“Modeling and visualization of leaf venation patterns” by Runions, Fuhrer, Lane, Federl, Rolland-Lagan, et al. …

  • ©Adam Runions, Martin Fuhrer, Brendan Lane, Pavol Federl, Anne-Gaëlle Rolland-Lagan, and Przemyslaw Prusinkiewicz

Conference:


Type(s):


Title:

    Modeling and visualization of leaf venation patterns

Presenter(s)/Author(s):



Abstract:


    We introduce a class of biologically-motivated algorithms for generating leaf venation patterns. These algorithms simulate the interplay between three processes: (1) development of veins towards hormone (auxin) sources embedded in the leaf blade; (2) modification of the hormone source distribution by the proximity of veins; and (3) modification of both the vein pattern and source distribution by leaf growth. These processes are formulated in terms of iterative geometric operations on sets of points that represent vein nodes and auxin sources. In addition, a vein connection graph is maintained to determine vein widths. The effective implementation of the algorithms relies on the use of space subdivision (Voronoi diagrams) and time coherence between iteration steps. Depending on the specification details and parameters used, the algorithms can simulate many types of venation patterns, both open (tree-like) and closed (with loops). Applications of the presented algorithms include texture and detailed structure generation for image synthesis purposes, and modeling of morphogenetic processes in support of biological research.

References:


