Modified differential box-counting method using weighted triangle-box partition

Differential box-counting (DBC) is one of the commonly used methods to estimate fractal dimension (FD) for gray scale images. It has been successfully applied in many applications such as image segmentation, pattern recognition, texture analysis and medical signal analysis. However, the accuracy improvement of FD estimation is still a grand challenge. This paper proposes a modified differential box-counting method using weighted triangle-box partition (MDBC) to reduce the estimation error caused by an undercounting problem. The proposed method is derived from two assumptions: (i) increasing the precision of box-counts by using unequally triangle box partition, and (ii) weighting the box-counts in proportion to the size of triangle-box partition. Based on these assumptions, on each grid a square box is divided into four asymmetric triangle-box patterns. Each pattern is calculated the box-counts by a weighted box-counting technique. The maximum number of box-counts represents the better estimation. In this way, the experimental results show that MDBC outperforms the baseline methods in terms of fitting error. Furthermore, the proposed method applies to finger-knuckle-print recognition in order to test its efficiency. The results illustrate that it significantly enhances the recognition rate when compared with the conventional differential box-counting (DBC) and improved triangle box-counting in combination with DBC (ITBC-DBC) methods.