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Image segmentation based on Mumford-Shah functional.

Xu-feng Chen1, Zhi-cheng Guan

  • 1Department of Mathematics, Zhejiang University, Hangzhou 310027, China. chxfhz@21cn.com

Journal of Zhejiang University. Science
|December 10, 2003
PubMed
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This study introduces a novel active contours model for image segmentation, improving upon existing methods. The new model offers advantages by avoiding Dirac function regularization and proving a unique viscosity solution.

Area of Science:

  • Computer Vision
  • Image Processing
  • Mathematical Modeling

Background:

  • Active contours models are crucial for image segmentation.
  • Existing models like Chan-Vese have limitations, including regularization needs.
  • The Mumford-Shah functional provides a robust theoretical basis for segmentation.

Purpose of the Study:

  • To propose a new active contours segmentation model.
  • To leverage the Mumford-Shah functional for improved image segmentation.
  • To address limitations of previous active contours methods.

Main Methods:

  • Developing a model based on the Mumford-Shah functional.
  • Formulating the model as a system of differential and integral equations.
  • Theoretical analysis to prove the existence and uniqueness of solutions.

Related Experiment Videos

Main Results:

  • The proposed model retains the advantages of the Chan-Vese model.
  • The model successfully avoids the need for Dirac function regularization.
  • Theoretical proof confirms the system possesses a unique viscosity solution.

Conclusions:

  • The new active contours model offers enhanced performance in image segmentation.
  • This work provides a theoretically sound and practically advantageous segmentation method.
  • The model represents a significant advancement in active contours segmentation techniques.