    1. Aloni, R., Schwalm, K., Langhans, M., and Ullrich, C. 2003. Gradual shifts in sites of free auxin-production during leaf-primordium development and their role in vascular differentiation and leaf morphogenesis in Arabidopsis. Planta 216, 841–853.Google ScholarCross Ref
    2. Andrade, D., and De Figueiredo, L. 2001. Good approximations for the relative neighbourhood graph. In Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG’01), 25–28.Google Scholar
    3. Baranoski, G., and Rokne, J., 2002. Light interaction with plants. SIGGRAPH 2002 Course Notes 26.Google Scholar
    4. Bentley, J. L., Weide, B. W., and Yao, A. C. 1980. Optimal expected-time algorithms for closest point problems. ACM Transactions on Mathematical Software 5, 4, 563–580. Google ScholarDigital Library
    5. Bloomenthal, J. 1995. Skeletal design of natural forms. PhD thesis, University of Calgary, Calgary, Alberta. Google ScholarDigital Library
    6. Bohn, S., Andreotti, B., Douady, S., Munzinger, J., and Couder, Y. 2002. Constitutive property of the local organization of leaf venation networks. Physical Review E 65.Google Scholar
    7. Bowyer, A. 1981. Computing Dirichlet tessellations. The Computer Journal 24, 2, 162–166.Google ScholarCross Ref
    8. Coen, E., Rolland-Lagan, A.-G., Matthews, M., Bangham, J. A., and Prusinkiewicz, P. 2004. The genetics of geometry. Proceedings of the National Academy of Sciences 101, 14, 4728–4735.Google ScholarCross Ref
    9. Cook, R. L. 1986. Stochastic sampling in computer graphics. ACM Transaction on Graphics 5, 1, 225–240. Google ScholarDigital Library
    10. Couder, Y., Pauchard, L., Allain, C., Adda-Bedia, M., and Douady, S. 2002. The leaf venation as formed in a tensorial field. European Physical Journal B 28, 135–138.Google ScholarCross Ref
    11. Dengler, N., and Kang, J. 2001. Vascular patterning and leaf shape. Current Opinion in Plant Biology 4, 1, 50–56.Google ScholarCross Ref
    12. Desbenoit, B., Galin, E., and Akkouche, S. 2004. Simulating and modeling lichen growth. Computer Graphics Forum 23, 3, 341–350.Google ScholarCross Ref
    13. Donner, C., and Wann Jensen, H. 2005. Light diffusion in multilayered transluscent materials. This volume. Google ScholarDigital Library
    14. Federl. P., and Prusinkiewicz. P. 2004. Finite element model of fracture formation on growing surfaces. In Proceedings of the International Conference on Computational Science 2004, Springer, vol. 3037 of Lecture Notes in Computer Science, 138–145.Google ScholarCross Ref
    15. Fowler. D. R., Meinhardt, H., and Prusinkiewicz, P. 1992. Modeling seashells. In Computer Graphics, vol. 26. 379–387. (Proceedings of SIGGRAPH 1992). Google ScholarDigital Library
    16. Gomes. J., Darsa, L., Costa, B., and Velho, L. 1999. Warping and morphing of graphical objects. Morgan Kaufmann, San Francisco. Google ScholarDigital Library
    17. Gottlieb, M. E. 1993. Angiogenesis and vascular networks: complex anatomies from deterministic non-linear physiologies. In Growth patterns in physical sciences and biology, J. M. Garcia-Ruiz, E. Louis, P. Meakin, and L. M. Sander, Eds. Plenum Press, New York, 267–276.Google Scholar
    18. Hanrahan, P., and Krueger, W. 1993. Reflection from layered surfaces due to subsurface scattering. In Proceedings of SIGGRAPH 1993, 165–174. Google ScholarDigital Library
    19. Hejnowicz, Z., and Romberger, J. 1984. Growth tensor of plant organs. Journal of Theoretical Biology 110, 93–114.Google ScholarCross Ref
    20. Hickey, L. 1979. A revised classification of the architecture of dicotyledonous leaves. In Anatomy of the dicotyledons. Second Edition, Vol. 1, C. R. Metcalfe and L. Chalk, Eds. Clarendon Press, Oxford, 25–39.Google Scholar
    21. Jaromczyk, J. W., and Toussaint, G. T. 1992. Relative neighborhood graphs and their relatives. Proceedings of the IEEE 80, 9, 1502–1517.Google ScholarCross Ref
    22. Judd, W. W., Campbell, C. S., Kellogg, E. A., and Stevens, P. F. 1999. Plant systematics: A phylogenetic approach. Sinauer Associates, Sunderland, MA.Google Scholar
    23. Lefebvre, S., and Neyret, F. 2002. Synthesizing bark. In Proceedings of the 13th Eurographics Workshop on Rendering, 105–116. Google ScholarDigital Library
    24. MacDonald, N. 1983. Trees and networks in biological models. J. Wiley & Sons, New York.Google Scholar
    25. Meinhardt, H. 1976. Morphogenesis of lines and nets. Differentiation 6, 117–123.Google ScholarCross Ref
    26. Mitchell, D. 1987. Generating antialiased images at low sampling densities. In Computer Graphics, vol. 21, 65–78. (Proceedings of SIGGRAPH 1987). Google ScholarDigital Library
