Analysis of trabecular patterns using fractal dimensions

Abstract

The authors analyse trabecular patterns which appear in the X-ray bone images using fractal geometry. The trabecular structures contain the information about the bone strength or the inner minerals. Fractal dimensions are useful for analyzing of these trabecular structures because they can express complex patterns quantitatively. The authors calculated the fractal dimensions of the trabecular structures by using the surface area method which treats the structures as a three-dimensional "mountain". More precisely, the method uses the surface areas of the structures and the basis rulers. To study the relationship between a fractal dimension and patient's age or diseases, the authors used 38 radiographic images in which the trabecular structures appeared. As a result, the authors found that the fractal dimension of the trabecular bone structure was related to the age of the patients.