A Critical Appraisal of the Box Counting Method to Assess the Fractal Dimension of Tree Crowns

  • D. Da Silva
  • F. Boudon
  • C. Godin
  • O. Puech
  • C. Smith
  • H. Sinoquet
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4291)


In this paper, we study the application of the box counting method (BCM) to estimate the fractal dimension of 3D plant foliage. We use artificial crowns with known theoretical fractal dimension to characterize the accuracy of the BCM and we extend the approach to 3D digitized plants. In particular, errors are experimentally characterized for the estimated values of the fractal dimension. Results show that, with careful protocols, the estimated values are quite accurate. Several limits of the BCM are also analyzed in this context. This analysis is used to introduce a new estimator, derived from the BCM estimator, whose behavior is characterized.


Fractal Dimension Voxel Size Leaf Size Iterate Function System Peach Tree 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • D. Da Silva
    • 1
    • 5
  • F. Boudon
    • 2
    • 5
  • C. Godin
    • 2
    • 3
    • 5
  • O. Puech
    • 4
    • 5
  • C. Smith
    • 4
    • 5
  • H. Sinoquet
    • 6
  1. 1.Université de Montpellier II 
  2. 2.CIRAD 
  3. 3.INRIA 
  4. 4.INRA 
  5. 5.Virtual Plants Team, UMR AMAP TA/40EFrance
  6. 6.INRA-UBP, UMR PIAFClermont-FerrandFrance

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