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Trees

, Volume 28, Issue 6, pp 1577–1588 | Cite as

Constructing tree stem form from digitized surface measurements by a programming approach within discrete mathematics

  • Atsushi Yoshimoto
  • Peter Surový
  • Masashi Konoshima
  • Winfried Kurth
Original Paper

Abstract

Key message

The main message of this work is the demonstration of possibility of creation of stem shape from digitized points using integer-programming approach. The points are digitized by magnetic motion tracker which in contrast to the laser scanning allows the reconstruction of complete cross-section of stem even in the “hidden (invisible)” part.

Abstract

Three-dimensional information on tree stem form plays an important role in understanding the structure and strength of a standing tree against the forces of wind, snow, and other natural pressure. It also contributes to precision in volume measurement compared to conventional two-dimensional measurement. We investigate approaches for obtaining three-dimensional information of tree stem form from partially organized surface measurements, acquired using a three-dimensional digitizing device (Polhemus FASTRAK® motion tracking device). We then propose a new programming approach from discrete mathematics to construct tree stem form. Our method is based on an optimal connection of neighbor triangles for surface construction, which is created by locally possible combination of three digitized points on the stem surface. We compare the proposed method to the existing heuristic methods of contour tracing and region growing. Our analysis shows that the proposed method provides a consistent construction of tree stem form, for even stems with extremely irregular structure such as those from bent trees and mangrove trees with unique root spread, while the other methods are incapable for constructing such tree stems.

Keywords

3D shape reconstruction Shape from contour Tree stem shape Discrete optimization 

Notes

Acknowledgments

This work was supported by JSPS KAKENHI Grant Numbers 22252002, 23.01400. The second author would like to thank JSPS for funding the post-doctoral fellowship No. P11400.

