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IJAT Vol.18 No.2 pp. 287-294
doi: 10.20965/ijat.2024.p0287
(2024)

Research Paper:

Leaf Reconstruction Based on Gaussian Mixture Model from Point Clouds of Leaf Boundaries and Veins

Yukie Nagai ORCID Icon and Hikaru Tanaya

Graduate School of Systems Design, Tokyo Metropolitan University
6-6 Asahigaoka, Hino, Tokyo 191-0065, Japan

Corresponding author

Received:
June 30, 2023
Accepted:
November 7, 2023
Published:
March 5, 2024
Keywords:
leaves, point clouds, surface mesh, Gaussian mixture model, implicit functions
Abstract

Three-dimensional (3D) models of leaves are expected to contribute to a wide range of applications, including the study of plant morphology and leaf design. Leaf boundaries and veins are key factors in determining leaf shape in both botany and design. This motivated us to design a leaf-shape generator that uses leaf boundaries and veins. We propose an algorithm to reconstruct leaf geometry as a surface mesh generated from point clouds of leaf boundaries and veins. First, it determines the interior region of the leaf using the multi-level partition of unity implicits approach. Then, based on the Gaussian mixture model, it expresses the 3D shape of the leaf, where the values vary depending on the distances from the leaf boundary to veins. The use of differentiable functions for leaf shapes realizes smooth underlying surfaces and enables various shape analyses using differential operations.

