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Local and Global Fractal Behaviour in Mammographic Images

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Part of the book series: IFMBE Proceedings ((IFMBE,volume 57))

Abstract

Breast cancer is the most common cancer among women. Most studies attempt to perform segmentation of tumors highlighted in mammogaphic images, or analyze the contours of tumors for classification purposes. Successful segmentation and classification of tumors can assist physicians in revealing suspicious regions or masses, or in differentiating malignant from benign tumors by mammography. However, relevant studies do not focus on the tumor surface statistics for the purpose of clustering and/or classification. In this work, we present a statistical, fractal-based approach, for the analysis of annotated tumors, reduced from the DDSM database. We explore local and global fractal properties, obtained from the tumor surface, and present preliminary results on the properties of benign and malignant tumors.

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References

  1. Subashini T. S., Ramalingam V., Palanivel S.. Automated assessment of breast tissue density in digital mammograms Comput. Vis. Image Underst.. 2010;114:33–43.

    Google Scholar 

  2. Braz Junior Geraldo, Cardoso de Paiva Anselmo, Corrêa Silva Aristó fanes, Cesar Muniz de Oliveira Alexandre. Classification of breast tissues using Moran’s index and Geary’s coefficient as texture signatures and SVM. Comput. Biol. Med.. 2009;39:1063–72.

    Google Scholar 

  3. Cheng H. D., Shi X. J., Min R., Hu L. M., Cai X. P., Du H. N. Approaches for automated detection and classification of masses in mammograms Pattern Recognit.. 2006;39:646–668.

    Google Scholar 

  4. McCormack Valerie a, dos Santos Silva Isabel. Breast density and parenchymal patterns as markers of breast cancer risk: a meta-analysis. Cancer Epidemiol. Biomarkers Prev.. 2006;15:1159–69.

    Google Scholar 

  5. Wolfe John N. Breast patterns as an index of risk for developing breast cancer Am. J. Roentgenol.. 1976;126:1130–1137.

    Google Scholar 

  6. Gong Yang Can, Brady Michael, Petroudi Styliani. Texture based mammogram classification and Segmentation Digit. Mammogr.. 2006:616–625.

    Google Scholar 

  7. Mcgarry Gregory, Deriche Mohamed. Modelling mammographic images using fractional Brownian motion in Proc. IEEE Speech Image Technol. Comput. Telecommun.:299–302 1997.

    Google Scholar 

  8. Lopes R., Dubois P., Bhouri I., Bedoui M.H., Maouche S., Betrouni N.. Local fractal and multifractal features for volumic texture characterization Pattern Recognit.. 2011;44:1690–1697.

    Google Scholar 

  9. Swiniarski RW, Lim HK, Shin JH, Skowron A. Independent Component Analysis, Princpal Component Analysis and Rough Sets in Hybrid Mammogram Classification. IPCV. 2006.

    Google Scholar 

  10. Nicolis O, Jeon S, Vidakovic B. Mammogram Diagnostics via 2D Complex Wavelet-based Self-similarity Measures São Paulo J. Math. Sci.. 2014;8:265–284.

    Google Scholar 

  11. Verma Brijesh, McLeod Peter, Klevansky Alan. Classification of benign and malignant patterns in digital mammograms for the diagnosis of breast cancer Expert Syst. Appl.. 2010;37:3344–3351.

    Google Scholar 

  12. Zielinski Jerzy, Bouaynaya Nidhal, Schonfeld Dan. Two-Dimensional ARMA Modeling for Breast Cancer Detection and Classification IEEE Int. Conf. Signal Process. Commun.. 2010:1–4.

    Google Scholar 

  13. Ramírez-Cobo Pepa, Vidakovic Brani. A 2D wavelet-based multiscale approach with applications to the analysis of digital mammograms Comput. Stat. Data Anal.. 2013;58:71–81.

    Google Scholar 

  14. Pentland A. P.. Fractal-based description of natural scenes. IEEE Trans. Pattern Anal. Mach. Intell.. 1984;6:661–74.

    Google Scholar 

  15. Rangayyan R M, El-Faramawy N M, Desautels J E, Alim O a. Measures of acutance and shape for classification of breast tumors. IEEE Trans. Med. Imaging. 1997;16:799–810.

