A modified triangle box-counting with precision in error fit

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Abstract
Fractal dimension is required to estimate the complexity of digital image. Researchers have proposed different techniques for evaluating fractal dimension such as Differential box counting (DBC), Modified DBC (MDBC), Relative DBC (RDBC), Improved box counting (IBC), Improved DBC (IDBC), Triangle box counting (TBC), and Improved Triangle box counting (ITBC). ITBC is one of the most recently used techniques in digital domain. However, the accuracy of an algorithm for fractal dimension estimation is still a great challenge. In this paper, we have presented modified differential box counting technique by implementing asymmetric triangle box partition of grid. Our proposed approach is to optimize the performance of the method in terms of less fitting error for individual image and also produce less average fitting error for all images and more precision box count by means of triangle box partition. It also solves both over counting and under counting problem simultaneously. The experiments are carried out on two sets of brodatz database images and one set of synthetic images. The results show that the proposed method has a better performance in terms of less fit error and yields better recognition in scaled images as compared to existing methods.

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