Fractal Dimension of Color Fractal Images With Correlated Color Components

Abstract

We mathematically prove that color fractal images with two and three correlated color components generated with the midpoint displacement approach obey the property of self-similarity, thus enabling the estimation of their color fractal dimension. We generate various sets of color fractal images with two and three correlated color components, controlled both by the Hurst parameter and the variance-covariance matrix, with and without a global normalization, and use them for the calibration of the embraced color fractal dimension estimator. We improve the existing fractal dimension estimator based on probabilistic box-counting by reducing the variance of the regression line estimators through the iterative elimination of most error-ed measurement points. We independently estimate the variance-covariance matrix and Hurst parameter for the sets of generated color fractal images with correlated color components. We show the experimental results and discuss both the improvements and the limitations of the proposed approach.