A Multi-spectral Fractal Image Model and its Associated Fractal Dimension Estimator

We propose both a probabilistic fractal model and fractal dimension estimator for multi-spectral images. The model is based on the widely-known fractional Brownian motion fractal model, extended to the case of images with multiple spectral bands. The model is validated mathematically, under the assumption of statistically independence of the spectral components. Using this model, we generated several synthetic multi-spectral fractal images of varying complexity, with 7 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 validated the estimator on the previously-generated synthetic multi-spectral images having fractal properties. Furthermore, we deployed the proposed multi-spectral fractal image estimator for the complexity assessment of real remotely-sensed data sets and  howed the usefulness of the proposed approach.