**Title: A FAST ALGORITHM FOR SIMULTANEOUS
SEGMENTATION AND REGULARIZATION OF IMAGES**

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__Gunay____ Dogan__*, Ricardo H. Nochetto,
Pedro Morin

*Affiliation: Mathematical and Computational Sciences Division,

NIST Gaithersburg, MD 20899.

We introduce a novel computational method for a Mumford-Shah functional, which decomposes a given image into smooth regions separated by closed curves. Our goal is to distinguish the foreground objects on a background and regularize the image in a way that respects the object boundaries. We cast this problem as a shape optimization problem, and develop a gradient descent approach at the continuous level that yields non-linear PDE flows. We propose time discretizations that linearize the problem, and space discretization by continuous piecewise linear finite elements. Our method incorporates topological changes, such as splitting and merging of curves for detection of multiple objects, space-time adaptivity and a coarse-to-fine approach to process large images efficiently. We present several simulations that illustrate the performance of the method, and investigate the model sensitivity to various parameters.

Reference: G. Dogan,
R.H. Nochetto, P. Morin, SIAM Journal on Scientific
Computing, **30**, 6, 3028-3049 (2008)

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**CATEGORY: Mathematics**

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**Mentors Name:Stephen
A. Langer**

**Mathematical and Computational
Sciences Division**

**Information Technology Laboratory**

** Building 225, Mail stop 891**

**Tel: (301) 975-8883**

**Fax: (301) 975-3800**

**Email: gunay.dogan@nist.gov**

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**Is your mentor a Sigma Xi
Member? No**