Estimating fractal dimension with fractal interpolation function models
Estimating fractal dimension with fractal interpolation function models
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DOI：
10.1109/42.650889
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发表时间：
1997-12-01
影响因子：
10.6
通讯作者：
Loew, MH
中科院分区：
文献类型：
--
作者：
Penn, AI;Loew, MH
分形维数（Fractal dimension，fd）是一种被广泛用于表征医学图像的特征，以往研究表明，fd可以区分重要的图像类别，并提供关于纹理的独特信息。本文分析了两种主要的估计fd的方法：盒计数（box counting，BC）和功率谱（power spectrum，PS）的局限性，BC在数据有限的低分辨率图像中是无效的; PS是基于分数布朗运动（fBM）模型，这是不普遍适用的模型，我们还提出了使用分形插值函数（FIF）模型来估计FD的数据，可以表示在一个函数的形式的背景信息。本文提出了一种新的估计分形维数的方法，该方法构造了多个FIF模型，取FIF模型的平均值作为原始数据的分形维数的估计值，用FIF模型的标准差作为估计值的置信度。我们在正常红细胞和镰状细胞受试者的红细胞图像的周边周围生成曲率值的曲线图。与BC和PS方法相比，新方法显示出改进的图像类别分离。
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.