    Google Scholar 

  16. Rangayyan Rangaraj M, Oloumi Faraz, Nguyen Thanh M. Fractal analysis of contours of breast masses in mammograms via the power spectra of their signatures. Conf. Proc. IEEE Eng. Med. Biol. Soc..2010;2010:6737–40.

    Google Scholar 

  17. Mudigonda N R, Rangayyan R M, Desautels J E. Detection of breast masses in mammograms by density slicing and texture flow-field analysis. IEEE Trans. Med. Imaging. 2001;20:1215–27.

    Google Scholar 

  18. Nguyen Thanh, Rangayyan Rangaraj. Shape Analysis of Breast Masses in Mammograms via the Fractal Dimension. Conf. Proc. IEEE Eng. Med. Biol. Soc.. 2005;3:3210–3.

    Google Scholar 

  19. Sie Angela C, Hansen Gail C, Prince Jeffrey S, et al. Benign versus Malignant Solid Breast Masses: US Differentiation Radiology. 1999;213:889–894.

    Google Scholar 

  20. Richard Frédéric, Bierme Hermine. Statistical Tests of Anisotropy for Fractional Brownian Textures. Application to Full-field Digital Mammography J. Math. Imaging Vis.. 2009;36:227–240.

    Google Scholar 

  21. Mandelbrot Benoit B, Van Ness John W. Fractional Brownian motions, fractional noises and applications SIAM Rev.. 1968;10:422–437.

    Google Scholar 

  22. Peltier Romain Francois, Levy-vehel Jacques. Multifractional Brownian motion: definition and preliminary results tech. rep. INRIA 1995.

    Google Scholar 

  23. Legrand Pierrick, Vehel Jacques Levy. Signal and Image processing with FracLab Fractal. 2004:4–7.

    Google Scholar 

  24. Daubechies Ingrid, Others. Ten lectures on wavelets;61. SIAM 1992.

    Google Scholar 

  25. Pesquet-Popescu Beatrice, Vehel Jacques L. Stochastic fractal models for image processing IEEE Signal Process. Mag.. 2002;19:48– 62.

    Google Scholar 

  26. Heath Michael, Bowyer Kevin, Kopans Daniel, Moore Richard, Kegelmeyer W. Philip. The Digital Database for Screening Mammography. Medical Physics Publishing 2001.

    Google Scholar 

  27. Parra Carlos, Iftekharuddin Khan, Rendon David. Wavelet Based Estimation of the Fractal Dimension in fBm Images in IEEE Conf. Neural Eng.no. 9:533–536 2003.

    Google Scholar 

  28. Nafornita Corina, Isar Alexandru, Nelson James. Regularised, semi-local Hurst estimation via generalised lasso and dual-tree complex wavelets in Proc. IEEE Int. Conf. Image Process. 2014.

    Google Scholar 

  29. Selesnick W, Baraniuk R. G., Kingsbury N. G.. the Dual-Tree Complex Wavelet Transform IEEE Signal Proc. Mag.. 2005:1–29.

    Google Scholar 

  30. Talmon Ronen, Coifman Ronald R. Empirical intrinsic geometry for nonlinear modeling and time series filtering. Proc. Natl. Acad. Sci. U. S. A.. 2013;110:12535–40.

    Google Scholar 

  31. Shawe-Taylor John, Christianini Nello. Kernel methods for Pattern Analysis. Cambridge 2004.

    Google Scholar 

  32. Ripley Brian D. Pattern recognition and neural networks. Cambridge university press 1996.

    Google Scholar 

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Correspondence to Ido Zachevsky .

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Zachevsky, I., Zeevi, Y.Y. (2016). Local and Global Fractal Behaviour in Mammographic Images. In: Kyriacou, E., Christofides, S., Pattichis, C. (eds) XIV Mediterranean Conference on Medical and Biological Engineering and Computing 2016. IFMBE Proceedings, vol 57. Springer, Cham. https://doi.org/10.1007/978-3-319-32703-7_46

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  • DOI: https://doi.org/10.1007/978-3-319-32703-7_46

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  • Online ISBN: 978-3-319-32703-7

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