Penn A I, Loew M H
Alan Penn & Associates, Rockville, MD 20850, USA.
IEEE Trans Med Imaging. 1997 Dec;16(6):930-7. doi: 10.1109/42.650889.
Fractal dimension (fd) is a feature which is widely used to characterize medical images. Previously, researchers have shown that fd separates important classes of images and provides distinctive information about texture. We analyze limitations of two principal methods of estimating fd: box-counting (BC) and power spectrum (PS). BC is ineffective when applied to data-limited, low-resolution images; PS is based on a fractional Brownian motion (fBm) model-a model which is not universally applicable. We also present background information on the use of fractal interpolation function (FIF) models to estimate fd of data which can be represented in the form of a function. We present a new method of estimating fd in which multiple FIF models are constructed. The mean of the fd's of the FIF models is taken as the estimate of the fd of the original data. The standard deviation of the fd's of the FIF models is used as a confidence measure of the estimate. We demonstrate how the new method can be used to characterize fractal texture of medical images. In a pilot study, we generated plots of curvature values around the perimeters of images of red blood cells from normal and sickle cell subjects. The new method showed improved separation of the image classes when compared to BC and PS methods.
分形维数（fd）是一种广泛用于表征医学图像的特征。此前，研究人员表明，分形维数能够区分重要的图像类别，并提供有关纹理的独特信息。我们分析了估计分形维数的两种主要方法的局限性：盒计数法（BC）和功率谱法（PS）。当应用于数据有限、低分辨率的图像时，盒计数法无效；功率谱法基于分数布朗运动（fBm）模型——一种并非普遍适用的模型。我们还介绍了使用分形插值函数（FIF）模型来估计可以表示为函数形式的数据的分形维数的背景信息。我们提出了一种估计分形维数的新方法，其中构建了多个分形插值函数模型。将分形插值函数模型的分形维数的平均值作为原始数据分形维数的估计值。分形插值函数模型的分形维数的标准差用作估计的置信度度量。我们展示了如何使用新方法来表征医学图像的分形纹理。在一项初步研究中，我们生成了正常和镰状细胞受试者的红细胞图像周边曲率值的图。与盒计数法和功率谱法相比，新方法在图像类别分离方面表现出了改进。
