Chung H W, Chu C C, Underweiser M, Wehrli F W
Department of Radiology, University of Pennsylvania Medical Center, Philadelphia 19104.
Med Phys. 1994 Oct;21(10):1535-40. doi: 10.1118/1.597263.
Fractal analysis has recently been suggested [Med. Phys. 20, 1611-1619 (1993)] as a means to characterize the structure of cancellous bone by measuring the fractal dimension using a box counting algorithm. This work re-examines the possible fractal nature of such structures on nuclear magnetic resonance (NMR) images of cancellous bone by estimating the trabecular boundary length as a function of box size under various experimental conditions. On high-resolution images (pixel sizes on the order of 50 microns) and signal-to-noise ratios of 30, the trabecular boundary turns out to be a smooth surface relative to the achievable resolution and is thus nonfractal. The fractal dimension of the trabecular structure is undefined and can vary significantly as a function of image signal-to-noise ratio. The present work further indicates the "apparent" fractal dimension obtained by box counting to be a reflection of marrow pore size. In conclusion, the results indicate that, at the currently achievable resolution, the box counting algorithm is not suitable for fractal analysis on images of cancellous bone and that the fractal appearance of the trabecular network reported previously is artifactual.
分形分析最近被提出[《医学物理》20, 1611 - 1619 (1993)]，作为一种通过使用盒计数算法测量分形维数来表征松质骨结构的方法。这项工作通过在各种实验条件下估计作为盒大小函数的小梁边界长度，重新审视了松质骨核磁共振（NMR）图像上此类结构可能的分形性质。在高分辨率图像（像素大小约为50微米）和信噪比为30的情况下，相对于可实现的分辨率，小梁边界是一个光滑表面，因此是非分形的。小梁结构的分形维数未定义，并且会作为图像信噪比的函数而显著变化。目前的工作进一步表明，通过盒计数获得的“表观”分形维数是骨髓孔隙大小的反映。总之，结果表明，在当前可实现的分辨率下，盒计数算法不适用于松质骨图像的分形分析，并且先前报道的小梁网络的分形外观是人为的。
