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http://dx.doi.org/10.5302/J.ICROS.2016.16.0049

Enhancement of the Box-Counting Algorithm for Fractal Dimension Estimation  

So, Hye-Rim (OST Graduate School, Korea Maritime and Ocean University)
So, Gun-Baek (OST Graduate School, Korea Maritime and Ocean University)
Jin, Gang-Gyoo (Division of IT, Korea Maritime and Ocean University)
Publication Information
Journal of Institute of Control, Robotics and Systems / v.22, no.9, 2016 , pp. 710-715 More about this Journal
Abstract
Due to its simplicity and high reliability, the box-counting(BC) method is one of the most frequently used techniques to estimate the fractal dimensions of a binary image with a self-similarity property. The fractal calculation requires data sampling that determines the size of boxes to be sampled from the given image and directly affects the accuracy of the fractal dimension estimation. There are three non-overlapping regular grid methods: geometric-step method, arithmetic-step method and divisor-step method. These methods have some drawbacks when the image size M becomes large. This paper presents a BC algorithm for enhancing the accuracy of the fractal dimension estimation based on a new sampling method. Instead of using the geometric-step method, the new sampling method, called the coverage ratio-step method, selects the number of steps according to the coverage ratio. A set of experiments using well-known fractal images showed that the proposed method outperforms the existing BC method and the triangular BC method.
Keywords
fractal dimension; data sampling; coverage ratio; box-counting method; binary image;
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