Journal of Mathematical Imaging and Vision

, Volume 48, Issue 1, pp 53–71 | Cite as

Generation of Random Digital Simple Curves with Artistic Emulation



This paper presents two novel interdependent techniques for random digital simple curve generation. The first one is about generating a curve of finite length, producing a sequence of points defining a digital path ρ ‘on the fly’. The second is for the creation of artistic sketches from line drawings and edge maps, using multiple instances of such random digital paths. A generated digital path ρ never intersects or touches itself, and hence becomes simple and irreducible. This is ensured by detecting every possible trap formed by the previously generated part of ρ, which, if entered into, cannot be exited without touching or intersecting ρ. The algorithm is completely free of any backtracking and its time complexity is linear in the length of ρ. For artistic emulation, a curve-constrained domain is defined by the Minkowski sum of the input drawing with a structuring element whose size varies with the pencil diameter. An artist’s usual trait of making irregular strokes and sub-strokes, with varying shades while sketching, is thus captured in a realistic manner. Algorithmic solutions of non-photorealism are perceived as an enrichment of contemporary digital art. Simulation results for the presented algorithms have been furnished to demonstrate their efficiency and elegance.


Random curve Random polyomino Non-photorealism Minkowski sum Digital art 



This paper is based on work published in PSIVT 2010 [3] and CAIP 2011 [28]. The authors thank O. Pal, S. Roy, and R. Chatterjee for their contributions to those two conference papers.


