Linear transformation based error correction algorithm for fractal dimension estimation of images

The paper proposes the idea of the error correction algorithm for the fractal dimension estimation based on the linear transformation approach allowing the estimation accuracy to be improved essentially. The proposed algorithm is based on the use of the isarithm and triangular prism estimation methods. The results of comparison of a few fractal dimension estimation methods with the use of artificial images generated by several surface generation algorithms are discussed. It is demonstrated that the surface generation algorithm on the base of Fourier filtering is the most suitable for generating artificial images with known fractal dimension. The experimental results of the error correction algorithm evaluation with artificial images demonstrated that the estimation error rate is decreased several times after linear transformation and correction and does not depend on fractal dimension of the image estimated. The results obtained in the work can be considered as general and the proposed error correction algorithm can be applied to accurate fractal dimension estimation of most natural phenomena.