Uniform density estimates for  Blake & Zisserman functional

Michele Carriero; Antonio Leaci; Franco Tomarelli

doi:10.3934/dcds.2011.31.1129

Article Contents

2011, Volume 31, Issue 4: 1129-1150. Doi: 10.3934/dcds.2011.31.1129

This issue Previous Article Optimal shape for elliptic problems with random perturbations Next Article An existence and uniqueness result for flux limited diffusion equations

Uniform density estimates for Blake & Zisserman functional

1.
Università del Salento, Dipartimento di Matematica “Ennio De Giorgi”, 73100 Lecce
2.
Politecnico di Milano, Dipartimento di Matematica “Francesco Brioschi”, 20133 Milano

Received: November 2009

Revised: March 2010

Published: October 2011

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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.

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