Fractal Dimension Estimation in Diagnosing Alzheimer’s Disease

Abstract

Estimated entropies from a limited data set are always biased. Consequently, it is not a trivial task to calculate the entropy in real tasks. In this paper, we used a generalized definition of entropy to evaluate the Hartley, Shannon, and Collision entropies. Moreover, we applied the Miller and Harris estimations of Shannon entropy, which are well known bias approaches based on Taylor series. Finally, these estimates were improved by Bayesian estimation of individual probabilities. These methods were tested and used for recognizing Alzheimer’s disease, using the relationship between entropy and the fractal dimension to obtain fractal dimensions of 3D brain scans.

Keywords

• entropy
• fractal dimension
• Alzheimer’s disease
• boxcounting
• Rényi entopy.