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Proceedings Paper

An open level set framework for image segmentation and restoration using the Mumford and Shah model
Author(s): Rami Mohieddine; Luminita A. Vese
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Paper Abstract

In two dimensions, the Mumford and Shah functional for image segmentation and regularization15 has minimizers (u,K), where u is a piecewise-smooth approximation of the image data f, and K represents the set of discontinuities of u (a union of curves). Theoretically, the edge set K could include both closed and open curves. The current level set and piecewise-smooth Mumford-Shah based segmentation algorithms4, 23, 24 can only detect objects with closed edges, which are boundaries of open sets. We propose an efficient Mumford-Shah and level set based algorithm for segmenting images with edges which are made up of open curves or crack-tips. By adapting Smereka's open level set formulation21 to variational problems, we are able to extend the current piecewise-smooth and level-set based image segmentation methods, such as4, 23, 24 to the case of open curve segmentation. The algorithm retains many of the advantages of using level sets, such as well-defined boundaries and ability to change topology. We solve the resulting Euler-Lagrange equations by Sobolev H1 gradient descent, avoiding instability and the need for additional regularization of the level set functions, while also accelerating convergence to the reconstructed image. Finally, we present the numerical implementation and experimental results on various noisy images.

Paper Details

Date Published: 7 February 2011
PDF: 11 pages
Proc. SPIE 7873, Computational Imaging IX, 787309 (7 February 2011); doi: 10.1117/12.872457
Show Author Affiliations
Rami Mohieddine, Univ. of California, Los Angeles (United States)
Luminita A. Vese, Univ. of California, Los Angeles (United States)

Published in SPIE Proceedings Vol. 7873:
Computational Imaging IX
Charles A. Bouman; Ilya Pollak; Patrick J. Wolfe, Editor(s)

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