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Applications of Pseudo-Boolean Polynomials in Medical Imaging

In: Trends in Biomathematics: Modeling Health Across Ecology, Social Interactions, and Cells

Author

Listed:
  • Tendai M. Chikake

    (Moscow Institute of Physics and Technology, Department of Discrete Mathematics, Phystech School of Applied Mathematics and Informatics)

  • Boris I. Goldengorin

    (Moscow Institute of Physics and Technology, Department of Discrete Mathematics, Phystech School of Applied Mathematics and Informatics
    The Scientific and Educational Mathematical Center “Sofia Kovalevskaya Northwestern Center for Mathematical Research” in Pskov State University)

  • Panos M. Pardalos

    (University of Florida, Center for Applied Optimization, Department of Industrial and Systems Engineering)

Abstract

We describe novel methodologies for the analysis of medical imaging data through the application of pseudo-Boolean polynomials. We demonstrate the capability of encoding medical imaging data, characterized by physical measurements in discrete dimensions, into pseudo-Boolean polynomials. These polynomials exhibit beneficial properties such as equivalence and compacting, which are leveraged to enhance the reproducibility and interpretability of clustering tasks. Additionally, we explore the detection of edges and blobs within medical images by analysing the polynomial degrees of pseudo-Boolean polynomials applied to image patches. This approach is predicated on the observation that image patches encompassing edge regions yield pseudo-Boolean polynomials of higher degrees in comparison to those covering blob regions. The methodologies presented are grounded in the principles of reduction, compacting, truncation and equivalence, inherent to penalty-based pseudo-Boolean polynomials, offering a novel perspective in medical imaging analysis.

Suggested Citation

  • Tendai M. Chikake & Boris I. Goldengorin & Panos M. Pardalos, 2025. "Applications of Pseudo-Boolean Polynomials in Medical Imaging," Springer Books, in: Rubem P. Mondaini (ed.), Trends in Biomathematics: Modeling Health Across Ecology, Social Interactions, and Cells, pages 39-60, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-97461-8_3
    DOI: 10.1007/978-3-031-97461-8_3
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