ESTIMATING FRACTAL DIMENSION WITH FRACTAL INTERPOLATION FUNCTION MODELS

Fractal dimension (fd) is a feature which is widely used to characteri ze medical images, Previously, researchers have shown that fd separate s important classes of images and provides distinctive information abo ut texture, We analyze limitations of two principal methods of estimat ing fd: box-counting (BC) and power spectrum (PS), BC is ineffective w hen applied to data-limited, low-resolution images; PS is based on a f ractional Brownian motion (fBm) model-a model which is not universally applicable, We also present background information on the use of frac tal interpolation function (FIF) models to estimate fd of data which c an be represented in the form of a function. We present a new method o f estimating fd in which multiple FIF models are constructed, The mean of the fd's of the FIF models is taken as the estimate of the fd of t he original data, The standard deviation of the fd's of the FIF models is used as a confidence measure of the estimate, We demonstrate how t he new method can be used to characterize fractal texture of medical i mages, In a pilot study, we generated plots of curvature values around the perimeters of images of red blood cells from normal and sickle ce ll subjects, The new method showed improved separation of the image cl asses when compared to BC and PS methods.