A robust algorithm for the fractal dimension of images and its applications to the classification of natural images and ultrasonic liver images

The calculation of the fractal dimension is crucial in fractal geometry. The popular approach is based on box-counting. However, this scheme is easily disturbed by noise and produces many non-negligible plateaus that cause an underestimation. This paper proposes a more robust and efficient method for computing the fractal dimension. To validate its performance, a feature vector based on fractal dimension and M-band wavelet transform was applied to the classification of natural textured images and ultrasonic liver images based on four different classifiers. The experimental results revealed the proposed computation method is trustworthy.