Improved Triangle Box-Counting Method for Fractal Dimension Estimation

Abstract

A fractal dimension (FD) is an effective feature, which characterizes roughness and self-similarity of complex objects. However, the FD in nature scene requires the effective method for estimation. The existing methods focus on the improvement of selecting the suitable height of box-counts. This cannot overcome the overcounting problem, which is a key factor to have an impact on the accuracy of the FD estimation. This paper proposes a more accurate FD estimation, an improved triangle box-counting method, to increase the precision of box-counts associated with box sizes. The triangle-box-partition technique provides the double precision for box-counts, thus it can solve the overcounting issue and enhance the accuracy of the FD estimation. The proposed method is evaluated its performance in terms of fitting error. The experimental results show that the proposed method outperforms the existing methods, including differential box-counting (DBC), improved DBC (IDBC), and box-counting with adaptable box height (ADBC) methods.