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Proceedings Paper

Sobolev gradients and joint variational image segmentation, denoising, and deblurring
Author(s): Miyoun Jung; Ginmo Chung; Ganesh Sundaramoorthi; Luminita A. Vese; Alan L. Yuille
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Paper Abstract

We consider several variants of the active contour model without edges, extended here to the case of noisy and blurry images, in a multiphase and a multilayer level set approach. Thus, the models jointly perform denoising, deblurring and segmentation of images, in a variational formulation. To minimize in practice the proposed functionals, one of the most standard ways is to use gradient descent processes, in a time dependent approach. Usually, the L2 gradient descent of the functional is computed and discretized in practice, based on the L2 inner product. However, this computation often requires theoretically additional smoothness of the unknown, or stronger conditions. One way to overcome this is to use the idea of Sobolev gradients. We compare in several experiments the L2 and H1 gradient descents for image segmentation using curve evolution, with applications to denoising and deblurring. The Sobolev gradient descent is preferable in many situations and gives smaller computational cost.

Paper Details

Date Published: 3 February 2009
PDF: 13 pages
Proc. SPIE 7246, Computational Imaging VII, 72460I (3 February 2009); doi: 10.1117/12.806067
Show Author Affiliations
Miyoun Jung, Univ. of California, Los Angeles (United States)
Ginmo Chung, Yale Univ. (United States)
Ganesh Sundaramoorthi, Univ. of California, Los Angeles (United States)
Luminita A. Vese, Univ. of California, Los Angeles (United States)
Alan L. Yuille, Univ. of California, Los Angeles (United States)

Published in SPIE Proceedings Vol. 7246:
Computational Imaging VII
Charles A. Bouman; Eric L. Miller; Ilya Pollak, Editor(s)

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