Abstract
In this paper, we present a two-level statistical model for characterizing the stochastic and specific nature of trees. At the low level, we define plantons, which are a group of similar organs, to depict tree organ details statistically. At the high level, a set of transitions between plantons is provided to describe the stochastic distribution of organs.
Based on such a tree model, we propose a novel tree modeling approach, synthesizing trees by plantons, which are extracted from tree samples. All tree samples are captured from the real world. We have designed a maximum likelihood estimation algorithm to acquire the two-level statistical tree model from single samples or multi- samples. Experimental results show that our new model is capable of synthesizing new trees with similar, yet visually different shapes.
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Aono, M., Kunii, T.L.: Botanical tree image generation. IEEE Comput. Graph. Applic. 4(5), 10–34 (1984)
Boudon, F., Prusinkiewicz, P., Federl, P., Godin, C., Karwowski, R.: Interactive design of bonsai tree models. Comput. Graph. Forum 22(3), 591–599 (2003)
Dempster, N.M., Laird, A.P., Rubind, B.: Maximum likelihood from incomplete data via the EM algorithm. J. R. Statist. Soc. B 39, 185–197 (1977)
Drake, A.W.: Observation of a Markov process through a noisy channel. PhD thesis, Massachusetts Institute of Technology (1962)
Durand, J.B., Guédon, Y., Caraglio, Y.: Analysis of the plant architecture via tree-structured statistical models: the hidden Markov trees. In: Proceedings of the Fourth International Workshop on Functional-Structural Plant Models, pp. 61–64, Montpellier, France (2004)
Efros, A. A., Freeman, W. T.: Image quilting for texture synthesis and transfer. In: Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, pp. 341–346 (2001)
Fournier, A., Fussel, D., Carpenter, L.: Computer rendering of stochastic models. Communic. ACM 25(6), 371–384 (1982)
Fournier, A., Grindal, D.A.: The stochastic modeling of trees. In: Proceedings of Graphics Interface’86, pp. 164–172 (1986)
Galbraith, C., Muendermann, L., Wyvill, B.: Implicit visualization and inverse modeling of growing trees. Comput. Graph. Forum 23(3), 351–360 (2004)
Galbraith, C., Muendermann, L., Wyvill, B.: Blob Tree Trees. Proceedings of Computer Graphics International Conference, CGI, pp. 78–85, 2004.
Greene, N.: Voxel space automata: modeling with stochastic growth processes in voxel space. (In: Proceedings of Siggraph 89) Comput. Graph. 23(4), 175–184 (1989)
Guédon, Y., Barthélémy, D., Caraglio, Y., Costes E.: Pattern analysis in branching and axillary flowering sequences. J. Theoret. Biol. 212, 481–520 (2001)
Holton, M.: Strands, gravity, and botanical tree imagery. Comput. Graph. Forum 13(1), 57–67 (1994)
Honda, H.: Description of the form of trees by the parameters of the tree-like body: effects of the branching angle and the branch length on the shape of the tree-like body. J. Theoret. Biol. 31, 331–338 (1971)
Julesz, B.: Textons, the elements of texture perception and their interactions. Nature 290, 91–97 (1981)
Li, Y., Wang, T., Shum, H.: Motion texture: a two-level statistical model for character motion synthesis. ACM Trans. Graph. 21(3), 465–472 (2002)
Liang, L., Liu, C., Xu, Y., Guo, B., SHUM, H.: Real-time texture synthesis by patch-based sampling. ACM Trans. Graph. 20(3), 127–150 (2001)
Lintermann, B., Deussen, O.: Interactive modeling of plants. IEEE Comput. Graph. Applic. 19(1), 56–65 (1999)
Lindenmayer, A.: Mathematical models for cellular interaction in development. Parts I and II. J. Theoret. Biol. 18, 280–315 (1968)
Loop, C.: Smooth subdivision surfaces based on triangles. Master’s thesis, University of Utah, Department of Mathematics (1987)
Mandelbrot, B.B.: The Fractal Geometry of Nature. Freeman and Co., San Francisco, CA (1982)
Mortensen, E.N., Barret, W.A.: Intelligent scissors for image composition. In: SIGGRAPH’1995, pp. 191–199 (1995)
Oppenheimer, P.E.: Real-time design and animation of fractal plants and trees. (SIGGRAPH 86 Conference Proceedings) Comput. Graph. 20, 55–64 (1986)
Prusinkiewicz, P., Hammel, M., Mjolsness, E.: Animation of plant development. In: SIGGRAPH 93 Conference Proceedings, pp. 351–360, August (1993)
Prusinkiewicz, P., James, M., Mech, R.: Synthetic topiary. In: Proceedings of SIGGRAPH, pp. 351–358. ACM SIGGRAPH, New York (1994)
Prusinkiewicz, P., Lindenmayer, A.: The Algorithmic Beauty of Plants. Springer, Berlin Heidelberg New York (1996)
Prusinkiewicz, P., Mundermann, L., Karwowski, R., Lane, B.: The use of positional information in the modeling of plants. In: Proceeding of SIGGRAPH 2001, pp. 289–300 (2001)
Rabiner, L.: A tutorial on hidden Markov models and selected applications in speech recognition. Proc. IEEE 77(2), 257–285 (1989)
Reche, A., Martin, I., Drettakis, G.: Volumetric reconstruction and interactive rendering of trees from photographs. (SIGGRAPH Conference Proceedings) ACM Trans. Graph. 23(3), 720–727 (2004)
Reeves, W.T.: Particle systems-a technique for modeling a class of fuzzy objects. ACM Trans. Graph. 2(2), 91–108 (1983)
Reffye, D.P., Edelin, C., Francon, J., Jaeger, M., Puech, C.: Plant model faithful to botanical structure and development. SIGGRAPH Comput. Graph. 22, 151–158 (1988)
Reissell, L.M., Dinesh K.P.: Modeling stochastic dynamical systems for interactive simulation. Comput. Graph. Forum 20(3), 339–348 (2001)
Sakaguchi, T., Ohya, J.: Modeling and animation of botanical trees for interactive virtual environments. In: Proceedings of the ACM Symposium on Virtual Reality Software and Technology, pp. 139–146, London (1999)
Schodl, A., Szeliski, R., Salesin, D.H., Essa, I.: Video textures. In: Proceedings of ACM SIGGRAPH 2000, pp. 489–498 (2000)
Shlyakhter, I., Rozenoer, M., Dorsey, J., Teller, S.: Reconstructing 3D tree models from instrumented photographs. Comput. Graph. Appl. 21(3), 53–61 (2001)
Ulam, S.M.: On some mathematical problems connected with patterns of growth of figures. In: Proceedings of the Symposia in Applied Mathematics, vol. 14, pp. 215–224, Am. Math. Soc., Providence, RI (1962)
Viennot, X.G., Eyrolles, G., Janey, N., Arques, D.: Combinatorial analysis of ramified patterns and computer imagery of trees. In: Computer Graphics (SIGGRAPH 89 Conference Proceedings), vol. 23, pp. 31–40 (1989)
Weber, J., Penn, J.: Creation and rendering of realistic trees. In: SIGGRAPH 1995, pp. 119–128 (1995)
Zhang, J., Zhou, K., Velho, L., Guo, B., Shum, H.: Synthesis of progressively-variant textures on arbitrary surfaces. ACM Trans. on Graph. 22(3), 295–302 (2003)
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Wang, R., Hua, W., Dong, Z. et al. Synthesizing trees by plantons. Visual Comput 22, 238–248 (2006). https://doi.org/10.1007/s00371-006-0002-x
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DOI: https://doi.org/10.1007/s00371-006-0002-x