Estimating fractal dimension of medical images

Alan I. Penn; Murray H. Loew

doi:10.1117/12.237990

16 April 1996 Estimating fractal dimension of medical images

Alan I. Penn, Murray H. Loew

Proceedings Volume 2710, Medical Imaging 1996: Image Processing; (1996) https://doi.org/10.1117/12.237990
Event: Medical Imaging 1996, 1996, Newport Beach, CA, United States

Abstract

Box counting (BC) is widely used to estimate the fractal dimension (fd) of medical images on the basis of a finite set of pixel data. The fd is then used as a feature to discriminate between healthy and unhealthy conditions. We show that BC is ineffective when used on small data sets and give examples of published studies in which researchers have obtained contradictory and flawed results by using BC to estimate the fd of data-limited medical images. We present a new method for estimating fd of data-limited medical images. In the new method, fractal interpolation functions (FIFs) are used to generate self-affine models of the underlying image; each model, upon discretization, approximates the original data points. The fd of each FIF is analytically evaluated. The mean of the fds of the FIFs is the estimate of the fd of the original data. The standard deviation of the fds of the FIFs is a confidence measure of the estimate. The goodness-of-fit of the discretized models to the original data is a measure of self-affinity of the original data. In a test case, the new method generated a stable estimate of fd of a rib edge in a standard chest x-ray; box counting failed to generate a meaningful estimate of the same image.

Citation Download Citation

Alan I. Penn and Murray H. Loew "Estimating fractal dimension of medical images", Proc. SPIE 2710, Medical Imaging 1996: Image Processing, (16 April 1996); https://doi.org/10.1117/12.237990

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