Calculus of Variations and Geometric Measure Theory

M. Carriero - A. Leaci - F. Tomarelli

Variational Approach to Image Segmentation

created by leaci on 09 Oct 2009
modified on 20 Dec 2010


Published Paper

Inserted: 9 oct 2009
Last Updated: 20 dec 2010

Journal: Pure Math. Appl.
Volume: 20
Number: 1
Pages: 141-156
Year: 2009


This paper focuses on a second order functional depending on free discontinuity and free gradient-discontinuity, whose minimizers provide a variational solution to contour detection problem in image segmentation.

We briefly resume the state of the art about Blake & Zisserman functional under different types of boundary condition which are related to contour enhancement in image segmentation.

We prove a new Caccioppoli inequality suitable to study regularity of minimizers of related boundary value problems in any dimension $n\geq 1$ and deduce that there are no nontrivial local minimizers in half-space.

Keywords: calculus of variations, free discontinuity problems, Regularity of weak solution