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Analyzing and Synthesizing Images by Evolving Curves with the Osher-Sethian Method

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Abstract

Numerical analysis of conservation laws plays an important role in the implementation of curve evolution equations. This paper reviews the relevant concepts in numerical analysis and the relation between curve evolution, Hamilton-Jacobi partial differential equations, and differential conservation laws. This close relation enables us to introduce finite difference approximations, based on the theory of conservation laws, into curve evolution. It is shown how curve evolution serves as a powerful tool for image analysis, and how these mathematical relations enable us to construct efficient and accurate numerical schemes. Some examples demonstrate the importance of the CFL condition as a necessary condition for the stability of the numerical schemes.

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Authors and Affiliations

  1. Lawrence Berkeley Laboratory, University of California, Mail-Stop 50A-2152, Berkeley, CA, 94720

    Ron Kimmel

  2. Electrical Engineering Department, TECHNION, Haifa, 32000, Israel

    Nahum Kiryati

  3. Computer Science Department, TECHNION, Haifa, 32000, Israel

    Alfred M. Bruckstein

Authors
  1. Ron Kimmel
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  2. Nahum Kiryati
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  3. Alfred M. Bruckstein
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Kimmel, R., Kiryati, N. & Bruckstein, A.M. Analyzing and Synthesizing Images by Evolving Curves with the Osher-Sethian Method. International Journal of Computer Vision 24, 37–55 (1997). https://doi.org/10.1023/A:1007970107971

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  • DOI: https://doi.org/10.1023/A:1007970107971

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