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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Uniform density estimates for Blake & Zisserman functional

Pages: 1129 - 1150, Volume 31, Issue 4, December 2011      doi:10.3934/dcds.2011.31.1129

 
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Michele Carriero - Università del Salento, Dipartimento di Matematica “Ennio De Giorgi”, 73100 Lecce, Italy (email)
Antonio Leaci - Università del Salento, Dipartimento di Matematica “Ennio De Giorgi”, 73100 Lecce, Italy (email)
Franco Tomarelli - Politecnico di Milano, Dipartimento di Matematica “Francesco Brioschi”, 20133 Milano, Italy (email)

Abstract: We prove density estimates and elimination properties for minimizing triplets of functionals which are related to contour detection in image segmentation and depend on free discontinuities, free gradient discontinuities and second order derivatives. All the estimates concern optimal segmentation under Dirichlet boundary conditions and are uniform in the image domain up to the boundary.

Keywords:  Calculus of variations, free discontinuity, necessary conditions for local minimizer, image segmentation.
Mathematics Subject Classification:  Primary: 49K10, 49K20, 49J45.

Received: November 2009;      Revised: March 2010;      Available Online: September 2011.

 References