    27. Mitchison, G. J. 1980. A model for vein formation in higher plants. Proc. R. Soc. London B 207, 79–109.Google ScholarCross Ref
    28. Murray, C. D. 1926. The physiological principle of minimum work. Proceedings of the National Academy of Sciences 12, 207–214.Google ScholarCross Ref
    29. Okabe, A., Boots, B., and Sugihara, K. 1992. Spatial tesselations: Concepts and applications of Voronoi diagrams. J. Wiley and Sons, Chichester. Google ScholarDigital Library
    30. Popinet, S., 2004. The GNU triangulated surface library. http://gts.sourceforge.net.Google Scholar
    31. Preparata, F., and Shamos, M. 1985. Computational geometry: An introduction. Springer, New York. Google ScholarDigital Library
    32. Prusinkiewicz, P., Hammel, M., and Mjolsness, E. 1993. Animation of plant development. In Proceedings of SIGGRAPH 1993, 351–360. Google ScholarDigital Library
    33. Prusinkiewicz, P. 1994. Visual models of morphogenesis. Artificial Life 1, 1/2, 61–74. Google ScholarDigital Library
    34. Prusinkiewicz, P. 1998. In search of the right abstraction: the synergy between art, science, and information technology in the modeling of natural phenomena. In Art @ Science, C. Sommerer and L. Mignonneau, Eds. Springer, Wien, 60–68.Google Scholar
    35. Roberts, J. 2001. Sticky pixels: Evolutionary growth by random drop ballistic aggregation. In Eurographics UK 2001 Conference Proceedings, 149–155.Google Scholar
    36. Rodkaew, Y., Siripant, S., Lursinsap, C., and Chongstitvatana, P. 2002. An algorithm for generating vein images for realistic modeling of a leaf. In Prodeedings of the International Conference on Computational Mathematics and Modeling, 9 pp.Google Scholar
    37. Rolland, A.-G., Bangham, J. A., and Coen, E. 2003. Growth dynamics underlying petal shape and asymmetry. Nature 422, 161–163.Google ScholarCross Ref
    38. Rolland-Lagan, A.-G., Federl, P., and Prusinkiewicz, P. 2004. Reviewing models of auxin canalisation in the context of vein pattern formation in Arabidopsis leaves. In Proceedings of the 4th International Workshop on Functional-Structural Plant Models, 376–381.Google Scholar
    39. Roth-Nebelsick, A., Uhl, D., Mosbugger, V., and Kerp, H. 2001. Evolution and function of leaf venation architecture: a review. Annals of Botany 87, 553–566.Google ScholarCross Ref
    40. Sachs, T. 1981. The control of patterned differentation of vascular tissues. In Advances in botanical research, H. W. Woolhouse, Ed., vol. 6. Academic Press, London, 152–262.Google Scholar
    41. Sachs, T. 2003. Collective specification of cellular development. BioEssays 25.9, 897–903.Google ScholarCross Ref
    42. Scarpella, E., Francis, P., and Berleth, T. 2004. Stage-specific markers define early steps of procambium development in Arabidopsis leaves and correlate termination of vein formation with mesophyll differentiation. Development 131, 3445–3455.Google ScholarCross Ref
    43. Scholten, H., and Lindenmayer, A. 1981. A mathematical model for the laminar development of simple leaves. In Morphologie-Anatomie und Systematic der Pflanzen 5, W. van Cotthem, Ed. Waegeman, Ninove, Belgium, 29–37.Google Scholar
    44. Sieburth, L. E. 1999. Auxin is required for leaf vein pattern in Arabidopsis. Plant Physiology 121, 1179–1190.Google ScholarCross Ref
    45. Smith, C., Prusinkiewicz, P., and Samavati, F. 2003. Relational specification of surface subdivision algorithms. In Proceedings of AGTIVE 2003, vol. 3062 of Lecture Notes in Computer Science, 313–327.Google Scholar
    46. Toussaint, G. T. 1980. The relative neighborhood graph of a finite planar set. Pattern Recognition 12, 261–268.Google ScholarCross Ref
    47. Turk, G. 1991. Generating textures on arbitrary surfaces using reaction-diffusion. Computer Graphics 25, 4, 289–298. (Proceedings of SIGGRAPH 1991). Google ScholarDigital Library
    48. Urquhart, R. B. 1980. Algorithms for computation of relative neighbourhood graph. Electronics Letters 16, 14, 556–557.Google ScholarCross Ref
    49. Walter, M., Fournier, A., and Reimers, M. 1998. Clonal mosaic model for the synthesis of mammalian coat patterns. In Proceedings of Graphics Interface ’98, 82–91.Google Scholar
    50. Wang, I., Wan, J., and Baranoski, G. 2004. Physically-based simulation of plant leaf growth. Computer Animation and Virtual Worlds 15, 3–4, 237–244. Google ScholarDigital Library
    51. Wang, L., Wang, W., Dorsey, J., Yang, X., Guo, B., and Shum, H.-Y. 2005. Real-time rendering of plant leaves. This volume. Google ScholarDigital Library
    52. Watson, D. F. 1981. Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes. The Computer Journal 24, 2, 167–172.Google ScholarCross Ref


ACM Digital Library Publication:



Overview Page: