A Multi-Spectral Fractal Image Model and Its Associated Fractal Dimension Estimator

Abstract

We propose both a probabilistic fractal model and fractal dimension estimator for multispectral images. The model is based on the widely known fractional Brownian motion fractal model, which is extended to the case of images with multiple spectral bands. The model is validated mathematically under the assumption of statistical independence of the spectral components. Using this model, we generate several synthetic multi-spectral fractal images of varying complexity, with seven statistically independent spectral bands at specific wavelengths in the visible domain. The fractal dimension estimator is based on the widely used probabilistic box-counting classical approach extended to the multivariate domain of multi-spectral images. We validate the estimator on the previously generated synthetic multi-spectral images having fractal properties. Furthermore, we deploy the proposed multi-spectral fractal image estimator for the complexity assessment of real remotely sensed data sets and show the usefulness of the proposed approach.