Fractal signature and lacunarity in the measurement of the texture of trabecular bone in clinical CT images
Fractal signature and lacunarity in the measurement of the texture of trabecular bone in clinical CT images
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DOI：
10.1016/s1350-4533(01)00057-1
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发表时间：
2001-07-01
影响因子：
2.2
通讯作者：
Henebry, GM
中科院分区：
文献类型：
--
作者：
Dougherty, G;Henebry, GM
分形分析是一种表征复杂形状（例如骨小梁结构）的方法。已经描述了用于估计分形维数的多种算法，但是傅里叶功率谱方法特别适用于自仿射分形，并且有助于校正图像中的噪声和模糊的影响。我们发现它可以准确估计合成分形图像的分形维数。对于自然纹理图像，分形仅限于一定的尺度范围，并且分形维数作为空间频率的函数呈现为分形特征。我们发现，分形特征在区分这些纹理方面比全局分形维数或其他指标（例如谱密度图的平均宽度和均方根宽度）更成功。使用空隙图也可以轻松地区分不同的自然纹理，该图明确地表征了图像内结构子单元的平均大小和空间组织。在对成像系统噪声和 MTF 进行校正后，在频域中计算出感兴趣的小区域（32x32 像素）的分形特征，能够表征 CT 图像中椎骨小梁骨的纹理。即使由于采集切片厚度而导致的纹理微小差异也会导致明显不同的分形特征。这些差异在空隙图中也很明显，这表明如果不想丢失重要的架构信息，则需要 I 圈或更小的切片厚度。由于腔隙度测量间隙大小并且不以分形为基础，因此它对于表征小梁骨的纹理可能特别有用。 (C) 2001 年 IPEM。由爱思唯尔科学有限公司出版。保留所有权利。
Fractal analysis is a method of characterizing complex shapes such as the trabecular structure of bone. Numerous algorithms for estimating fractal dimension have been described, but the Fourier power spectrum method is particularly applicable to self-affine fractals, and facilitates corrections for the effects of noise and blurring in an image. We found that it provided accurate estimates of fractal dimension for synthesized fractal images. For natural texture images fractality is limited to a range of scales, and the fractal dimension as a function of spatial frequency presents as a fractal signature. We found that the fractal signature was more successful at discriminating between these textures than either the global fractal dimension or other metrics such as the mean width and root-mean-square width of the spectral density plots. Different natural textures were also readily distinguishable using lacunarity plots, which explicitly characterize the average size and spatial organization of structural sub-units within an image. The fractal signatures of small regions of interest (32x32 pixels), computed in the frequency domain after corrections for imaging system noise and MTF, were able to characterize the texture of vertebral trabecular bone in CT images. Even small differences in texture due to acquisition slice thickness resulted in measurably different fractal signatures. These differences were also readily apparent in lacunarity plots, which indicated that a slice thickness 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 texture of trabecular bone. (C) 2001 IPEM. Published by Elsevier Science Ltd. All rights reserved.