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. Bernardini F, Bajaj CL, Chen J, Schikore DR (1996) Automatic reconstruction of 3D CAD models from digital scans. Comput Geom Appl 9:27–70Google Scholar
  2. Bernardini F, Mittleman J, Rushmeier H, Silva C, Taubin G (1999) The ball pivoting algorithm for surface reconstruction. IEEE Trans Vis Comput Graph 5:349–359CrossRefGoogle Scholar
  3. Bertram JEA (1989) Size-dependent differential scaling in branches: the mechanical design of trees revisited. Trees 4:241–253Google Scholar
  4. Boissonnat JD (1984) Geometric structures for three-dimensional shape representation. ACM Trans Graph 3:266–286CrossRefGoogle Scholar
  5. Bonser SP, Asarssen LW (1994) Plastic allometry in young sugar maple (Acer saccharum): adaptive responses to light availability. Am J Bot 81:400–406CrossRefGoogle Scholar
  6. Constant T, Mothe F, Badia MA, Saint-Andre L (2003) How to relate the standing tree shape to internal wood characteristics: proposal of an experimental method applied to poplar trees. Ann For Sci 60:371–378CrossRefGoogle Scholar
  7. Cormen TH, Leiserson CE, Rivest RL, Stein C (2001) [1990]. “33.3: Finding the convex hull”. Introduction to algorithms (2nd edn), MIT Press and McGraw-Hill, pp 955–956Google Scholar
  8. Danjon F, Reubens B (2008) Assessing and analyzing 3D architecture of woody root systems, a review of methods and applications in tree and soil stability, resource acquisition and allocation. Plant Soil 303(1–2):1–34CrossRefGoogle Scholar
  9. Dean TJ, Long JN (1986) Validity of constant-stress and elastic-instability principles of stem formation in Pinus contorta and Trifolium pretense. Ann Bot 58:833–840Google Scholar
  10. Figueiredo-Filho A, Borders BE, Hitch KL (1996) Number of diameters required to represent stem profiles using interpolated cubic splines. Can J For Res 26:1113–1121CrossRefGoogle Scholar
  11. FORMATH Group (2013) FastrakDigitizer v1.0. (http://www.formath.jp/ FastrakDigitizer)
  12. Fuchs H, Kedem ZM, Uselton SP (1977) Optimal surface reconstruction from planar contours. Commun ACM 20:693–702CrossRefGoogle Scholar
  13. Holbrook NM, Putz FE (1989) Influence of neighbors on tree form: effects of lateral shade and prevention of sway on the allometry of Liquidambar styraciflua (sweet gum). Am J Bot 76:1740–1749CrossRefGoogle Scholar
  14. Hoppe H, DeRose T, Duchamp T, McDonald J, Stuetzle W (1992) Surface reconstruction from unorganized points, Proceedings of the 19th annual conference on Computer graphics and interactive techniques, ACM, pp 71–78Google Scholar
  15. Keppel E (1975) Approximating complex surfaces by triangulation of contour lines. IBM J Res Dev 19:2–11CrossRefGoogle Scholar
  16. King D, Loucks OL (1978) The theory of tree bole and branch form. Radiat Environ Biophys 15:141–165PubMedCrossRefGoogle Scholar
  17. Koizumi A, Ikeda K, Sawata K, Hirai T (2011) Nondestructive measurement of cross-sectional shape of a tree trunk. J Wood Sci 57:276–281CrossRefGoogle Scholar
  18. Küppers M (1989) Ecological significance of above ground architectural patters in woody plants: a question of cost-benefit relationships. Trends Evol Ecol 4:375–378CrossRefGoogle Scholar
  19. Lahtinen A, Laasasenaho J (1979) On the construction of taper curves by using spline functions. For Fenn 95:1–63Google Scholar
  20. Lin HW, Tai CL, Wang GJ (2004) A mesh reconstruction algorithm driven by an intrinsic property of a point cloud. Comput Aided Des 36:1–9CrossRefGoogle Scholar
  21. McMahon TA (1973) Size and shape in biology. Science 179:1201–1204PubMedCrossRefGoogle Scholar
  22. McMahon TA, Kronauer RE (1976) Tree structures: deducing the principle of mechanical design. J Theor Biol 59:443–466PubMedCrossRefGoogle Scholar
  23. Niklas KJ (1995) Size-dependent allometry of tree height, diameter and trunk-taper. Ann Bot 75:217–227Google Scholar
  24. Norberg RÅ (1988) Theory of growth geometry of plants and self-thinning of plant population: geometric similarity, elastic similarity, and different growth modes of plant parts. Am Nat 131:220–256CrossRefGoogle Scholar
  25. Pulkkinen M (2012) On non-circularity of tree stem cross sections: effect of diameter selection on cross-section area estimation, Bitterlich sampling and stem volume estimation in Scots Pine. Silva Fenn 46:749–848CrossRefGoogle Scholar
  26. Qiang W, Pan Z, Chun C, Jianjun B (2007) Surface rendering for parallel slices of contours from medical imaging. Comput Sci Eng 9:32–37CrossRefGoogle Scholar
  27. Rich PM, Helenurm K, Kerns D, Morse SR, Palmer MW, Short L (1986) Height and stem diameter relationships for dicotyledonous trees and arborescent palms of Costa Rica tropical wet forest. Bull Torrey Bot Club 113:241–246CrossRefGoogle Scholar
  28. Sloboda B (1970) Der QF-Rechner. Ein neues Instrument zur Ermittlung des Flächeninhalts von Stammquerschnitten (zugleich Beitrag zur Theorie der Stammquerschnitte). Mitteilungen der Baden-Württembergischen Forstlichen Versuchs- und Forschungsanstalt, Heft 24, p 18Google Scholar
  29. Surový P, Ribeiro NA, Pereira JS (2011) Observations on 3-dimensional crown growth of Stone pine. Agrofor Syst 82:105–110CrossRefGoogle Scholar
  30. Weiner JG, Thomas SC (1992) Competition and allometry in three species of annual plants. Ecology 73:648–656CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Atsushi Yoshimoto
    • 1
  • Peter Surový
    • 1
  • Masashi Konoshima
    • 2
  • Winfried Kurth
    • 3
  1. 1.Department of Mathematical Analysis and Statistical InferenceThe Institute of Statistical MathematicsTachikawaJapan
  2. 2.Faculty of AgricultureUniversity of the RyukyusNishihara ChoJapan
  3. 3.Department of Ecoinformatics, Biometrics and Forest GrowthGeorg-August University of GöttingenGöttingenGermany

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