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Sobolev gradients for segmentation of vector-valued texture images

Author

Listed:
  • Ullah, Fahim
  • Badshah, Noor
  • Shah, Hassan
  • Ullah, Asmat

Abstract

In this article, we proposed a new variational approach to smooth and segment vector-valued texture images. The given image F0 in first stage before segmentation, we smooth texture it through L0 norm in order to get smooth image I. Then in the segmentation model, the internal energy/curve length is minimized using Sobolev gradients while the external enrgy/fidelity term is minimized through L2 norm/gradient. The use of Sobolev gradients helps in fast convergence of the model. Semi-Implicit (SI) method is used for the solution of the partial differential equation that arises from the proposed model. Numerical results of the proposed model are compared with state-of-the-art L2 gradients. Experimental results illustrate better performance of the proposed method compared to two other PDE-based methods.

Suggested Citation

  • Ullah, Fahim & Badshah, Noor & Shah, Hassan & Ullah, Asmat, 2021. "Sobolev gradients for segmentation of vector-valued texture images," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    • Handle: RePEc:eee:apmaco:v:402:y:2021:i:c:s0096300321000102
    DOI: 10.1016/j.amc.2021.125962
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    Keywords

    Vector-valued texture images; L0 norm; L2 norm; Sobolev gradients; Level sets; Partial differential equations; Semi-implicit method;
    All these keywords.

    JEL classification:

    • L0 - Industrial Organization - - General
    • L2 - Industrial Organization - - Firm Objectives, Organization, and Behavior

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