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Pseudo-Boolean Polynomials Approach to Edge Detection and Image Segmentation

In: Data Analysis and Optimization

Author

Listed:
  • Tendai Mapungwana Chikake

    (Moscow Institute of Physics and Technology)

  • Boris Goldengorin

    (Moscow Institute of Physics and Technology
    New Uzbekistan University
    Pskov State University
    Moscow Institute of Physics and Technology, Dolgoprudny)

  • Alexey Samosyuk

    (Moscow Institute of Physics and Technology)

Abstract

We introduce a deterministic approach to edge detection and image segmentation by formulating pseudo-Boolean polynomials on image patches. The approach works by applying a binary classification of blob and edge regions in an image based on the degrees of pseudo-Boolean polynomials calculated on patches extracted from the provided image. We test our method on simple images containing primitive shapes of constant and contrasting colour and establish the feasibility before applying it to complex instances like aerial landscape images. The proposed method is based on the exploitation of the reduction, polynomial degree, and equivalence properties of penalty-based pseudo-Boolean polynomials.

Suggested Citation

  • Tendai Mapungwana Chikake & Boris Goldengorin & Alexey Samosyuk, 2023. "Pseudo-Boolean Polynomials Approach to Edge Detection and Image Segmentation," Springer Optimization and Its Applications, in: Boris Goldengorin & Sergei Kuznetsov (ed.), Data Analysis and Optimization, pages 73-87, Springer.
    • Handle: RePEc:spr:spochp:978-3-031-31654-8_5
    DOI: 10.1007/978-3-031-31654-8_5
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