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

David da Silva (1) , Frédéric Boudon (1) , Christophe Godin (1, 2) , Olivier Puech (1) , Colin Smith (1) , Hervé Sinoquet (3)

1 UMR AMAP - Botanique et Modélisation de l'Architecture des Plantes et des Végétations
2 VIRTUAL PLANTS - Modeling plant morphogenesis at different scales, from genes to phenotype
3 PIAF - Laboratoire de Physique et Physiologie Intégratives de l'Arbre Fruitier et Forestier

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.

Mots clés: Modelisation; Dimension fractale; Couronne; Arbre

Domaines: Biologie végétale; Modélisation et simulation

David da Silva, Frédéric Boudon, Christophe Godin, Olivier Puech, Colin Smith, et al.. A Critical Appraisal of the Box Counting Method to Assess the Fractal Dimension of Tree Crowns. Second International Symposium, ISVC 2006, 2006, France. pp.751-760. ⟨hal-00120795⟩