, 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


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.


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.


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



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.


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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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