An open level set framework for image segmentation and restoration using the Mumford and Shah model

Rami Mohieddine; Luminita A. Vese

doi:10.1117/12.872457

7 February 2011 An open level set framework for image segmentation and restoration using the Mumford and Shah model

Rami Mohieddine, Luminita A. Vese

Proceedings Volume 7873, Computational Imaging IX; 787309 (2011) https://doi.org/10.1117/12.872457
Event: IS&T/SPIE Electronic Imaging, 2011, San Francisco Airport, California, United States

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 algorithms^{4, 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 as^{4, 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.

Citation Download Citation

Rami Mohieddine and Luminita A. Vese "An open level set framework for image segmentation and restoration using the Mumford and Shah model", Proc. SPIE 7873, Computational Imaging IX, 787309 (7 February 2011); https://doi.org/10.1117/12.872457

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available