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Variational image segmentation using boundary functions.

G A Hewer1, C Kenney, B S Manjunath

  • 1Naval Air Warfare Center, China Lake, CA 93555, USA.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|February 16, 2008
PubMed
Summary

A new variational framework simplifies image segmentation and approximation using a continuous line-process for edge representation. This method offers flexibility with Lp norms and a fast PDE descent for optimal results.

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Area of Science:

  • Computer Vision
  • Image Processing
  • Mathematical Modeling

Background:

  • Image segmentation and approximation are crucial in computer vision.
  • Existing methods often involve complex objective functions and optimization processes.

Purpose of the Study:

  • Introduce a general variational framework for image approximation and segmentation.
  • Develop a method that simplifies boundary representation and optimization.

Main Methods:

  • Utilized a continuous 'line-process' to represent edge boundaries.
  • Formulated a variational theory incorporating arbitrary Lp norms for flexibility.
  • Derived a partial differential equation (PDE) descent method for minimizing objective functionals.

Main Results:

  • Achieved an explicit form for the boundary function in terms of the approximation function.
  • Demonstrated the framework's generality by applying it to Mumford-Shah and Geman functionals.
  • The PDE descent method proved to be fast and effective on real and synthetic images.

Conclusions:

  • The proposed variational framework offers a unified and flexible approach to image segmentation and approximation.
  • The explicit boundary formulation and PDE descent method provide an efficient solution.
  • The method yields excellent results, applicable to diverse image processing tasks.