期刊
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
卷 40, 期 6, 页码 2351-2391出版社
SIAM PUBLICATIONS
DOI: 10.1137/070697823
关键词
image segmentation; total variation models; staircase effect; higher order regularization; relaxation; curvature dependent functionals
资金
- NSF [DMS-0405343, DMS-0635983, DMS-040171, DMS-0405423, DMS-0708039]
- Calculus of Variations
- Problemi di Calcolo delle Variazioni in Meccanica e in Scienza dei Materiali
- Italian Ministry of Education, University, and Research
- Variational Problems with Multiple Scales
The higher order total variation-based model for image restoration proposed by Chan, Marquina, and Mulet in [SIAM J. Sci. Comput., 22 (2000), pp. 503-516] is analyzed in one dimension. A suitable functional framework in which the minimization problem is well posed is being proposed, and it is proved analytically that the higher order regularizing term prevents the occurrence of the staircase effect. The generalized version of the model considered here includes, as particular cases, some curvature dependent functionals.
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