of noisy digital contours with maximal primitives based on multi-scale/irregular geometric representation and generalized linear programming. In: Kropatsch, W.G., Artner, N.M., Janusch, I. (eds.) DGCI 2017. LNCS, vol. 10502, pp. 291–303. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66272-5_24

    Chapter  Google Scholar 

  23. Vacavant, A., Roussillon, T., Kerautret, B., Lachaud, J.: A combined multi-scale/irregular algorithm for the vectorization of noisy digital contours. Comput. Vis. Image Underst. 117(4), 438–450 (2013)

    Article  Google Scholar 

  24. Valdivieso, H.: Polyline defined NC trajectories parametrization. A compact analysis and solution focused on 3D printing. arXiv preprint arXiv:1808.01831 (2018)

  25. Welzl, E.: Smallest enclosing disks (balls and ellipsoids). In: Maurer, H. (ed.) New Results and New Trends in Computer Science. LNCS, vol. 555, pp. 359–370. Springer, Heidelberg (1991). https://doi.org/10.1007/BFb0038202

    Chapter  Google Scholar 

  26. Wirjadi, O.: Survey of 3D image segmentation methods. Technical report, Berichte des Fraunhofer ITWM (2007)

    Google Scholar 

  27. Xiong, X., Feng, J., Zhou, B.: Real-time contour image vectorization on GPU. In: Braz, J., et al. (eds.) VISIGRAPP 2016. CCIS, vol. 693, pp. 35–50. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-64870-5_2

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Antoine Vacavant .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Vacavant, A., Kerautret, B., Feschet, F. (2021). Segment- and Arc-Based Vectorizations by Multi-scale/Irregular Tangential Covering. In: Nguyen, M., Yan, W.Q., Ho, H. (eds) Geometry and Vision. ISGV 2021. Communications in Computer and Information Science, vol 1386. Springer, Cham. https://doi.org/10.1007/978-3-030-72073-5_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-72073-5_15

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-72072-8

  • Online ISBN: 978-3-030-72073-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics