Using spectral fractal dimension in image classification

Abstract

There were great expectations in the 1980s in connection with the practical applications of mathematical processes which were built mainly upon Fractal Dimension (FD) mathematical basis. Significant results were achieved in the 1990s in practical applications in the fields of information technology, certain image processing areas, data compression, and computer classification. In the present publication the so far well known algorithms calculating fractal dimension in a simple way will be introduced (CISSE SCSS 2005), [6] as well as the new mathematical concept named by the author 'Spectral Fractal Dimension - SFD'. Thus it will be proven that the SFD metrics can directly be applied to classify digital images as an independent parameter. Independent classification methods will be established based on SFD (SSFD - Supervised classification based on Spectral Fractal Dimension, USFD - Unsupervised classification based on Spectral Fractal Dimension). Using mathematical methods, estimation will be given to a maximum real (finite geometric resolution) SFD value measurable on digital images, thus proving the connection between FD and SFD as well as their practical dependence. © Springer Science+Business Media B.V. 2010.