Robust fractal characterization of one-dimensional and two-dimensional signals

Fractals have been shown to be useful in the analysis of time series data and in classification of natural shapes and textures. A Maximum Likelihood Estimator is used to measure the parameter H which is directly related to the fractal dimension. The robustness of the estimator is shown in the presence of noise. The performance of the method is demonstrated on datasets generated using a variety of techniques. Finally the performance of the estimator is shown by characterization of homogenous textures and by the segmentation of noisy composite images of natural textures.