Cite this article as:
Y. Nagai and H. Tanaya, “Leaf Reconstruction Based on Gaussian Mixture Model from Point Clouds of Leaf Boundaries and Veins,” Int. J. Automation Technol., Vol.18 No.2, pp. 287-294, 2024.
Data files:
References
  1. [1] J.-D. Boissonnat, “Geometric structures for three-dimensional shape representation,” ACM Trans. Graph., Vol.3, No.4, pp. 266-286, 1984. https://doi.org/10.1145/357346.357349
  2. [2] H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, and W. Stuetzle, “Surface reconstruction from unorganized points,” ACM SIGGRAPH Comput. Graph., Vol.26, No.2, pp. 71-78, 1992. https://doi.org/10.1145/142920.134011
  3. [3] B. Curless and M. Levoy, “A volumetric method for building complex models from range images,” Proc. 23rd Annu. Conf. Comput. Graph. Interact. Tech. (SIGGRAPH’96), pp. 303-312, 1996. https://doi.org/10.1145/237170.237269
  4. [4] G. Turk and M. Levoy, “Zippered polygon meshes from range images,” Proc. 21st Annu. Conf. Comput. Graph. Interact. Tech. (SIGGRAPH’94), pp. 311-318, 1994. https://doi.org/10.1145/192161.192241
  5. [5] H.-C. Nguyen and B.-R. Lee, “3D model reconstruction system development based on laser-vision technology,” Int. J. Automation Technol., Vol.10, No.5, pp. 813-820, 2016. https://doi.org/10.20965/ijat.2016.p0813
  6. [6] T. K. Dey and J. Giesen, “Detecting undersampling in surface reconstruction,” Proc. 17th Annu. Symp. Comput. Geom. (SCG’01), pp. 257-263, 2001. https://doi.org/10.1145/378583.378682
  7. [7] N. Amenta, M. Bern, and M. Kamvysselis, “A new Voronoi-based surface reconstruction algorithm,” Proc. 25th Annu. Conf. Comput. Graph. Interact. Tech. (SIGGRAPH’98), pp. 415-421, 1998. https://doi.org/10.1145/280814.280947
  8. [8] T. K. Dey and S. Goswami, “Tight cocone: A water-tight surface reconstructor,” Proc. 8th ACM Symp. Solid Model. Appl. (SM’03), pp. 127-134, 2003. https://doi.org/10.1145/781606.781627
  9. [9] T. K. Dey and S. Goswami, “Provable surface reconstruction from noisy samples,” Comput. Geom., Vol.35, Nos.1-2, pp. 124-141, 2006. https://doi.org/10.1016/j.comgeo.2005.10.006
  10. [10] N. Amenta, S. Choi, and R. K. Kolluri, “The power crust,” Proc. 6th ACM Symp. Solid Model. Appl. (SMA’01), pp. 249-266, 2001. https://doi.org/10.1145/376957.376986
  11. [11] H. Edelsbrunner and E. P. Mücke, “Three-dimensional alpha shapes,” ACM Trans. Graph., Vol.13, No.1, pp. 43-72, 1994. https://doi.org/10.1145/174462.156635
  12. [12] C. L. Bajaj, F. Bernardini, and G. Xu, “Automatic reconstruction of surfaces and scalar fields from 3D scans,” Proc. 22nd Annu. Conf. Comput. Graph. Interact. Tech. (SIGGRAPH’95), pp. 109-118, 1995. https://doi.org/10.1145/218380.218424
  13. [13] J. C. Carr, R. K. Beatson, J. B. Cherrie, T. J. Mitchell, W. R. Fright, B. C. McCallum, and T. R. Evans, “Reconstruction and representation of 3D objects with radial basis functions,” Proc. 28th Annu. Conf. Comput. Graph. Interact. Tech. (SIGGRAPH’01), pp. 67-76, 2001. https://doi.org/10.1145/383259.383266
  14. [14] Y. Ohtake, A. Belyaev, and H.-P. Seidel, “3D scattered data interpolation and approximation with multilevel compactly supported RBFs,” Graph. Models, Vol.67, No.3, pp. 150-165, 2005. https://doi.org/10.1016/j.gmod.2004.06.003
  15. [15] C. Shen, J. F. O’Brien, and J. R. Shewchuk, “Interpolating and approximating implicit surfaces from polygon soup,” ACM SIGGRAPH 2004, pp. 896-904, 2004. https://doi.org/10.1145/1186562.1015816
  16. [16] S. Fleishman, D. Cohen-Or, and C. T. Silva, “Robust moving least-squares fitting with sharp features,” ACM Trans. Graph., Vol.24, No.3, pp. 544-552, 2005. https://doi.org/10.1145/1073204.1073227
  17. [17] J. Manson, G. Petrova, and S. Schaefer, “Streaming surface reconstruction using wavelets,” Comput. Graph. Forum, Vol.27, No.5, pp. 1411-1420, 2008. https://doi.org/10.1111/j.1467-8659.2008.01281.x
  18. [18] M. Alexa, J. Behr, D. Cohen-Or, S. Fleishman, D. Levin, and C. T. Silva, “Point set surfaces,” Proc. Conf. Vis. (VIS’01), pp. 21-29, 2001. https://doi.org/10.1109/VISUAL.2001.964489
