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Generation of Random Digital Simple Curves with Artistic Emulation

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Abstract

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.

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Notes

  1. A free path from a cell c i to a cell c i+k , k>1, is given by a sequence of cells, ρ(c i ,c i+k )=〈c i ,c i+1,…,c i+k 〉, such that each cell in 〈c i+1,…,c i+k−1〉 is free and distinct, and every two consecutive cells in ρ(c i ,c i+k ) are 1-adjacent.

  2. As mentioned in Sect. 2, the directional label δ(c) provides only an interim value, since δ(c) may be updated when ρ visits some other cell(s) in A 0(c) later on.

  3. For example, in Fig. 4(b), for \(c_{i+2}=c^{(2)}_{i+1}\), E i+1 is a hole; for \(c_{i+2}=c^{(4)}_{i+1}\) or \(c^{(6)}_{i+1}\), E i+1 is an ensuing hole as \(\delta(c^{(2)}_{i+1})\) changes from L to B.

  4. If p i happens to be a grid point, then we shift it to the left/right/top/bottom of its actual position by one pixel so that it is strictly an edge-point.

References

  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. 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)

    Article  Google Scholar 

  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. Canny, J.: A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. 8(6), 679–698 (1986)

    Article  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. Debled-Rennesson, I., Reveilles, J.P.: A linear algorithm for segmentation of digital curves. Int. J. Pattern Recognit. Artif. Intell. 9, 635–662 (1995)

    Article  Google Scholar 

  8. Deussen, O.: Oliver’s artistic attempts (random line). graphics.uni-konstanz.de/artlike (2010)

  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)

    Article  Google Scholar 

  10. Einstein, A.: In: Investigations on the Theory of Brownian Movement. Dover Publications, New York (reprinted in 1926)

    Google Scholar 

  11. Epstein, P., Sack, J.-R.: Generating triangulations at random. ACM Trans. Model. Comput. Simul. 4(3), 267–278 (1994)

    Article  MATH  Google Scholar 

  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. Gooch, B., Gooch, A.: Non-photorealistic Rendering. A.K. Peters Ltd., New York (2001)

    MATH  Google Scholar 

  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)

    Article  Google Scholar 

  15. Kang, H.W., He, W., Chui, C.K., Chakraborty, U.K.: Interactive sketch generation. Vis. Comput. 21(8), 821–830 (2005)

    Article  Google Scholar 

  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. 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. 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. Majumder, A., Gopi, M.: Hardware accelerated real time charcoal rendering. In: ACM Proc. NPAR, pp. 59–66 (2002)

    Google Scholar 

  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)

    Article  Google Scholar 

  21. Mould, D.: A stained glass image filter. In: Proc. EGRW, pp. 20–25 (2003)

    Google Scholar 

  22. Olsen, L., Samavati, F.F., Sousa, M.C., Jorge, J.A.: Sketch-based modeling: a survey. Comput. Graph. 33(1), 85–103 (2009)

    Article  Google Scholar 

  23. Pòlya, G.: Über eine Aufgabe der Wahrscheinlichkeitsrechnung betreffend die Irrfahrt im Strassennetz. Math. Ann. 84(1–2), 149–160 (1921)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  25. Rosenfeld, A., Kak, A.C.: Digital Picture Processing, 2nd edn. Academic Press, New York (1982)

    Google Scholar 

  26. Rosenfeld, A., Klette, R.: Digital straightness. Electronic Notes in Theoretical Computer Sc. vol. 46 (2001). www.elsevier.nl/locate/entcs/volume46.html

    Google Scholar 

  27. Rourke, J., Virmani, M.: Generating random polygons. TR 011, CS Dept., Smith College, Northampton, MA 01063 (1991)

  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. Rudolf, D., Mould, D., Neufeld, E.: Simulating wax crayons. In: IEEE Proc. Pacific Conf. Computer Graphics Applications, pp. 163–172 (2003)

    Google Scholar 

  30. Smeulders, A.W.M., Dorst, L.: Decomposition of discrete curves into piecewise segments in linear time. Contemp. Math. 119, 169–195 (1991)

    Article  MathSciNet  Google Scholar 

  31. Velho, L., Gomes, J.d.M.: Digital halftoning with space filling curves. SIGGRAPH Comput. Graph. 25(4), 81–90 (1991)

    Article  Google Scholar 

  32. Verevka, O., Buchanan, J.W.: Halftoning with image-based dither screens. In: Proc. Conf. Graphics Interface, pp. 167–174 (1999)

    Google Scholar 

  33. Zhu, C., Sundaram, G., Snoeyink, J., Mitchell, J.S.B.: Generating random polygons with given vertices. Comput. Geom. 6(5), 277–290 (1996)

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgements

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.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology, Kharagpur, India

    Partha Bhowmick

  2. Computer Science Department, The University of Auckland, Auckland, New Zealand

    Reinhard Klette

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  1. Partha Bhowmick
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  2. Reinhard Klette
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Correspondence to Partha Bhowmick.

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Bhowmick, P., Klette, R. Generation of Random Digital Simple Curves with Artistic Emulation. J Math Imaging Vis 48, 53–71 (2014). https://doi.org/10.1007/s10851-012-0388-1

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