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Volume 6, Number 4, 2016, Pages 1114-1125                                                                DOI:10.11948/2016073
An improved box-counting method to estimate fractal dimension of images
Jundong Yan,Yuanyuan Sun,Shanshan Cai,Xiaopeng Hu
Keywords:Ddifferential box-counting (DBC) method, fractal dimension, improved DBC method.
      Fractal dimension (FD) reflects the intrinsic self-similarity of an image and can be used in image classification, image segmentation and texture analysis. The differential box-counting (DBC) method is a common approach to calculating the FD values. This paper proposes an improved DBC-based approach to optimizing the performance of the method in the following ways: reducing fitting errors by decreasing step lengths, considering under-counting boxes on the border of two neighboring box-blocks and making better use of all the pixels in the blocks while not neglecting the middle parts. The experimental results show that the fitting error of the new method can be decreased to 0.012879. The average distance of the FD values is decreased by 16.0/% in the divided images and the average variance of the FD values is decreased by 30/% in the scaled images, compared with other modified methods. The results show that the new method has a better performance in the recognition of the same type of images and the scaled images.
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