  19. [19] G. Guennebaud and M. Gross, “Algebraic point set surfaces,” ACM Trans. Graph., Vol.26, No.3, Article No.23, 2007. https://doi.org/10.1145/1276377.1276406
  20. [20] A. Hornung and L. Kobbelt, “Robust reconstruction of watertight 3D models from non-uniformly sampled point clouds without normal information,” Proc. 4th Eurogr. Symp. Geom. Process. (SGP’06), pp. 41-50, 2006.
  21. [21] Y. Ohtake, A. G. Belyaev, M. Alexa, G. Turk, and H.-P. Seidel, “Multi-level partition of unity implicits,” ACM Trans. Graph., Vol.22, No.3, pp. 463-470, 2003. https://doi.org/10.1145/882262.882293
  22. [22] Y. Nagai, Y. Ohtake, and H. Suzuki, “Smoothing of partition of unity implicit surfaces for noise robust surface reconstruction,” Comput. Graph. Forum, Vol.28, No.5, pp. 1339-1348, 2009. https://doi.org/10.1111/j.1467-8659.2009.01511.x
  23. [23] M. Kazhdan, M. Bolitho, and H. Hoppe, “Poisson surface reconstruction,” Proc. 4th Eurogr. Symp. Geom. Process. (SGP’06), pp. 61-70, 2006.
  24. [24] M. Kazhdan and H. Hoppe, “Screened Poisson surface reconstruction,” ACM Trans. Graph., Vol.32, No.3, Article No.29, 2013. https://doi.org/10.1145/2487228.2487237
  25. [25] R. Hanocka, G. Metzer, R. Giryes, and D. Cohen-Or, “Point2Mesh: A self-prior for deformable meshes,” ACM Trans. Graph., Vol.39, No.4, Article No.126, 2020. https://doi.org/10.1145/3386569.3392415
  26. [26] J. J. Park, P. Florence, J. Straub, R. Newcombe, and S. Lovegrove, “DeepSDF: Learning continuous signed distance functions for shape representation,” 2019 IEEE/CVF Conf. Comput. Vis. Pattern Recognit. (CVPR), pp. 165-174, 2019. https://doi.org/10.1109/CVPR.2019.00025
  27. [27] R. Chabra, J. E. Lenssen, E. Ilg, T. Schmidt, J. Straub, S. Lovegrove, and R. Newcombe, “Deep local shapes: Learning local SDF priors for detailed 3D reconstruction,” Proc. 16th Eur. Conf. Comput. Vis. (ECCV 2020), Part 29, pp. 608-625, 2020. https://doi.org/10.1007/978-3-030-58526-6_36
  28. [28] L. Mescheder, M. Oechsle, M. Niemeyer, S. Nowozin, and A. Geiger, “Occupancy networks: Learning 3D reconstruction in function space,” 2019 IEEE/CVF Conf. Comput. Vis. Pattern Recognit. (CVPR), pp. 4455-4465, 2019. https://doi.org/10.1109/CVPR.2019.00459
  29. [29] M. Berger, A. Tagliasacchi, L. M. Seversky, P. Alliez, G. Guennebaud, J. A. Levine, A. Sharf, and C. T. Silva, “A survey of surface reconstruction from point clouds,” Comput. Graph. Forum, Vol.36, No.1, pp. 301-329, 2017. https://doi.org/10.1111/cgf.12802
  30. [30] P. Prusinkiewicz, L. Mündermann, R. Karwowski, and B. Lane, “The use of positional information in the modeling of plants,” Proc. 28th Annu. Conf. Comput. Graph. Interact. Tech. (SIGGRAPH’01), pp. 289-300, 2001. https://doi.org/10.1145/383259.383291
  31. [31] S. M. Hong, B. Simpson, and G. V. G. Baranoski, “Interactive venation-based leaf shape modeling,” Comput. Animat. Virtual Worlds, Vol.16, Nos.3-4, pp. 415-427, 2005. https://doi.org/10.1002/cav.88
  32. [32] W. Wen, B. Li, B.-J. Li, and X. Guo, “A leaf modeling and multi-scale remeshing method for visual computation via hierarchical parametric vein and margin representation,” Front. Plant Sci., Vol.9, Article No.783, 2018. https://doi.org/10.3389/fpls.2018.00783
  33. [33] P. Cignoni, M. Callieri, M. Corsini, M. Dellepiane, F. Ganovelli, and G. Ranzuglia, “MeshLab: An open-source mesh processing tool,” Eurogr. Ital. Chapter Conf., pp. 129-136, 2008. http://dx.doi.org/10.2312/LocalChapterEvents/ItalChap/ItalianChapConf2008/129-136
  34. [34] C. M. Bishop, ”Pattern Recognition and Machine Learning,” Springer, 2006.
  35. [35] F. Bernardini, J. Mittleman, H. Rushmeier, C. Silva, and G. Taubin, “The ball-pivoting algorithm for surface reconstruction,” IEEE Trans. Vis. Comput. Graph., Vol.5, No.4, pp. 349-359, 1999. https://doi.org/10.1109/2945.817351

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Last updated on Jun. 03, 2024