  1. 1.
    Auer, T., Held, M.: Heuristics for the generation of random polygons. In: Proc. 8th Canad. Conf. Comput. Geom, pp. 38–44 (1996) Google Scholar
  2. 2.
    Bhowmick, P., Bhattacharya, B.B.: Fast polygonal approximation of digital curves using relaxed straightness properties. IEEE Trans. Pattern Anal. Mach. Intell. 29(9), 1590–1602 (2007) CrossRefGoogle Scholar
  3. 3.
    Bhowmick, P., Pal, O., Klette, R.: A linear-time algorithm for generation of random digital curves. In: IEEE Proc. PSIVT, pp. 168–173 (2010) Google Scholar
  4. 4.
    Canny, J.: A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. 8(6), 679–698 (1986) CrossRefGoogle Scholar
  5. 5.
    Curtis, C.J., Anderson, S.E., Seims, J.E., Fleischer, K.W., Salesin, D.H.: Computer-generated watercolor. In: Proc. SIGGRAPH, pp. 421–430 (1997) CrossRefGoogle Scholar
  6. 6.
    Debled-Rennesson, I., Jean-Luc, R., Rouyer-Degli, J.: Segmentation of discrete curves into fuzzy segments. In: Proc. IWCIA. Electronic Notes in Discrete Mathematics, vol. 12, pp. 372–383 (2003) Google Scholar
  7. 7.
    Debled-Rennesson, I., Reveilles, J.P.: A linear algorithm for segmentation of digital curves. Int. J. Pattern Recognit. Artif. Intell. 9, 635–662 (1995) CrossRefGoogle Scholar
  8. 8.
    Deussen, O.: Oliver’s artistic attempts (random line). (2010)
  9. 9.
    Einstein, A.: Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Ann. Phys. 322(8), 549–560 (1905) CrossRefGoogle Scholar
  10. 10.
    Einstein, A.: In: Investigations on the Theory of Brownian Movement. Dover Publications, New York (reprinted in 1926) Google Scholar
  11. 11.
    Epstein, P., Sack, J.-R.: Generating triangulations at random. ACM Trans. Model. Comput. Simul. 4(3), 267–278 (1994) CrossRefMATHGoogle Scholar
  12. 12.
    Finch, S.: Pòlya’s random walk constant. In: Mathematical Constants, pp. 322–333. Cambridge University Press, Cambridge (2003). Section 5,9 Google Scholar
  13. 13.
    Gooch, B., Gooch, A.: Non-photorealistic Rendering. A.K. Peters Ltd., New York (2001) MATHGoogle Scholar
  14. 14.
    Kang, H.W., Chui, C.K., Chakraborty, U.K.: A unified scheme for adaptive stroke-based rendering. Vis. Comput. 22(9), 814–824 (2006) CrossRefGoogle Scholar
  15. 15.
    Kang, H.W., He, W., Chui, C.K., Chakraborty, U.K.: Interactive sketch generation. Vis. Comput. 21(8), 821–830 (2005) CrossRefGoogle Scholar
  16. 16.
    Klette, R., Rosenfeld, A.: Digital geometry: geometric methods for digital picture analysis. In: Morgan Kaufmann Series in Computer Graphics and Geometric Modeling. Morgan Kaufmann, San Francisco (2004) Google Scholar
  17. 17.
    Kopf, J., Neubert, B., Chen, B., Cohen, M., Cohen-Or, D., Deussen, O., Uyttendaele, M., Lischinski, D.: Deep photo: model-based photograph enhancement and viewing. In: Proc. SIGGRAPH Asia, pp. 1–10 (2008) Google Scholar
  18. 18.
    Lake, A., Marshall, C., Harris, M., Blackstein, M.: Stylized rendering techniques for scalable real-time 3d animation. In: ACM Proc. NPAR, pp. 13–20 (2000) Google Scholar
  19. 19.
    Majumder, A., Gopi, M.: Hardware accelerated real time charcoal rendering. In: ACM Proc. NPAR, pp. 59–66 (2002) Google Scholar
  20. 20.
    Mieghem, J.A.V., Avi-Itzhak, H.I., Melen, R.D.: Straight line extraction using iterative total least squares methods. J. Vis. Commun. Image Represent. 6, 59–68 (1995) CrossRefGoogle Scholar
  21. 21.
    Mould, D.: A stained glass image filter. In: Proc. EGRW, pp. 20–25 (2003) Google Scholar
  22. 22.
    Olsen, L., Samavati, F.F., Sousa, M.C., Jorge, J.A.: Sketch-based modeling: a survey. Comput. Graph. 33(1), 85–103 (2009) CrossRefGoogle Scholar
  23. 23.
    Pòlya, G.: Über eine Aufgabe der Wahrscheinlichkeitsrechnung betreffend die Irrfahrt im Strassennetz. Math. Ann. 84(1–2), 149–160 (1921) CrossRefMATHMathSciNetGoogle Scholar
  24. 24.
    Pusch, R., Samavati, F., Nasri, A., Wyvill, B.: Improving the sketch-based interface: forming curves from many small strokes. Vis. Comput. 23(9), 955–962 (2007) CrossRefGoogle Scholar
  25. 25.
    Rosenfeld, A., Kak, A.C.: Digital Picture Processing, 2nd edn. Academic Press, New York (1982) Google Scholar
  26. 26.
    Rosenfeld, A., Klette, R.: Digital straightness. Electronic Notes in Theoretical Computer Sc. vol. 46 (2001). Google Scholar
  27. 27.
    Rourke, J., Virmani, M.: Generating random polygons. TR 011, CS Dept., Smith College, Northampton, MA 01063 (1991) Google Scholar
  28. 28.
    Roy, S., Chatterjee, R., Bhowmick, P., Klette, R.: MAESTRO: making art-enabled sketches through randomized operations. In: Proc. CAIP, pp. 318–326 (2011) Google Scholar
  29. 29.
    Rudolf, D., Mould, D., Neufeld, E.: Simulating wax crayons. In: IEEE Proc. Pacific Conf. Computer Graphics Applications, pp. 163–172 (2003) Google Scholar
  30. 30.
    Smeulders, A.W.M., Dorst, L.: Decomposition of discrete curves into piecewise segments in linear time. Contemp. Math. 119, 169–195 (1991) CrossRefMathSciNetGoogle Scholar
  31. 31.
    Velho, L., Gomes, J.d.M.: Digital halftoning with space filling curves. SIGGRAPH Comput. Graph. 25(4), 81–90 (1991) CrossRefGoogle Scholar
  32. 32.
    Verevka, O., Buchanan, J.W.: Halftoning with image-based dither screens. In: Proc. Conf. Graphics Interface, pp. 167–174 (1999) Google Scholar
  33. 33.
    Zhu, C., Sundaram, G., Snoeyink, J., Mitchell, J.S.B.: Generating random polygons with given vertices. Comput. Geom. 6(5), 277–290 (1996) CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringIndian Institute of TechnologyKharagpurIndia
  2. 2.Computer Science DepartmentThe University of AucklandAucklandNew Zealand

Personalised recommendations