Inserted: 9 oct 2009
Last Updated: 20 dec 2010
Journal: Pure Math. Appl.
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