Fractal dimension in the analysis of medical images

The analysis of cardiac magnetic resonance (MR) images and X-rays of bone is considered. Each image type is approached using a different form of fractal parameterization. For the MR images, the goal of the study is segmentation, and to this end small regions of the image are assigned a local value of fractal dimension. For the bone X-rays, rather than segmentation, the large-scale structure is parameterized by its fractal dimension. In both cases, the use of fractals leads to the classification of the parameters of interest. When applied to segmentation, this analysis yields boundary discrimination unavailable through previous methods. For the X-rays, texture changes are quantified and correlated with physical changes in the subject. In both cases, the parameterizations are robust with regard to noise present in the images, as well as to variable contrast and brightness.<<ETX>>

[1]  H. E. Hurst,et al.  Long-Term Storage Capacity of Reservoirs , 1951 .

[2]  B. Mandelbrot,et al.  Fractional Brownian Motions, Fractional Noises and Applications , 1968 .

[3]  J. R. Wallis,et al.  Noah, Joseph, and Operational Hydrology , 1968 .

[4]  J. R. Wallis,et al.  Computer Experiments with Fractional Gaussian Noises: Part 3, Mathematical Appendix , 1969 .

[5]  J. R. Wallis,et al.  Computer Experiments with Fractional Gaussian Noises: Part 2, Rescaled Ranges and Spectra , 1969 .

[6]  J. R. Wallis,et al.  Robustness of the rescaled range R/S in the measurement of noncyclic long run statistical dependence , 1969 .

[7]  J. R. Wallis,et al.  Some long‐run properties of geophysical records , 1969 .

[8]  Robert N. McDonough,et al.  Detection of signals in noise , 1971 .

[9]  Donald S. Fussell,et al.  Computer rendering of stochastic models , 1982, Commun. ACM.

[10]  P. A. Burrough,et al.  Multiscale sources of spatial variation in soil. I: The application of fractal concepts to nested levels of soil variation , 1983 .

[11]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[12]  P. A. Burrough,et al.  Multiscale sources of spatial variation in soil. II. A non‐Brownian fractal model and its application in soil survey , 1983 .

[13]  W M Schaffer,et al.  Effects of noise on some dynamical models in ecology , 1986, Journal of mathematical biology.

[14]  S. Kay,et al.  Fractional Brownian Motion: A Maximum Likelihood Estimator and Its Application to Image Texture , 1986, IEEE Transactions on Medical Imaging.

[15]  D. Saupe.  Algorithms for random fractals , 1988 .

[16]  J. Bassingthwaighte.  Physiological Heterogeneity: Fractals Link Determinism and Randomness in Structures and Functions. , 1988, News in physiological sciences : an international journal of physiology produced jointly by the International Union of Physiological Sciences and the American Physiological Society.

[17]  Richard F. Voss,et al.  Fractals in nature: from characterization to simulation , 1988 .

[18]  H. Vincent Poor,et al.  Signal detection in fractional Gaussian noise , 1988, IEEE Trans. Inf. Theory.

[19]  J. Bassingthwaighte,et al.  Fractal Nature of Regional Myocardial Blood Flow Heterogeneity , 1989, Circulation research.

[20]  J B Bassingthwaighte,et al.  Regional myocardial flow heterogeneity explained with fractal networks. , 1989, The American journal of physiology.

[21]  Patrick Flandrin,et al.  On the spectrum of fractional Brownian motions , 1989, IEEE Trans. Inf. Theory.

[22]  A. Provenzale,et al.  Finite correlation dimension for stochastic systems with power-law spectra , 1989 .

[23]  R. Schmukler,et al.  Measurement Of Bone Structure By Use Of Fractal Dimension , 1990, [1990] Proceedings of the Twelfth Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[24]  A. Goldberger,et al.  Fractal Electrodynamics of the Heartbeat a , 1990, Annals of the New York Academy of Sciences.

[25]  Ramdas Kumaresan,et al.  Estimation of the fractal dimension of a stochastic fractal from noise-corrupted data , 1992 .