Fractal dimension of low-resolution medical images

Fractal dimension (fd) is a feature which is widely used to characterize medical images. Previously, researchers have shown that fd separates important classes of images and is orthogonal to other texture measures. Existing methods of estimating fd, however, are unable to distinguish many images with similar characteristics, limiting the effectiveness of fd as a feature. This paper analyzes the limitation of box-counting (BC) and fractional Brownian motion (fBm) methods of estimating fd. Estimation by BC is ineffective when applied to data-limited images. Estimation by fBm uses a restrictive model which is not applicable to Iterated Function Systems or to noisy images. The authors present a new method of estimating fd which is applicable to data-limited medical images. In the authors´ method, Fractal Interpolation Functions (FIFs) are used to generate self-affine models of graphical representations of image data. The fd of each FIF is analytically evaluated, and measures of confidence and self-affinity are computed. The new method is demonstrated in a test study of red blood cells