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Applying a modified version of Lyapunov exponent for cancer diagnosis in biomedical images: the case of breast mammograms

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Abstract

Recently, there has been a great interest in the application of Lyapunov exponents for calculation of chaos levels in dynamical systems. Accordingly, this study aims at presenting two new methods for utilizing Lyapunov exponents to evaluate the spatiotemporal chaos in various images. Further, early detection of cancerous tumors could be obtained by measuring the chaotic indices in biomedical images. Unlike the available systems described by partial differential equations, the proposed method employs a number of interactive dynamic variables for image modeling. Since the Lyapunov exponents cannot be applied to such systems, the image model should be modified. The mean Lyapunov exponent is defined as a chaotic index for measuring the contour borders irregularities in images to detect benign or malignant tumors. Moreover, a two-dimensional mean Lyapunov exponent is incorporated to identify irregularities existing in each axis of the targeted images. Experiments on a set of region of interest in breast mammogram images yielded a sensitivity of 95 % and a specificity of 97.3 % and verified the remarkable precision of the proposed methods in classifying of breast lesions obtained from breast mammogram images.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Science and Research Branch, Islamic Azad University, Tehran, 14778-93855, Iran

    Hamed Khodadadi

  2. Department of Electrical Engineering, Industrial Control Center of Excellence, K. N. Toosi University of Technology, Tehran, 14317-14191, Iran

    Ali Khaki-Sedigh

  3. Department of Electrical Engineering, University of Isfahan, Isfahan, 81746-73441, Iran

    Mohammad Ataei

  4. Department of Electrical Engineering, Iran University of Science and Technology, Tehran, 16846-13114, Iran

    Mohammad Reza Jahed-Motlagh

Authors
  1. Hamed Khodadadi
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  2. Ali Khaki-Sedigh
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  3. Mohammad Ataei
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  4. Mohammad Reza Jahed-Motlagh
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Correspondence to Ali Khaki-Sedigh.

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Khodadadi, H., Khaki-Sedigh, A., Ataei, M. et al. Applying a modified version of Lyapunov exponent for cancer diagnosis in biomedical images: the case of breast mammograms. Multidim Syst Sign Process 29, 19–33 (2018). https://doi.org/10.1007/s11045-016-0446-8

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  • DOI: https://doi.org/10.1007/s11045-016-0446-8

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