Fractal signature and lacunarity in the measurement of the texture of trabecular bone in clinical CT images

Fractal analysis is a method of characterizing complex shapes such as the t rabecular structure of bone. Numerous algorithms for estimating fractal dim ension have been described, but the Fourier power spectrum method is partic ularly applicable to self-affine fractals, and facilitates corrections for the effects of noise and blurring in an image. We found that it provided ac curate estimates of fractal dimension for synthesized fractal images. For n atural texture images fractality is limited to a range of scales, and the f ractal dimension as a function of spatial frequency presents as a fractal s ignature. We found that the fractal signature was more successful at discri minating between these textures than either the global fractal dimension or other metrics such as the mean width and root-mean-square width of the spe ctral density plots. Different natural textures were also readily distingui shable using lacunarity plots, which explicitly characterize the average si ze and spatial organization of structural sub-units within an image. The fr actal signatures of small regions of interest (32x32 pixels), computed in t he frequency domain after corrections for imaging system noise and MTF, wer e able to characterize the texture of vertebral trabecular bone in CT image s. Even small differences in texture due to acquisition slice thickness res ulted in measurably different fractal signatures. These differences were al so readily apparent in lacunarity plots, which indicated that a slice thick ness of I turn or less is necessary if essential architectural information is not to be lost. Since lacunarity measures gap size and is not predicated on fractality, it may be particularly useful for characterizing the textur e of trabecular bone. (C) 2001 IPEM. Published by Elsevier Science Ltd. All rights reserved.