Saturday, June 24, 2017 - 09:00 to 15:45
Z-Box merging: Ultra-fast computation of Fractal Dimension and Lacunarity
"In [1], a reasonably fast method of Fractal Dimension estimation was presented. However, it has a weak point: After each subdivision of the partition table, pixels that might have been quite far apart originally might end up needing to be merged. Thus, after each subdivision, the partition table needs to be re-sorted, which is a computationally expensive operation. The ideal solution would be to order the pixels of the image in such a way, that a) pixels that are in the same cube are consecutive and b) they remain in that order even after each subdivision. This paper provides a method that can do exactly that, and offers an example implementation. Afterwards, it offers a way to also calculate the lacunarity with negligible changes in algorithm structure and running time. To our knowledge, this marks the first time that the lacunarity can be computed in an acceptable time-frame. Finally, after offering some example applications and future improvements, the paper concludes."
Elias Aifantis's picture
Elias Aifantis