- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Computational and Mathematical Methods in Medicine
Volume 2013 (2013), Article ID 262931, 11 pages
Scale-Specific Multifractal Medical Image Analysis
1Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
2Department of Physics, San Diego State University, 5500 Campanile Drive, San Diego, CA 92182-1233, USA
Received 10 June 2013; Accepted 17 July 2013
Academic Editor: Ricardo Femat
Copyright © 2013 Boris Braverman and Mauro Tambasco. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- B. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman, New York, NY, USA, 1977.
- D. S. Coffey, “Self-organization, complexity and chaos: the new biology for medicine,” Nature Medicine, vol. 4, no. 8, pp. 882–885, 1998.
- D. Avnir, O. Biham, D. Lidar, and O. Malcai, “Is the geometry of nature fractal?” Science, vol. 279, no. 5347, pp. 39–40, 1998.
- R. Femat, J. Alvarez-Ramirez, and M. Zarazua, “Chaotic behavior from a human biological signal,” Physics Letters A, vol. 214, no. 3-4, pp. 175–179, 1996.
- A. Espinoza-Valdez, F. C. Ordaz-Salazar, E. Ugalde, and R. Femat, “Analysis of a model for the morphological structure of renal arterial tree: fractal structure,” Journal of Applied Mathematics, vol. 2013, Article ID 396486, 6 pages, 2013.
- R. Lopes and N. Betrouni, “Fractal and multifractal analysis: a review,” Medical Image Analysis, vol. 13, no. 4, pp. 634–649, 2009.
- O. Heymans, J. Fissette, P. Vico, S. Blacher, D. Masset, and F. Brouers, “Is fractal geometry useful in medicine and biomedical sciences?” Medical Hypotheses, vol. 54, no. 3, pp. 360–366, 2000.
- J. F. Veenland, J. L. Grashuis, F. van der Meer, A. L. D. Beckers, and E. S. Gelsema, “Estimation of fractal dimension in radiographs,” Medical Physics, vol. 23, no. 4, pp. 585–594, 1996.
- C. Fortin, R. Kumaresan, W. Ohley, and S. Hoefer, “Fractal dimension in the analysis of medical images,” IEEE Engineering in Medicine and Biology Magazine, vol. 11, no. 2, pp. 65–71, 1992.
- K. Falconer, Fractal Geometry: Mathematical Foundations and Applications., John Wiley & Sons, New York, NY, USA, 2nd edition, 2003.
- M. Ciccotti and F. Mulargia, “Pernicious effect of physical cutoffs in fractal analysis,” Physical Review E, vol. 65, no. 3, Article ID 037201, 2002.
- H.-W. Chung and H.-J. Chung, “Correspondence re: J. W. Baish and R. K. Jain, Fractals and Cancer. Cancer Research, 60: 3683–3688, 2000,” Cancer Research, vol. 61, no. 22, pp. 8347–8350, 2001.
- M. Tambasco and A. M. Magliocco, “Relationship between tumor grade and computed architectural complexity in breast cancer specimens,” Human Pathology, vol. 39, no. 5, pp. 740–746, 2008.
- M. Tambasco, “Scale issue in fractal analysis of histological specimens-reply,” Human Pathology, vol. 39, no. 12, pp. 1860–1861, 2008.
- M. Tambasco, B. M. Costello, A. Kouznetsov, A. Yau, and A. M. Magliocco, “Quantifying the architectural complexity of microscopic images of histology specimens,” Micron, vol. 40, no. 4, pp. 486–494, 2009.
- M. Tambasco, M. Eliasziw, and A. M. Magliocco, “Morphologic complexity of epithelial architecture for predicting invasive breast cancer survival,” Journal of Translational Medicine, vol. 8, no. 1, article 140, 2010.
- G. Landini and J. Paul Rigaut, “A method for estimating the dimension of asymptotic fractal sets,” Bioimaging, vol. 5, pp. 65–70, 1997.
- J. W. Dollinger, R. Metzler, and T. F. Nonnenmacher, “Bi-asymptotic fractals: fractals between lower and upper bounds,” Journal of Physics A, vol. 31, no. 16, pp. 3839–3847, 1998.
- R. Alfréd Rényi, “On measures of entropy and information,” in Proceedings of the 4th Berkeley Symposium on Mathematics, Statistics and Probability, vol. 1, pp. 547–561, 1960.
- M. J. Turner, J. M. Blackledge, and P. R. Andrews, Fractal Geometry in Digital Imaging, Academic Press, 1998.
- F. C. Crow, “Summed-area tables for texture mapping,” Computer Graphics, vol. 18, no. 3, pp. 207–212, 1984.
- P. Grassberger and I. Procaccia, “Characterization of strange attractors,” Physical Review Letters, vol. 50, no. 5, pp. 346–349, 1983.
- W. S. Cleveland, “Robust locally weighted regression and smoothing scatterplots,” Journal of the American Statistical Association, vol. 74, no. 368, pp. 829–836, 1979.
- H.-O. Peitgen, H. Jürgens, and D. Saupe, Chaos and Fractals: New Frontiers of Science, Springer, New York, NY, USA, 2nd edition, 2004.