King Mongkut’s Institute of Techonology, Thailand

 This study proposes a new approach, adaptive box counting, to estimate the fractal dimension of 3D objects. Here, the box is adapted to be ellipsoid in order to fit the objects. The objects which are used for the experiments here are theoretical plants. These plants are 3D IFS generated plants with the known dimensions. In the study, the dimensions of the plants estimated from the basic box counting, the most popular method to estimate 3D objects, and the adaptive box counting are compared. The results plotted in the log-log graphs show that for the IFS plants, with the ellipsoid shape leaves, the ellipsoid counting method estimate more accurate than the basic box counting method.

1. [1] B.B. Mandelbrot, The Fractal Geometry of Nature. W.N. Freeman, New York, USA, 1983.

2. D. Tang, A.G. “Marangoni 3D Fractal Dimension of Fat Crystal Network,” Chemical Physics Letters 433, 2006, pp. 248-252.

3. D. Zianis, M. Mencuccini, On Simplifying Allometric Analyses of Forest Biomass. Forest Ecology and Management 187, 2004, pp.311–332.

4. C.R. Tolle, et al, “Suboptimal Minimum Cluster Volume Cover-Based Method for Measuring Fractal Dimension,” IEEE Transaction on Pattern Analysis and Machine Intelligence, Vol. 25, No 1, 2003, pp 32-41.

5. B. Zeide, “Fractal Geometry in Forestry Applications,” Forest Ecology and Management 46, 1991, pp. 179-188.

6. R.E. Plotnick, et al, Lacunarity Analysis: A General Technique for the Analysis of Spatial Patterns. Physical Review E. 1996.

7. D.D. Silva, et al, “A Critical Appraisal of Box Counting Method to Access the Fractal Dimension of Tree Crowns,” ISVC (1), 2006, pp 751-760.

8. C. Godin, et al, “Space Occupation by Tree Crowns Obeys Fractals Laws: Evidence from 3D Digitized Plants.” Forth International Workshop on Functional-Structural Plant Models, Montpellier, France, 2004, pp. 79-83.

9. M. T. Suzuki, “A Three Dimensional Box Counting Method for Measuring Fractal Dimensions of 3D Models,” The 11th IASTED International Conference, Hawaii, USA, 2007.

10. Barnsley, M.F., Fractal Everywhere. Boston: Academic Press. 1988.

11. D. Nancy, et al, “The Fractal Forest: Fractal Geometry and Applications in Forest Science” General Technical Report NC-170, United States Department of Agriculture, 1994.