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Related Experiment Videos

Graph cuts via l1 norm minimization.

Arvind Bhusnurmath1, Camillo J Taylor

  • 1GRASP Laboratory, University of Pennsylvania, Philadelphia, PA 19104, USA. bhusnur4@seas.upenn.edu

IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 16, 2008
PubMed
Summary

This study reformulates graph cuts for energy minimization as an unconstrained l1 norm minimization problem. This approach enables effective solutions using interior point methods and parallel implementations for computer vision tasks.

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Area of Science:

  • Computer Vision
  • Optimization
  • Graph Theory

Background:

  • Graph cuts are vital for energy minimization in computer vision.
  • Existing methods face challenges in efficiency and scalability.

Purpose of the Study:

  • To reformulate the graph cut problem as an unconstrained l1 norm minimization.
  • To develop an efficient and scalable solution using interior point methods.
  • To explore connections with continuous optimization and enable parallel implementations.

Main Methods:

  • Reformulation of graph cuts as an unconstrained l1 norm minimization problem.
  • Application of interior point methods for solving the minimization problem.
  • Reduction to solving a sequence of sparse linear systems involving the graph Laplacian.
  • Exploitation of linear system structure for parallel implementation.

Main Results:

  • Demonstrated the effectiveness of the proposed l1 norm minimization approach.
  • Established connections between graph cuts and continuous optimization problems.
  • Showcased the suitability of the method for parallel processing.
  • Validated the procedure with experimental results on image processing graphs.

Conclusions:

  • The proposed l1 norm minimization reformulation offers an effective and efficient solution for graph cut problems.
  • The method facilitates parallel implementations, enhancing scalability for large-scale problems.
  • This work bridges graph-based and continuous optimization techniques in computer vision.